2020 Presenting the Swissmap Research Station (SRS)

SwissMAP Perspectives Issue 5 | 2020

Special Edition: Outreach & Education Contents of-the-box thinking and rigorous proofs. mathematics. The focus is on creative, out- week to engage in difficult extracurricularthe ages of 13 and 19Motivated come and to talented ETH students once between a Academy Presenting theETHMathYouth scientific interests and current research. Tseytlin. In this interview, we discuss heryears starting in October 2020 withwill Arkady move to Imperial College LondonFiona for is 2 finishing her PhD at ETH Zurich.She A conversationwithFionaSeibold to propose fun activities in mathematics. participates in various events.Its vocation isnumerous classes since 2015 and regularlyGeneva’s Scienscope, has been hosting The Mathscope, part of the University of Presenting Mathscope Les Diablerets, Switzerland. open in January 2021 and willthe be University based of in Geneva and ETHResearch Zurich, will Station (SRS), a joint ventureWe of are proud to announce thatResearch Station(SRS) the SwissMAP Presenting theSwissMAP 06 28 16 12 mathematics. in writing two theatre plays incorporatingoutreach activites, and even his experienceshares his story: from research interests,In this to article, our alumnus Fathi Ben Aribi SwissMAP stories:FathiBenAribi some current and former students. PhD students.This year, we also interviewedMaster Class aimed at Master andFor beginning the third time, SwissMAP hasClass 2019-20 organized a Presenting theSwissMAPMaster To mark the 500 Exhibition Leonardo enperspective wonderful project. came to be, and discover morestring about theory, this we discuss how theseFollowing videos the success of his twoSfondrini videos on A conversationwithAlessandro genius. an exhibition around this universally knownShaula Fiorelli and Joana Mailler, setda up Vinci’s death, SwissMAP members 08 14 32 18 th anniversary of Leonardo A. Zhiboedov! Gisin, M.Iacobelli, C.Saffirio, R.Renner and Welcome to J.Aru, A.Avila, N.Brunner, N. new collaborators within SwissMAP. We continue to expand and grow thanks to New Collaborators during this unusual year. Including all online events that happenedor co-organised by the NCCR SwissMAP. A brief overview of the events organised Upcoming Events years old students. extracurricular activity in Geneva for 10Maths) to since 16 the start of theUniversity NCCR.This of is Geneva’s an Maths Club (ClubSwissMAP de has supported the activities of the Presenting TheMathsClub interest in mathematics to the nextschool level. students who want to takesemester their long programme SPRING for highSwissMAP is proud to present its new one- Presenting SPRING 42 54 36 50 contributors. puzzles, kindly put together by someTest of our your math and logic skills with these The PuzzleCorner students. and grants received by our participantsWe and are pleased to announce the awards Awards andGrants specialist audience. video describing their research to aPostdocs non- who are invited to makelast a year, short is open to SwissMAPThe PhD SwissMAP and video competition launched Competition SwissMAP PhD&PostdocVideo who have shared their experience. former and two current Athena participantstwo years of high school. We spokephysics to and one mathematics and in theirprogramme final aimed at students interested inATHENA is a University of Geneva based ATHENA interviews 46 56 52 38 SwissMAP is proud to announce that the SwissMAP Research Station (SRS), a joint venture of the University of Geneva and ETH Zurich, will open Presenting the in January 2021 and will be based in Les Diablerets, Switzerland. The SRS will be dedicated to the organization of events in Mathematical Physics (conferences, workshops, thematic meetings) and also outreach. The (SRS) website (swissmaprs.ch) was launched early Spring this year.

Currently available online:

• SwissMAP Research Station 2021 programme;

• Call for 2022 proposals, submission deadline: 30th September 2020.

SwissMAP Research Station Goals:

• To ensure the sustainability of NCCR SwissMAP activities in Mathematics and Physics;

• Give international visibility to these activities and to increase their scope by organising international conferences on topical problems in Mathematics SwissMAP and Physics; • To promote collaborations between different areas of Mathematics and Physics and between different universities in Switzerland;

• To develop undergraduate and graduate studies in Mathematics and Research Station Physics, thus ensuring an internationally competitive succession; • To support equal opportunities and gender balance in the events organ- (SRS) ised by the Research Station.

SRS SwissMAP Research Station in Les Diablerets

6 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 7 a conversation with then, it was very important that we Yes, that was a very important part schools and make sure that not only were both engaged, because there of the process. At several stages of the students see the videos, but they are different ways to illustrate a the project, I got in touch with high also get a chance to talk about them. physical concept and it’s very easy to school students in Zurich and their With scientists, with their teachers make very small mistakes that can be teachers. The idea was first to under- and people who can tell them more misleading, but only a scientist would stand what could be interesting for about what doing science is actually recognise it as something misleading. them. And then, as the writing of the like. Alessandro script progressed, to get some feed- - What is the timescale for produc- back on the text. Because for some- - What channels where used to pro- ing a video like this, from concep- body who was in high school perhaps mote the videos? tion to completion? 10-20 years ago, it is very difficult to Sfondrini remember exactly what a high school Well the main channel was the It takes several months. First there student knows. And some metaphors Kurzgesagt YouTube channel and is the research period. Of course as a that are common language for people their social media. This is of course scientist, I’m already familiar with the from a certain generation are no for the English version of the videos. topic of the videos, but the people longer relevant for people who are Now we also have French, Italian working at Kurzgesagt, are not. So younger. You have to adapt your lan- and German versions as well. They they need time to read and under- guage in certain subtle ways. So this have been promoted through the After over four years at ETH Zu- - What gave you the idea to create ed people of the YouTube channel stand the material in their own way. sort of feedback was crucial and even Swiss- MAP YouTube channel and rich, Alessandro Sfondrini (Gaber- these videos? Kurzgesagt, which is German for “in And also, I need time to rethink the to this day, we try to be as engaged through the social media of SwissM- diel Group) has taken up a position a nutshell”. They have a lot of expe- material. I need to find the best way as possible with students and teach- AP, ETH Zurich and of course Kurzges- as “Rita Levi Montalcini Fellow” There are a lot of excellent videos rience in making videos on biology, to present my knowledge, which is ers for all parts of the project, such agt. This is a direct way to make the at the Department of Physics and on YouTube about science, such as engineering, energy, and so on. And mostly technical, in a way that can as finding the best way to distribute videos immediately available on the Astronomy of the University of physics and mathematics. But not in this case, it was really a matter of be absorbed by somebody who isn’t these videos to the schools. internet. Apart from that, we will Padova. many of them are done in collabora- putting together my expertise and a specialist. All this takes about 1-2 also contact the schools to make the tion with scientists. And not many of knowledge, with their experience months. After that, the scriptwriting - The videos have had great success. teachers aware of the existence of This position, equivalent to Assis- them are about string theory, or are on engaging people and having the starts, and that takes a few weeks. Did you expect this? these videos. This is very useful so tant Professor with tenure-track on the frontier of theoretical phys- best form of visual communication, There is the process of back and forth that people consider this project as ics and mathematical physics. So I the best choice of words, the best in the Swiss system, allows him to between drafts. Afterwards, the actu- It was a bit of a surprise. I knew that not only something that exists on the always wanted to bring a little bit of timing of our spoken sentences and carry out independent research al illustration and animation starts, by working with Kurzgesagt, who are internet, but a real world activity that what I know to this sort of medium, so on. So it was really crucial to work on the interplay between string and that also takes a few weeks. This a very talented group of people and is tangible and that they can work in order to reach more people, and together with them and there was a is actually a job for several people, are very well known on YouTube, I with on a person to person basis. theory, conformal field theory, and specifically students. This is some- lot of learning opportunities on both integrable systems. thing that I already had in mind, even sides. before coming to Switzerland. Then Until summer 2020 he will still be after coming here, I found that the - What was the role of Kurzgesagt? at the ETH Zurich as a long-term Swiss government, through the Swiss There are a lot of excellent videos on YouTube about science, such as physics and mathe- visitor to manage a related SNF National Science Foundation, and Their role was to help me put my “Spark” grant which he recently SwissMAP could be great partners idea, which was rather abstract, matics. But not many of them are done in collaboration with scientists. obtained. in supporting what is actually a very into the correct format. They helped complicated endeavour: to create choose the right length, the right Following the success of his two these videos, find the right partners, topic and the right way of phrasing videos on string theory, we con- find the right funds, and eventually the questions and sentences. So in because computer animated videos would have some amount of success. Another important resource is our ducted an interview with Alessan- publish the completed videos. practice, that meant that I told them require of course a lot of expertise In my original proposal I wrote that website: http://physdocu.ethz.ch/ dro to talk about how these videos about physics. I gave them mate- and a lot of hours. Then to top it all I would expect at least two million This collects all the material that we came to be. - To make such a video, you need a rial to read and we had numerous off, there is the recording of the voice people to view the videos. And now, have. Not only the videos in several scientific background, but you also discussions. Then we started writing actor, the creation of the music and although we are only at the beginning languages, but also materials for the The first video, “Why Black Holes need to develop skills as a filmmak- a script. They prepared a draft and other final touches. So all in all, you’re of the project, already millions of teachers, and for the students. There Could Delete The Universe – The er. So how do you navigate these I gave them my comments. And we looking at maybe 3-4 months from people have seen the videos. So this is are additional explanations and very Information Paradox”, has reached various roles to create the final went back and forth using this pro- the moment when you really start testimony to the quality of the vide- nice posters that you can put up in over 18 million views. The second product? cess, resulting in around 15 drafts for working on it. os, and the need for good outreach in your high school or university, to pop- each video. Eventually, when we were video, “String Theory Explained – theoretical physics and mathematics. ularise this event or events that you I could not have done it on my own. I both happy, they started preparing What is The True Nature of Reality?” - Did you consult with teachers or There is still of course an important can create related to this project. And had great help from the very talent- the art and the storyboard. Even has reached over 13 million views. students? step to make, which is to go to the it’s also the best way to contact us.

8 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 9 that takes time and energy. So before You should also be aware, that there thinking about that, I would like to is a lot of attention in Switzerland see this activity to the end. And may- towards outreach, from the govern- be convince some colleague that this ment, funding agencies and universi- is something that could be interesting ties. And you will find great support. for them. For instance in the realm You will find dedicated staff in the of mathematics, which we don’t universities that can explain to you really touch upon, but which suffers to some extent, from the same problems that theoretical physics suffer The videos will always be there. And the materials we pro- from. Some students find it un-engaging. They find it too difficult, without duce and the explanations that have to do with the videos ever being exposed to real world will always be there. We would like them to have a life of mathematics. And I’m sure that there their own. are numerous problems in mathematics that would be perfect for these types of videos. how to reach out to schools or people you don’t normally talk to. And there - Do you have any suggestions for are a lot of funding instruments to fellow scientists who want to do discover that can also support you. outreach? Not only financially, but also in better developing the concept of outreach. What I would say to other scientists So my advice to everybody would be who are thinking about doing out- to give it a try, even if you have just a reach, is not to be afraid to give it a little bit of time. try. At least start by dipping your feet in the water with some small activity. And then maybe look at the more Kurzgesagt – In a Nutshell. youtube.com/user/Kurzgesagt complicated and more rewarding activities that you can do thanks to There is a form for teachers or other dents a chance to think about what videos will always be there. And the the funding instruments of the Swiss interested people to get in touch is in the video and to start a con- materials we produce and the ex- National Science Foundation or in with us. versation with scientists. This could planations that have to do with the collaboration with entities like Swiss- You can watch both videos here: be a PhD student, a postdoc, or a videos will always be there. We would MAP or your own university. http://physdo cu.ethz.ch/ - Are the videos part of a larger professor. People who have their own like them to have a life of their own. activity? view of science; their own personal For instance, high school teachers can experience. And they can not only continue to work with these videos, Yes, indeed. The videos are just the talk about the topic of the videos, but show them in their classes, and invite tip of the iceberg. The important about the whole experience of being researchers from universities to their thing here for us, and for the Swiss a scientist. schools. National Science Foundation, is really to have a dialog between scientists - What is your long term vision for - Do you have any plans for future and the public, in this case high how the videos should be used? videos? school students. So just showing them a video would not be enough. We want to get these videos out Not right now. The important thing What is important here is to give stu- to as many people as possible. The is to get the word out on the videos that are already there. Of course, it is very tempting, given the success of these videos, to consider doing more. What is important here is to give students a chance to think But this is something that is very ex- Conversation with about what is in the video and start a conversation with sci- pensive. Not only in terms of money, Alessandro Sfondrini entists. They can not only talk about the topic of the vide- but also in terms of commitment. September 2018, Grindelwald os, but about the whole experience of being a scientist. Because if you want to do something like this, you should do it well, and Interviewed by Maria Kondratieva Alessandro Sfondrini during the interview at the SwissMAP General Meeting 2018. On behalf of the NCCR SwissMAP

10 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 11 2019 in Geneva, as part of the activities proposed by the Museum of History of Science around the theme Presenting: « Top Secret ». The issue of the accessibility of science for women is of great con- cern to Mathscope, who participates in two flagship events: Elargis tes horizons and the International Day of Women and Girls in Science. Every MATHSCOPE two years, Elargis tes horizons offers girls aged 11 to 14 years old the opportunity to discover science through workshops and booths throughout the day. For the International Day The Mathscope, part of the Universi- probability, algebra and topology. science. of Women and Girls in Science, the ty of Geneva’s Scienscope, has been Each activity lasts one hour and fo- The Mathscope, financed by Swiss- Mathscope, as well as other Scien- hosting numerous classes since 2015 cuses on the manipulation of objects, MAP, hires instructors who lead and scope platforms, the CERN and EPFL, and regularly participates in various which then allows the students to de- develop the activities as well as the send women researchers to local events. The Mathscope’s vocation velop their reasoning about a math- class materials. Credit: Joana Mailler schools to present their work. is to propose fun activities in mathematical problem. The Mathscope In 2019 alone, the Mathscope work- The Mathscope also took part in shops. dents. At first, students were invited ematics, in order to make students welcomes school students of all ages. shops welcomed around 6’000 Futur en tous genres, a programme Finally, two major events mobilized to the University to attend an inter- discover this discipline in a different Usually, teachers book a Mathscope visitors. In addition, there were also aimed at 12-13 years old students to the Mathscope and the Scienscope. active play written especially for the way than the one usually adopted by activity because they want to show visitors at the various events in which raise awareness among young people Firstly, the project « Et si j’étais scien- occasion by Fathi Ben Aribi, Swiss- schools. The activities allow the par- the students another perspective of the Mathscope participated. These about gender stereotypes related to tifique... ». The Scienscope has set up MAP post-doctoral fellow. A few days ticipants to explore different mathe- mathematics. Some groups are also are mainly based on three axes: activ- jobs; Mathscope offered two work- a program for 10-11 years old stu- after the play, students returned to matical subjects, from geometry to made up of adults who want to enjoy ities within schools, participation in the University, with their class, to vis- major public events and Scienscope’s it one of the Scienscope laboratories, own initiatives. Particular attention is Mathscope’s vocation is to propose fun activities including the Mathscope, and com- also paid to raising public awareness plete an activity related to the play. of mathematics, especially amongst in mathematics, in order to make students dis- The other event of great importance young girls. cover this discipline in a different way than the was the exhibition “Leonardo in Per- Like every year, the Mathscope took spective”. part in the a Scienscope initiative one usually adopted by schools. (R)amène ta Science. This project invites schoolchildren to take own- ership of science through kits that are presented to them and which they must then present in turn to their classmates and teachers at their Teacher’s message after visiting school. Three schools benefited from Mathscope: this programme for the year 2018- “I would like to sincerely thank you on 2019. behalf of our school for the remarkable In March 2019, the Mathscope was quality of the visit to Mathscope! Our invited by the Bibliothèque de Genève students and accompanying teachers to propose mathematical activities were all delighted. These moments are for the general public during a unique precious for our students.” event: the presentation to the public of Luca Pacioli’s manuscript, De Divina Proportione, in which hand drawings supposedly by Leonardo da Vinci, can be found. Authors: Joana Mailler and The Mathscope participated with the Shaula Fiorelli Scienscope in the Nuit des Musées UniGE Credit: Joana Mailler Credit: Joana Mailler

12 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 13 To mark the 500th anniversary of exhibition, which was very well doc- Leonardo da Vinci’s death, Swiss- umented, also presented facsimiles MAP members Shaula Fiorelli and Leonardo of manuscripts by Leonardo’s hand, Joana Mailler, respectively co-di- on loan from the Martin Bodmer rector and scientific assistant of the Foundation, as well as the facsimile Mathscope, set up an exhibition of Luca Pacioli’s manuscripts on loan around this universally known ge- from the Bibliothèque de Genève. nius. This project was set up under A wide programme of visits, work- the aegis of the Scienscope and the en perspective shops and activities was offered to University of Geneva, and involved the public with activities especially several partners: the Earth Sciences dedicated to families and classes. The Department’s Terrascope as well as exhibition also hosted a concert with the Astronomy Department of the the Polish musician and instrument Faculty of Sciences, the Depart- Exhibition maker, Sławomir Zubrzycki, who rec- ments of Musicology, Italian and reated the viola organista, an instru- History and Philosophy of Science ment conceptualized by Leonardo da of the Faculty of Arts, the NCCR Vinci. Finally, a corner dedicated to ChemBio, the Animuse and Mondes outreach displayed the work pro- Imaginaires associations, the Martin duced by both young and old for the Da Vinci Vernissage. Photo by B. Jreidi Bodmer Foundation and the Bibli- contest organised by the University’s othèque de Genève (BGE). The aim magazine Campus Junior: “Draw your a record for the University’s exhibi- In order to extend the benefit of this of the exhibition was to celebrate Mona Lisa”. tion hall. The feedback from visitors, exhibition a series of videos present- Leonardo’s genius by presenting teachers and participants has been ing different aspects of the exhibition some of his lesser-known research During the almost two months of extremely positive, proving once are available online through the and contributions in fields such as display, the exhibition benefited from again that Leonardo continues to SwissMAP YouTube channel. music, mathematics, astronomy, local and national press coverage fascinate throughout time. earth sciences and biochemistry. and welcomed over 4,000 visitors,

The exhibition was financially supported by the SNSF, through an Agora project, but also by the A wide programme of visits, workshops and activities was offered to the Wright Foundation and the Univer- public with activities especially dedicated to families and classes. sity of Geneva.

Polish musician and instrument maker, Sławomir Zubrzycki. Photo by N. Wenger

The idea for this exhibition came logical that the University should, after an event organised by the Bib- as everywhere else in Europe, par- liothèque de Genève several months ticipate in the celebrations linked to earlier: an invaluable manuscript pre- the 500th anniversary of Leonardo’s served at the BGE was presented to death. the public in 2019. It is a manuscript by Luca Pacioli, a Renaissance math- The exhibition took place in the exhi- ematician, which presents, among bition hall of the University of Gene- other things, magnificent drawings of va from 18th December 2019 to 20th polyhedra. These drawings are said to February 2020 and offered interactive have been conceptualized and pos- activities for the public (a perspecto- sibly executed by Leonardo da Vinci, grapher in math, videos on the viola who was a friend of Luca Pacioli. The organista in musicology, a model to event at the BGE was programmed observe the planetshine in astrono- over two days and welcomed over my, a device with sand and a pro- Author: Joana Mailler than 1000 visitors. In view of the jector to understand topographical UniGE great interest shown, it seemed only changes in earth science, etc.). The Da Vinci Vernissage. Photo by B. Jreidi

14 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 15 exactly is time, and why is it inevita- bly flowing in one direction? Where does all the matter come from? And A conversation with what is it made of? There are of course many other, more accessible, problems that I would like to see solved. For example, I have Fiona Seibold dedicated quite some time to studying string theory, so at some point I would like to know if it really is the theory of everything that we have been looking for, reconciling general My research touches on several tum group: they are q-deformations. relativity and quantum mechanics. aspects of theoretical physics, namely Then, some string theorists assume string theory, integrability, and also - What kind of tools are you using? that we have supersymmetry: for the AdS/CFT correspondence. For analytic calculations I use tools every particle there is a superpart- AdS/CFT is a duality between string from supergravity and integrability. ner. Will the LHC discover these new theories on Anti-de-Sitter space and I also need a lot of concepts from Lie particles in the future? A very trendy Fiona did her Bachelor and conformal field theories living in one (super)algebras and their q-deforma- question is also if we can build a Master in Physics at EPFL and has dimension less. The typical example tions. Often I have to handle involved quantum computer, and if this will defended her PhD on the 4th of is the duality between string theory expressions, in which case I use lead to drastic improvements of our 5 computing capabilities. I hope these May at ETH Zurich. on AdS5 x S and N = 4 super-Yang- computer programs to help me, for Mills. One thing that came up in the instance Mathematica. questions will get answered during She will move to Imperial College early 2000s is that these two theories this century, and who knows, maybe London for 2 years starting in are integrable. There exists a lot of - Is your problem something that I can even contribute to solving some of them... October 2020 with Arkady Tseytlin. conserved charges that can be used you think can be solved soon? to solve the theories exactly. This is There are several open problems in The q-deformation modifies the background on which the strings propagate. q-deforming the two- extremely important because it can the context of integrable deforma- sphere (in brown) results in a squashed geometry (in blue). Definitions: be used to obtain exact results for tions. Perhaps the most challenging • Anti-de-Sitter (AdS) space: The variant, which hindered their inter- still are analysing q-deformations of - How did you get into physics? strongly coupled quantum field theo- one concerns the nature of their CFT maximally symmetric Lorent- pretation as string theories. During CFTs, mainly in two dimensions, but Well, this started quite early on, ry, which is usually very hard, and also duals. We have these -deformations zian space of constant negative q my PhD, together with Ben Hoare, the link with the integrable defor- when I was maybe 12. At that time, opens the door to actually proving of the AdS x S5 superstring, but we curvature. It is the Lorentzian 5 I found a way to construct them so mations on the string theory side is I was very much into Maths, whose the duality. still have basically no idea of what version of the hyperbolic space. that they are Weyl invariant and thus missing. beauty I found fascinating. I also en- So, motivated by this success, people their CFT dual is. I think this is a very It is a solution of Einstein’s equa- define consistent string theories. I joyed looking at the stars and often also looked at what happens when interesting but also rather compli- tions of General Relativity with hope that this new result will help us - What are the problems in physics wondered how the universe works. you deform the theory away from cated question, and for the moment no matter and negative cosmo- make progress in finding the CFT dual. you’d like to see solved? When my parents got their first com- these most simple examples: for it is hard to see how to tackle it. But logical constant. At 12, at the time of my first encoun- puter at home, I took this opportuni- example, is it possible to deform the I think it will find its epilogue in the • Quantum group: A Hopf algebra 5 - Are some people attacking the ter with string theory, I thought phys- ty to browse the World Wide Web in AdS5 x S superstring while preserving next ten years. that depends on a parameter search of new interesting mathemati- integrability? It turns out that this is problem from the CFT side? ics could answer all questions that q and which becomes the There is ongoing progress to char- I had about the universe. But now I cal concepts. At some point I reached indeed possible and several integra- - What about the way you are at- universal enveloping algebra of acterise the CFT duals of integrable understand that many of them may a website where there was something ble deformations have been pro- tacking this problem? Is your angle a Lie algebra in the undeformed deformations. For some simple remain open forever, in particular about string theory as well. This first posed. I am studying these integrable new? q -> 1 limit. encounter with theoretical physics deformations. For the moment I focus on the string • Weyl invariance: invariance un- was very inspiring. Then, as I entered theory side of the duality, address- der Weyl transformations, corre- EPFL, I had to choose between the - So are you exploring one in par- ing the problem step by step. One My research touches on several aspects of theoretical sponding to a local rescaling of maths or physics sections. I don’t ticular? important question is if the deformed physics, namely string theory, integrability, and also the the metric tensor. In the context know exactly what pushed me into There are several deformations of the theories still define string theories. of string theory, Weyl invariance AdS x S5 superstring that preserve AdS/CFT correspondence. one direction or another, but I chose 5 This is important in the context of the ensures that the theory is con- Physics and I’m pretty happy it went integrability. A special class is given AdS/CFT correspondence because on sistent at the quantum level. this way. by the so-called Yang-Baxter defor- the AdS side we a priori need a string deformations, the CFT dual is actually the more philosophical ones, such as: mations, and these are the ones that theory. known. This is however not the case what happened during the big bang? - Can you tell us a bit more about I study. Their effect is to promote the The q-deformations that I mentioned for q-deformations. People have and Was there something before it? What Interviewed by Elise Raphael your research topic? initial symmetry algebra to a quan- were believed not to be Weyl in- UniGE

16 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 17 For the third time, SwissMAP is organizing a year-long master class Presenting the SwissMAP at the University of Geneva in the academic year 2019/2020 for master and beginning PhD students.

Participants enroll in a one-year program at the University of Geneva which started in September 2019, providing 60 ECTS credits. Partici- pants are offered the possibility of obtaining a Master Degree from the University of Geneva by completing a Master Thesis for 30 additional ECTS credits. Master Class The program started in September 2019 and will be completed in June 2020. 12 students from 8 different countries are enrolled in this Master Class alongside local stu- 2019-20 dents who were invited to attend the lectures.

On the following pages you will find in Mathematical Physics an introduction to the lecturers and the students.

18 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 19 Anton Alekseev Marcos Mariño Full list of courses: Quantum mechanics for mathematicians An introduction to topological field theory Anton Alekseev is a full professor at the Marcos Mariño is a full professor at the Fall: University of Geneva. His research interests university of Geneva. His research interests • Quantum mechanics for include: symplectic geometry, moment theory include mathematical aspects of string theory mathematicians (A. Alekseev) and mathematical physics. and quantum field theory, topological string theory and topological quantum field theory. • Random matrices and universality 1 (A. Knowles) Johannes Alt Stanislav Smirnov Random matrices and universality 2 Random growth and Loewer evolution • Introduction to Statistical Johannes Alt is a postdoc in the research group Stanislav Smirnov is a full professor of Mechanics 1 (Y. Velenik) of Prof. Antti Knowles at the University of mathematics at the University of Geneva. • Random growth and Loewer Geneva. His research interests are : random His research focuses on the fields of complex evolution (S. Smirnov and A. matrices, random graphs, mathematical physics analysis, dynamical systems and probability Turner) & Courses and functional analysis. theory. Zurich: Anna Beliakova Vincent Tassion Minicourse “Quantum invariants of links” Minicourse “Percolation Theory” • Minicourse “Percolation Theory” (V. Tassion)

The Lecturers Anna Beliakova is a full professor of Vincent Tassion is an assistant professor at mathematics at the University of Zurich. Her ETH Zurich. His research interests are in the • Minicourse “Quantum invariants areas of expertise are topology, in particular mathematical study of questions arising in of links” (A. Beliakova) knot theory, as well as quantum invariants and statistical mechanics, and more precisely in their categorization. percolation theory. Spring: Nicolas Brunner Amanda Turner • Introduction to Statistical Mechanics 2 (H. Duminil-Copin) Quantum information theory Random growth and Loewer evolution Nicolas Brunner is an Associate Professor Amanda Turner is a senior lecturer in • Random matrices and at the University of Geneva. His research Mathematics and Statistics at Lancaster universality 2 (J. Alt) interests are: quantum information theory, University. Her main research area is in foundations of quantum mechanics and probability with a specific focus on scaling • An introduction to topological quantum thermodynamics. limits of stochastic processes. field theory (M. Mariño) Hugo Duminil-Copin Yvan Velenik • Quantum information theory (N. Brunner) Introduction to Statistical Mechanics 2 Introduction to Statistical Mechanics 1 Hugo Duminil-Copin is a full professor of Yvan Velenik is a full professor of mathematics mathematics at the University of Geneva. at the University of Geneva. His research His research deals with mathematical interests lie mainly in the applications of physics, probability, complex analysis and probability theory to the study of rigorous combinatorics. classical statistical mechanics, especially lattice random fields and random walks. Antti Knowles Random matrices and universality 1 Antti Knowles is a tenure track assistant professor at the University of Geneva. His research lies in the areas of probability, analysis and mathematical physics. The Master Classes are filmed and are available online through our SwissMAP website in the videos section.

20 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 21 The Students João MAIA Benjamin STRITTMATTER João comes from Brazil and is Benjamin is from Germany and was The Master Classes have proven currently a PhD student in applied educated at ETH Zurich and Imperi- to be a highly successful way of mathematics at the University of al College London. He has a broad attracting talented young students São Paulo. In his research and stud- experience in research, beginning to Switzerland, with about 20% of ies, he is mainly interested in statis- as an undergraduate researcher in them enrolling for a PhD with a tical mechanics, more specifically on black hole astrophysics. His interests SwissMAP professor upon finishing problems involving large deviation evolved towards cosmology and in the programme in each edition. and phase transition on trees. particular field-theoretic generali- Students from more than 15 differ- sations of gravity. Currently, he is ent countries have participated and concerned with the mathematical SwissMAP has provided scholarships Tomas MEJIA GOMEZ intricacies surrounding approaches to some of these carefully selected to quantum gravity. Tomas was born in Colombia and students. Applications from female obtained his Bachelor’s and Master’s candidates have been strongly degrees from Universidad Nacional encouraged and the committee has Tatiana TIKHONOVSKAIA de Colombia, at Medellin. In 2018 he ensured gender balance. moved to the US to start his PhD at Tatiana comes from Russia and is All participants are integrated at Johns Hopkins University. Tomas is currently a master student in physics the start of the programme to the interested in topology and its inter- at the St. Petersburg State Univer- SwissMAP network and encouraged actions with geometry and mathe- sity. During her bachelors work, she to take part on other activities too, matical physics. studied integrable systems at the such as the annual SwissMAP Steklov Institute for Mathematics in General Meeting, the Winter schools St. Petersburg. Claudia RELLA and other SwissMAP seminars. From left to right: Prof. Anton Alekseev (SwissMAP Deputy Director), Elise Raphael (SwissMAP Scientific Officer), Ana Roldan, Sofia Amontova, Claudia was born in Rome, Italy. She Pascale VOEGTLI Pascale Voegtli, Claudia Rella, João Maia, Tatiana Tikhonovskaia, Ilya Losev, Vladislav Guskov. obtained the BSc in Physics from Previous Master Classes: Sapienza University of Rome in 2018 Pascale comes from Switzerland. The third SwissMAP Master Class and the MSc in Mathematical and She graduated from the University September 2015 - June 2016 2019-20 welcomed 12 internation- Haihua DENG Vladislav GUSKOV Theoretical Physics from Univer- of Basel in Mathematics and Physics. al students, hand-picked by our Master Class in Planar Statistical sity of Oxford in 2019. Among her Her main interests lie in algebraic committee based on their academic Haihua comes from China. He grad- Vlad comes from Russia. He stud- Physics research interests are random ma- geometry and topology. skills, knowledge and achievements. uated from Sun Yat-sen University in ied at the Moscow Institute of Participants: 12 students from 8 Guangdong Province with a Bach- Physics and Technology where he trices and applications of algebraic The students come from a variety of different countries, 50% men 50% elor’s degree in Mathematics and received his Bachelor diploma with geometry to QFTs. countries: Brazil, China, Colombia, women Applied Mathematics. He is inter- honors. As a bachelor student, he Ecuador, Germany, Italy, Russia and ested in number theory and some contributed to two journal papers Switzerland. Ana ROLDAN mathematical models. in Quantum Field Theory. Current- September 2016 – June 2017 We welcome this year’s Master Class ly, his interests include theoretical Ana was born in Ecuador. She Master Class in Geometry, Topology in Mathematical Physics students: research in statistical mechanics as obtained an Excellence Scholarship and Physics Dmitry GRINKO well as other topics in mathematical for her undergraduate studies. She Dmitry comes from Russia. He was a physics. received her Bachelor in Physics Participants: 18 students from 10 Sofia AMONTOVA prize winner in the Russian Physics from EPFL. She is currently finish- different countries, 59% men 41% Sofia is from Germany and did her Olympiad in high-school, he finished ing her Masters in Physics at ETH women Ilya LOSEV studies in mathematics at the Uni- Moscow Institute of Physics and Zurich, where her topic of research versity of Bonn and Campus Pierre Technology with distinction before Ilya comes from Russia. He ob- is BF Theory and Topological Grav- September 2019 – June 2020 et Marie Curie at the Sorbonne he got an Excellence Scholarship to tained his bachelor’s degree at the ity. While studying in Lausanne, University. For her master’s thesis study at ETH Zurich. Dmitry current- Saint-Petersburg State University she shared her passion for Physics Master Class in Mathematical project she worked on random sur- ly holds a Master degree in Physics and works there at the Chebyshev and Mathematics via her work as Physics a teaching assistant and President faces of high genus. Her interests lie from ETH Zurich. His research inter- Laboratory. He is studying problems Participants: 12 students from 8 in hyperbolic geometry, Teichmüller ests are in mathematical aspects related to complex analysis, prob- of the Young Physicists Forum, to inspire other students and support different countries, 58% men 42% and moduli spaces, low-dimensional of quantum information, statistical ability theory and mathematical women topology and geometry as well as mechanics and condensed matter physics. them with their studies. global analysis. physics.

22 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 23 Student Interviews my experience. Before the programme, my aim was Following the successful launch What initially attracted you to the than I had thought there would be. (TT) One hour seems to be very little to develop mathematical skills but of the third SwissMAP Master SwissMAP Master Class? As for the content, I was initially time for the practice, I feel there still continue with research in physics. Class, we decided to sit down with afraid that my level of mathematics Now I am quite certain that research (VG) A couple of things. First, it is a could be more time. three of our current Master Class would not be enough. After the first in mathematics is the way to go. unique programme with outstanding Students: Vladislav Guskov (VG), semester exams, I realized that there (IL) I think it was well organized lecturers. Second, it was a personal (TT) Although I am enjoying Statisti- Tatiana Tikhonovskaia (TT) and is nothing you can’t do if you attend because some courses require some challenge. I came from physics and cal Physics, I think for my PhD I will do Ilya Losev (IL) and talk about their all the classes and practices. background and this background my mathematical education was something different. studies and plans for the future. was provided before. Like for exam- not that advanced. So, I wanted to (IL) Yes, I expected the highest top ple for quantum information theory, (IL) It has helped me to confirm that change it. level education. In terms of content, quantum mechanics was explained statistical mechanics is the area that some parts were unexpected as some to us before. really interests me. courses were more geometric. Being less familiar with geometry and alge- What is your research area of inter- And what about influenced any bra for me it was very interesting to est? decision(s) concerning your future discover other areas. (VG) Generally speaking, it is sta- plans? If so, how? What have you so far found most tistical physics and things around (VG) Truth is, this programme made challenging? Tatiana Tikhonovskaia it. At the moment I am working on major adjustments in my plans. Due complex analysis could help to solve Bethe Ansatz with application to the to the course by Stanislav Smirnov (VG) The work on a master project. really beautiful problems. Heisenberg spin chain. I am also very and Amanda Turner last semester There is a lot of independent work: interested in random growth models I got to know a beautiful area of a supervisor gives you hints how to Can you cite one special moment? and Schramm-Loewner evolution. Schramm-Loewner evolution and tackle a problem but still you need to (VG) I’d like to mention special atti- (TT) In Geneva I started working on random growth models and now I am go through many research articles on tude of Prof. Anton Alexeev. Besides Statistical Physics but I expected going to do a PhD in this subject. your own and come up with ideas for well prepared lectures on Quantum something a bit different from what I your problem. I think this approach Mechanics, he also devoted a lot of (TT) For me it’s a difficult question am doing… is a good one at this point because his own time to be present at exercis- because I am going to change fields… it helps to understand if research in es sessions and our student seminar (IL) Statistical mechanics. (IL) It has helped me to confirm that mathematics is your thing or not. Vladislav Guskov helping out with solving problems Has the Master Class helped to de- Statistical mechanics is what I want (TT) I think the most challenging and giving valuable comments. That fine or confirm your research area to do in the future. is really appreciated. (TT) I first heard about this pro- thing was the exam session because of interest? What are your current & future gramme from my friend who partici- it is quite different from Russia. I was (TT) I thought I knew quite a lot (VG) Yes, indeed. The Master Class plans? pated in a previous SwissMAP Master expecting all exams to be written but about the Quantum Mechanics helped me understand that my (VG) I am going to Stockholm to Class three years ago. When I found I had only one written and 3 orals. I lectures as I had already studied the interests align more with a mathema- start my PhD at KTH with Fredrik out about this year’s programme I was particularly nervous because my subject before but it was great to find tical approach to solving problems. Viklund. Our first project will address was very interested in the subjects previous experience of exams was out that there is so much more in this Schramm-Loewner evolution and I and I also wanted to change from very different. field than I thought. look forward to it. where I was studying. (IL) Probably courses that require (IL) For me, it was surprising to see (TT) I’m going to stay in the Univer- (IL) In my previous University in St some concepts from geometry and that in many of the courses in the sity of Geneva in Antons Alekseev’s Petersburg, I studied complex anal- algebra that I do not know much end, professors were able to prove Group. ysis where I learnt about statistical about. It made it harder to follow. their own theorems. This is not mechanics. I found this Master Class And the most enjoyable? always the case in other universities, (IL) I want to continue with research. interesting as it offered great insight especially at master level. After the Master Class, I will return to into modern research in this area. (VG) People, of course. The interac- St Petersburg to finish my Master’s How did you find the structure of tion with professors and classmates there, because the programme there Was the level and content as you was the most enjoyable and valuable the course? expected? is for two years. After that, I will cer- part. (VG) All courses were well balanced: tainly continue with a PhD. (VG) Even better than I expected. (TT) I think people are the best thing 2/3 theory and 1/3 exercises which All the topics were introduced from at University. Both lecturers and I think is a really good proportion. scratch. This approach serves people students, it is really pleasant to be Moreover, we had opportunities to with a different background and I amongst people who are really inter- participate in the conferences organ- could easily catch up. ested in mathematics. ized by SwissMAP. The organization Interviewed by Mayra Lirot of both the conferences and the NCCR SwissMAP (TT) Perhaps there are less courses (IL) To see how my background in educational process was the best in Ilya Losev

24 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 25 You finished a B.A. in Mathematics The and Philosophy at the Lewis and Clark College before joining the SwissMAP Master Class in Geome- Master Class try, Topology and Physics in 2016. Can you briefly tell us about what Alumni Series initially attracted you at that time, to the SwissMAP Master Class? I was not the typical Master Class student as I was also enrolled at Cornell University in a PhD programme at the same time. I heard about the SwissMAP Master Class in Geometry, Topology and Physics in 2016, through one of the Professors at Cornell who knew of my interest Interview with to study in Switzerland. I was very attracted to the Master Class as it offered a great opportunity to learn more about the subjects that I was Benjamin Hoffman interested in.

Did the Master Class help you to define or confirm your research area Master Class in Geometry, of interest? For me it was also important to focus on research as well as the Master Topology and Physics 2016 Classes, so I asked Anton Alekseev if there were any ongoing projects and he gave me a problem to work on. I worked on it with Anton and one of his graduate students Yanpeng Li. We wrote a paper as a result of it and have continued the collaboration of canonical basis and representation since… theory and the other is focused on Lie theory and Hamiltonian mechanics.

Can you cite one special moment? What are your future plans? For me, the collaboration with Anton Alkeseev has been a really important I defended my thesis in April this year and a long lasting part of my career at Cornell. I will start a Postdoc at the and has also defined my PhD. The University of Toronto which I am very collaboration has continued and we excited about. are currently writing our fourth paper together. For SwissMAP it is important to keep closely connected with alumni, we strongly value this relationship and encourage our alumni to remain as part of the SwissMAP network. Can you briefly tell us what your current research area of interest is? Our alumnus Benjamin Hoffman speaks about his experience Interviewed by Mayra Lirot as a SwissMAP Master Class student of the second Master Class I’m interested in building a bridge between two areas, one is the study NCCR SwissMAP series in 2016 and how the Master Class helped him.

26 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 27 Presenting the: ETH Math Youth Academy

The inspiration for designing and 25-30 students take part in the level launching the program in 2015 was for first-year participants and about • Student: “If the the fact that even though Swit- 10 in the intermediate and advanced zerland consistently ranks high in levels. Some students even attend exponent were a prime, ETH Zurich Campus. Source: ETHZ the proof would be PISA studies measuring the average multiple levels in parallel. There is complete. Can we prove level of mathematical education in no formal credit associated with the The course for first-year students is is designed so that a student can al, which can be found under “Public schools, opportunities for the best classes - students attend entirely for that it is prime?” a survey of a broad range of topics, participate over the course of up to Talks” on the program’s webpage: students did not abound, at least in their own fulfilment and intellectual with 2-5 weeks devoted to a single 4-5 years and delve deeper into more https://www.math.ethz.ch/eth-math- comparison to other countries (in satisfaction. Some students com- topic. These include: mathematical sophisticated mathematics. youth-academy. • Instructor: “I absolutely Eastern Europe or the US, for exam- mute from outside of canton Zurich induction, the Pigeonhole principle, agree with the first part.” ple). Our goal has been to fix this gap. - for example, from Bern, Thun, or and invariants. An advanced num- I have developed an interactive While not the only goal, preparation Luzerne, and one student even takes ber theory course may start with lecture format of teaching namely, for mathematical olympiads is a fo- We started in 2015 with a total of the train from Lugano. They are • Another student: “But Gaussian integers and reach difficult students participate actively in solv- cus of the program. Out of the 6 best about 10 students across all 3 levels. passionate for opportunities to do Diophantine equations (for example, ing the problems, while I guide them scores at the preliminary round of we can assume without The participation rate has been grow- mathematics beyond what the regu- Fermat’s equation with exponent 3). in the process. In this way, I reach a the 2020 Swiss Math Olympiad, 2 are loss of generality that ing with steady pace, and now about lar school curriculum has to offer. We illustrate even the more theoreti- balance between on the one hand regular participants in the ETH Math it is prime, so we are cal topics with an abundance of vivid allowing them to work independently Youth Academy. One of them in fact done!” and nontrivial problems. An interme- and to arrive at the solutions them- got a perfect score and the other has diate geometry course would start selves, and introducing new material the highest score among girls, thus with cyclic quadrilaterals and reach and reaching harder topics on the qualifying (for a second consecutive the theorems of Ceva and Menelaus, other. In order to introduce new ideas year) for the upcoming European This is a typical snapshot from homothety, and power of a point. or to present problems that are dif- Girls’ Mathematical Olympiad. Also, 7 a class at the ETH Math Youth An advanced Euclidean geometry ficult for the students at the current of our students are in the top 22. The Academy. Motivated and talented course would focus on trigonome- stage, I start the discussion, let them performance in the Final Round this students between the ages of 13 try techniques or on inversion. An brainstorm ideas or proposals, and year was similar: 2 of our students and 19 come to ETH once a week to intermediate or advanced combina- then give them hints or highlight the are in the top 6 and 5 in the top 14. It engage in difficult extracurricular torics course may discuss generating proposed ideas that they can develop is impressive to watch the growth of mathematics. The focus is on cre- functions and other enumerative further. We have videotaped a num- our students over the years. ative, out-of-the-box thinking and techniques, again with plenty of ber of public talks given at various rigorous proofs. applications. In an advanced algebra schools that illustrate my interactive course, we prove various criteria lecture style and teaching philoso- for irreducibility of polynomials. We phy; these also give a good idea of do not touch standard topics that how an ETH Math Youth Academy Author: Kaloyan Slavov a mathematics major would later class looks like. By now, we have built ETH Zurich Kaloyan Slavov with students of the ETH Math Youth Academy. Source: ETH Math Youth Academy learn in a university. The curriculum a rich database of videotaped materi-

28 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 29 SwissMAP stories: I think of mathematics as a Alumnus - Fathi Ben Aribi language. I think of mathematics as a language. Most people see mathe- Research & Outreach matics as a set of tools to solve problems and that is not the full story. Obviously, it is a part of it, but at its core mathematics is a language. Math is a way to model abstract thoughts or objects of real life, which enables us to give them precise definitions andonly then to work with these objects (perhaps to solve real-world questions). My main research subject is topo- goal of knot theory. I went to the École Normale logy. Topology consists in studying Supérieure in Paris (ENS), where I objects up to deformation as if One might ask, why would anyone completed a Bachelor and a Mas- those objects were made of model- want to do this? In mathematics ter in mathematics. I had always ling clay. In this sense, a ball is the there are questions that arise in an considered the option of becoming same as a cube because you can abstract way. How can we define a full-time math teacher, but after deform one shape into the other. a pretty common object such as a my Master’s thesis it was clear to Topology is really fun because it is knot? How can we describe them me that I wanted to continue doing quite visual: you can draw pictures and identify them? What should we some research. I did my PhD in to understand why one object is name them? That is the basics of Université Paris 7 and from there I actually the same as another object mathematics, just to look at an ob- moved on as a postdoc in UniGE. I (up to deformation). More precisely, ject or theory and make sense of it. currently have a postdoc position my research focuses on knot the- Knot theory was founded by Lord at UCLouvain in Belgium, where I ory, which is the study of knots as Kelvin, a physicist who conjectured plan to continue and finish some of mathematical objects. Yes, just what that atoms and molecules were my previous research projects. In you might expect, these are the actually knots in an underlying the long term I would like to get a knots you obtain by tying up a piece “aether”. Hence, in order to clas- permanent position as a researcher, of rope. You might then like to know sify atoms, he needed to classify with or without teaching (which I if the knot you just tied is actually knots. This knot classification was always enjoy in conjunction with knotted or if it becomes undone if then begun by Tait, a mathematical research). you pull on the rope in a particularly physicist. More than a century after, smart way. You might also wonder knot theory finds applications in People often ask why I study math- if one knot is actually the same as many branches: biology, physics, ematics, if all the theorems have another knot (up to deformation of chemistry, for example via the study been proven… Far from it! In fact, the rope keeping its endpoints fixed of knotted molecules. you can always find more questions, in your hands), which in turn would there is always new ground to dis- allow you to classify knots. Such a In SwissMAP, I was a postdoc at Uni- cover. classification is the original main GE in Rinat Kashaev’s group in quan-

I was born in Paris, France, and I did most of my studies there. As far as I remember, I have always been interested in mathematics. One of the things People often ask why I study mathematics, if all the theorems have been proven… Far from that I enjoyed most about mathematics at school was that an answer was ei- it! In fact, you can always find more questions, there is always new ground to discover. ther true or false, and thus the grade could not vary according to the teacher.

32 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 33 ing joy and understanding to many 11 years old kids, we really wanted ordered. I think that one of the young students. to present science as a means to positive consequences of studying make possible what one would have mathematics is introducing order in On stage usually considered impossible, like your mind, which can help you ex- In Geneva I also had the opportunity seeing DNA with the naked eye. press an idea in an explicit way and to write two theatre plays for scien- Furthermore, the fact that science state a problem in a non-ambiguous tific outreach. proved useful to solve a mystery is way. Math is about knowing how to The first one, calledLe nœud du mys- related to the more profound idea talk, discuss and think logically. tère, was 10 minutes long and was that one of the goals of science is to made for the Nuit de la science 2018. get closer to the truth. This might sound obvious, but I In this play, a crime is solved thanks think that if you want to do long- to mathematics (more precisely For those considering mathema- term math studies, it’s better if you knot theory, hence the title). I wrote tics… fundamentally enjoy mathematics. and directed and my two colleagues The main difference between math- It is not a necessary condition, but Guillaume Bertoli and Adrien Lau- ematical research and mathematical if you find math fun it is already a rent carried it brilliantly on stage. studies is that in the studies you good sign for following this path! Subsequently, I had the opportu- learn things that have already been nity to write and perform a second discovered, mastered and refined, longer play (one hour long), called whereas in research you need to Mystère au Manoir Moutarde. It create something new. Mathemat- was made in collaboration with the ical research requires intuition and Scienscope for a project of the Pub- understanding of how things work lic Instruction Department. Again, together and are related to one there was a mystery that science another. In a way, mathematical helped to solve, but this time math- studies could be compared to learn- ematics teamed up with physics, ing a new language and mathemati- chemistry, computer science and cal research to writing novels in this biology. The detective in the play language. was able to solve the mystery via fun scientific experiments, that The personal qualities that have the audience members could try helped me to study mathematics themselves later at the Scienscope. are a good memory and the fact tum topology, a branch of topology of Geneva. The atmosphere there ready created and was done in such Since the play was written for 10 to that in general I like things to be related to knot theory. was really nice, everyone felt wel- a way that sometimes the children come, from first-year students to didn’t even realize that they were I found that SwissMAP offered a emeritus professors. doing maths! Unfortunately a lot of lot of opportunities, which I always people have negative biases about appreciated. They notably organized Outreach mathematics, for various reasons. several events, which led to many My experience with outreach in For instance they might think: math- fruitful discussions and getting to Geneva began when I helped out ematics are not for me, they are too know new people. Also, the Swiss- for the Nuit de la science in 2016 hard, they are boring. Thus, a nice MAP Master Classes offer a great (an event for the general public). trick we used in the Matshcope was opportunity of high-level but still Afterwards, I worked with the to introduce pupils to an idea with- introductory courses. Mathscope, by giving weekly one- out saying it was mathematical. hour long workshops for audiences I really appreciated my time in the ranging from 4 to 18 years old. Most I think the Scienscope is an excep- math department at the University of the workshop content was al- tional part of the University of Gene- va and thus needs to be preserved. Financially and logistically speaking, I have not seen support of such In SwissMAP, I was a postdoc at UniGE in Rinat Kashaev’s scale for an outreach department in group in quantum topology, a branch of topology related other universities. I really enjoyed to knot theory. being part of Scienscope, and I hope that it will live on and keep bring- Author: Fathi Ben Aribi UCLouvain

34 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 35 SwissMAP is proud to present its new one-semester long programme SPRING for high school students who want to take their interest in Presenting: mathematics to the next level. SPRING is available in both Geneva and Zurich, and is open to successful Athena and ETH Math Youth Academy participants.

Guided by a tutor (master student, PhD candidate or doctor in mathematics), students work in small groups of maximum four participants. A weekly meeting is the occasion for each individual to present and explain his/her reading to the rest of the group.

The semester ends in June with a group presentation of about 30 minutes to other SPRING participants from both Zürich and Geneva. Students who successfully follow the SPRING programme will be granted a SwissMAP certificate of participation.

In 2020, two groups of students (each consisting of two participants per group, 1 girl and 3 boys) are currently taking part in the SPRING programme in Geneva. One of them is working in topology: their goal is to understand the theorem of classification of surfaces. The other is working towards building the mathematical background necessary to work on neural networks SPRING and machine learning. (SwissMAP Programme for Reading IN Groups)

Image: Nikita Nikolaev

36 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 37 ATHENA is a UniGE based pro- - Was the level and content as you ing it is like learning a language, like physics. It is perfect that I study math gramme aimed at students inter- had expected? you are part of a secret club where and physics in high school, because ested in physics and mathematics Sylvia: Yes and no. I did expect it to only the members know this secret even though the classes will then be and in their final two years of high be hard, but I didn’t expect the sort language. I love all the symbols and more biology oriented, maths, phys- school. The programme provides of curve that happens in almost every how they can be keys used to solve ics and programming will still be the them with the chance to attend class, where the class starts with problems that are both trivial and base and tools to everything. first year university classes in a ATHENA interviews: something basic enough, that I can extremely complicated. I love physics supported environment. totally understand, and then in a few even more because I get to under- - Would you like to follow an aca- minutes, becomes something compli- stand how the world around me demic path? Since 2015 SwissMAP has support- cated. I need time to wrap my brain works and it’s simply fascinating. Sylvia: Of course! I’m planning on around it. getting a PhD, though I don’t know in ed this initiative and we are proud Sylvia and Tran Tran: I like maths because unlike what yet… to announce that 5 former Athena Tran: It’s the same for me. It al- many subjects, it is very straightfor- participants from the first ever Current students ways surprises me how in one class, ward. In maths, something is either Tran: I just want to do what interests Athena session, received their university students can learn about true or false. When you finish a maths me at the moment. I like the idea of Bachelor in Mathematics from a topic that high school students test, based on your answer, you can studying for as long as possible and UniGE last year. need a month to grasp. So, in the immediately predict your grade. having at least a PhD. But anything end, I guess I didn’t learn as much as Whereas with subjects like literature can happen in the future and I might We spoke to one former and two I expected during the Athena pro- or philosophy, many things you said change my mind, so there’s no point current Athena participants who gramme, not because it is not inter- can be right, wrong or somewhere thinking about it now. have shared their experience. esting, but because many things were in between, depending on the point too advanced for me. of view. For physics, I just believe that learning about physics makes - What did you enjoy most about you understand how things work and the programme? that, can make your life way easier. Sylvia: Seeing what university lec- Personally I think it is the most useful tures were like, experiencing univer- subject I learn at school. sity life in general, and meeting new people. - What are your current & future study plans? Tran: One of the great things about Sylvia: Right now, I am in the physics this programme is that we have a and maths option at college, but a study session with a Master/PhD few months ago, I got an offer from student every week where we can Cambridge to read Education and ask questions. Our tutor, Charlotte, is another one from UCL in London to very passionate about maths and has study Arts and Sciences, so I would helped us a lot. take classes in Physics and History of art, Film, Philosophy and English - How did you find the structure of Literature. So, Plan (A) is Cambridge From left to right: Tran and Sylvia. Current Athena students. the course? and plan (B) is UCL. Even though my Sylvia: I liked how every class was studies now don’t correspond to - When and how did you first hear Tran: I think it’s a great opportunity focused on one aspect of the subject, those I will be doing next year, I don’t about the Athena programme? to get a glimpse of math classes at that there’s a beginning and an end. regret them at all. I have learned so Sylvia: 2 years ago, from my physics university. It’s always good to see Also, during the second class, there much, and I think these are things teacher, also a friend of ours partici- what’s waiting for you if you choose were shorter, but more frequent that everyone should know! pated which allowed us to learn more the scientific path. breaks, which I also liked. I think that, about it. in a field such as mathematics, it’s Tran: I am also in the physics and - How long did you participate? very hard to only listen to theory for maths option. I plan to study Life Tran: I’m in the same class as Sylvia so Sylvia: 1 semester for 2 years. two hours straight. sciences at EPFL next year because it was the same for me. I’ve always been fascinated by the Tran: Yes, we chose Math methods Conversation with two current Tran: I guess it’s the same for me. connection between maths, physics - Why were you interested in it? for physicists the first year and Logic Athena students and biology. I also like the idea of Sylvia: I just love participating in ac- and introduction to Set Theory the - Why do you like maths / physics? working in a domain related to living tivities where I can learn things. second year. Interviewed by Mayra Lirot Sylvia: I love maths because learn- creatures more than pure maths and NCCR SwissMAP

38 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 39 basics (e.g. Euclid’s Elements) and I was able to keep up and follow the programme without much difficul- ty. And when it was getting harder sometimes I had a tutor who helped me with assignments and who helped ATHENA interviews: me understand the lectures. - What did you enjoy most about the programme? Ekaterina Golubeva During the programme I discovered a different aspect of Mathematics, one that we don’t learn at school. I Former student discovered its beauty and fell in love. I remember what absolutely fascinated me when I first learned about non- Euclidean geometries: the hyperbolic tiling of the Poincaré disc. I also heard about complex numbers for the first Ekaterina Golubeva. Former Athena student. time in the Géométrie I course. “Mathematics is a language in which open to new opportunities. I still have What was even more engaging was God has written the Universe” said so much to learn and to discover in being coached by a tutor. I was sur- Galileo and I recognize in it a unifying the different fields of maths. I would rounded by people who were writing entity. With its universal language love to be helpful and share all the their PhD thesis and they used to talk maths unite men and women, nations knowledge, passion and enthusiasm about their research areas with such and cultures and I find this really with people as much as I can. The idea passion that it encouraged me to try wonderful. of popularizing Mathematics inspires and also find my own passion. Since me. I like making it more accessible then I decided that I would also want - What are your current & future to people who may struggle with it. to find some area where I could solve study plans? My project and my tutoring allow me a question or help a further under- At the beginning of this academic to convey some of the meanings and standing of a topic. I really enjoyed year I was trying to launch a start- insights that I can access, because I the stimulating environment I was in up (called Mathbridge) and I have have the chance of studying it deeply. and I thank everyone who contribut- chosen to extend my Bachelor’s to I am really grateful for that. ed to it. 4 years to be able to develop the project besides my studies. I had to - Did the programme help you to stop my entrepreneurship activities Ekaterina Golubeva. Former Athena student. confirm your interest in physics and temporarily, but I prefer to keep the in Mathematics? current rate (i.e. taking half of the - When and how did you first hear - How long did you participate? It was definitely the trigger for me to classes). I now can go back to savour- about the Athena programme? I followed the one-semester course of choose to pursue my academic path ing Mathematics with less pressure I first heard about Athena during a Géométrie I in Mathematics and, the in Mathematics. due to exams or deadlines. I have Mathematics class in high school in following year, I took another semes- reduced my anxiety and I can study 2016, one year after the programme ter in a Physics course, called Math- - Why do you like maths / physics? my current subjects much deeper. was launched. My math teachers en- ematical methods for physicists. In I firstly fell in love with Geometry, couraged me to join the programme. short, I participated twice. shapes and symmetries. Then I real- - Would you like to follow an aca- ized everything in maths was about demic path? - Why were you interested in it? - Was the level and content as you patterns and structures. I love math I would love to try working in the I was able to discover what the had expected? for its inner beauty, mystery and for field of research if one day I get University looks like while still in high I had no expectations at the be- its sense of fulfilment and satisfac- the chance to do so. However, I’m school. This was a unique occasion for ginning, it was all new to me. I was not against the idea of working for Conversation with a former Athena tion. In moments when I get to under- student me at that time; to see where I would conscious that it was going to be stand a topic or solve a problem I feel industries, in the fields of applied be studying later on. harder than in high school but the like it’s worth it. Mathematics as well as in scientific Interviewed by Mayra Lirot programme actually started with the communication or popularization. I’m NCCR SwissMAP

40 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 41 Then, we focus on the challenge at and the number of components. the heart of knot theory: being able During the last session, we add the to tell one knot from another with following invariants to the list: certainty. Students quickly realize that it is very hard to work with 3D • unknotting number Presenting: knots and we teach them how to • tricolorability (and eventually The represent the objects they can ma- five-colorability) nipulate via diagrams. • linking number.

Maths Club The main goal of the Club de Maths is to stimulate the participants’ intuition and mathematical curiosity. SwissMAP has supported the activ- One of the small group activities ities of the University of Geneva’s proposed by Club de Maths is ded- Maths Club (Club de Maths) since icated to introducing the basics of When students master the diagrams At the end, a recapitulative table is the start of the NCCR. This is an knot theory. The central idea is to of basic knots and links (trefoils, constructed with the students, stat- extracurricular activity in Geneva immerse children into some exotic figure eight, Hopf, Whitehead, ing which invariant allows to differ- for 10 to 16 years old students. This mathematics, very different from unknot...), we discuss Reidemester entiate which pair of knots studied. year, there were 34 participants what they experience at school. movements. The depth of the dis- For advanced groups, some of the divided into 4 groups. This activity takes place over three cussion depends on the age of the following notions may be added: weeks. Here is the activity walk- students. through presented by its creator • Connected sum of knots, abelian An enthusiastic team of bachelor Terence. We then go back to the list of crite- monoidal structure and master students, working with ria proposed by the students and • Construction of the Alexander SwissMAP Outreach Officer Shaula Students are first given the material try them on diagrams: the number polynomial (historical approach Fiorelli, welcome participants for (knots made of iron wire and elec- of crossings is eliminated from the and using skein relations) two hours per week throughout the trical cables) without any instruc- candidates. • Extension of knot theory to academic year, which they alternate tion and can freely manipulate the graph theory. between sessions of problem solv- different objects. Once they are a bit A proper definition of invariant is ing and small group activities. familiar with it and the excitement given and the list is generally nar- We present some of this year’s of discovery is vanishing, it is time to rowed down to the trivial invariant Olympiad des Maths problems on the The main goal of the Club de Maths ask them the first question: “What next pages. is to stimulate the participants’ in- is this?” tuition and mathematical curiosity. Topics are very different from those Once the word “knot” arises (or is covered at school and the approach elicited from students if necessary) also differs: there are no assign- and is given as the name of such ments or exams. Our approach aims objects, the next question is asked: at being recreational, so that partic- “How can one differentiate these ipants can develop a real pleasure objects quickly?” in doing mathematics. Different criteria are listed at the Every year a Mathematical Olympiad board by students with the help of is organized: students work on a set tutors, and the word “invariant” is of problems (depending on their introduced. age group) for 4 hours. An award ceremony is later held in presence Once all the ideas have been gath- of all Club de Maths tutors and the ered, it is time for a little history of Authors: Lucia Camenisch & SwissMAP Outreach Officer. the subject and possible applications Terence Wenger to real life. UniGE

42 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 43 Here are some of the problems from this 3. Perfect Potatoes You have found seven perfectly identical and spherical potatoes with a year’s Math Olympiad diameter of 3cm. This is such a rare occurence that you decide to show organised by the Club them in a vegetables fair, nicely tied with a silk ribbon. You hesitate between the two configurations below. de Maths How much silk can you save (in cm) by adopting the most cost-efficient configuration?

1. Frieze Decorating In Charlotte’s class, students are using the Mathematics’ week as an occasion to redecorate the classroom’s walls with a frieze. The pattern they chose is made from a 21cm square as you can see below.

What is the exact area of the shaded area? Solution: eighteen cm eighteen Solution:

4. Blackboard Numbers

Vladimir and Lucy are both facing a blackboard on which they can read:

Solution: 183,75 cm 183,75 Solution: 2 4 – 11 – 15 – 18 – 25 Olga randomly picks 2 of these 5 numbers, then tells Vladimir their difference and Lucy their sum. Olga then asks: - What are the two numbers I picked? - I cannot know, says Vladimir. - I couldn’t know either, but since Vlad doesn’t know it, now I do!

What are the two numbers chosen by Olga? Solution: eleven and eighteen and eleven Solution:

2. Rectangle Frieze Leo’s students are less imaginative: their frieze is made from the rectangle below, with all bisectors drawn. What is the area of the quadrangle obtained this way?

5. The SOS Game The SOS game is played on a 1 x 7 grid as follows: Two players take turns writing an S or an O in one of the empty cells. The first player to complete the word SOS wins. If the grid is full but no SOS appears, it is a draw. You are the first to play. Show that there exists a strategy allowing you to

win.

other player’s turn to play: S _ _ S _ _ S play: to turn player’s other

configuration is on the grid and it’s the the it’s and grid the on is configuration Source: Rallye Mathématique

Solution: sixty cm sixty Solution:

cell. You are in a winning position if this this if position winning a in are You cell. d’Aquitaine Solution: Start with an S in the middle middle the in S an with Start Solution: https://www.math.u-bordeaux.fr/ IREM/rallye/

44 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 45 The SwissMAP video competition launched last year, is open to SwissMAP PhD students and Postdocs who are invited to make a short video describing their research to a non-specialist audience.

The challenge is in making it accessible, interesting and fun for both the researchers and the general public. SwissMAP PhD & Postdoc Videos are judged on the quality of the scientific explanation as well as creativity and overall presentation. Video Competition

46 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 47 First Prize: Ofir David Second Prize: Nikita Nikolaev Researching the mathematics Abelianisation of Differential of billiard tables Equations

- Did you get help from other peo- Probably the biggest obstacle that I ber of iterations, because although the audience goes a long way. ple? If so, what were their qualifica- had to overcome in the beginning is ideas involved are often not neces- tions? learning how to do some simple video sarily complicated, explaining them - What part did you enjoy the most? I created the video by myself. After and audio editing, since out of the requires a fair amount of language Designing the video and the script, I finished the first draft I got some whole video making process this is the and/or other ideas. This makes it diffi- finding the right and accessible words remarks about the presentation from one area which I had zero knowledge, cult to find the optimal way to convey to explain the essence of the ideas, a couple of colleagues which I incorpo- and I believe that this is true for many the essence without either drowning in was intellectually a very fulfilling rated in the final version. people in the academy. If you can find indiscernible jargon or turning the dis- challenge. Also, editing the video was someone who knows how to do this cussion into an interminable overlong a wonderful way to let free an artistic Ofir David (UZH, C. Ulcigrai Group) - How long would you say the video sort of stuff and is willing to help you, Nikita Nikolaev (UniGE, A. Alekseev Group) tedium. side. took to make in total? then you already made your first step. - What was your main motivation - What was your main motivation The making of the video spread over The abstract nature of mathematics - Did you get help from other peo- to participate in the video compe- to participate in the video compe- a few weeks, though I only worked on There is also a big difference between is the chief culprit here, and some ple? If so, what were their qualifica- tition? tition? it (namely the coding, editing, etc) a presenting a subject in a video than areas of mathematics suffer more than tions? I actually started working on the video It seemed like an interesting technical couple of hours each week. in other settings, like a classroom or a others. My area, algebraic geometry, Yes, my wife, Beatriz, who is also a before I knew about the competition. and artistic challenge to find a way to paper. I would suggest to try and find is more towards the inauspicious end mathematician, albeit for an unrelated The competition began at a good present something about my research as many people as you can to give of this scale, though the geometric area. Her help was absolutely indis- timing, giving me extra motivation to - What comments have people in a succinct, accessible, and engaging you remarks about the video (and try nature of many ideas does have some pensable! work on the video. made to you about the video? way. I got very few comments on the video. to avoid experts in your field which way of being malleable to visualis- already know everything that you are ation. Abstractness sometimes inevi- - What parts did you find most chal- - What parts did you find most chal- - How long would you say the video trying to present). tably forces you to sacrifice accuracy lenging in the project? - What advice would you give to lenging in the project? took to make in total? over clarity: you have to come to terms The part which is almost always the someone who is considering partic- By far the biggest challenge was to Designing the script and the video with the realisation that a precise and most challenging is finding a good way ipating? come with exactly what to say, and took the longest, spread over several accurate message which is completely to present the subject. This usually Making a video to present a math- specifically to find the right balance weeks. All the filming was done over lost on the audience has no use, whilst starts with an idea that I think about ematical idea (or in general any between clarity and accuracy. Formu- two days, and the editing took one full an imprecise message with the right for weeks and even months before I research area) is not an easy task. lating the script took a very large num- day. flavour which actually reaches the even begin to think about making a video. The second part is to think of a - What comments have people visual way to do the presentation that made to you about the video? I could actually create in a reasona- There has been an overwhelming ble time. Once this is done, the rest is amount of positive comments and mostly manual work of writing down feedback, for which I am truly thank- the code for the animation, creating ful. Probably the most rewarding and synchronizing the narration, writ- comment, which several people have ing notes of the subject etc. made, is that watching the video they felt like they were watching a BBC - What part did you enjoy the most? documentary. Thinking about ways to present mathematical ideas is always the - What advice would you give to most enjoyable part for me. This is one someone who is considering partic- of the main ways of transforming a ipating? subject that I know to a subject that I Clarity over accuracy. Always keep in understand. mind your target audience.

Interviewed by Mayra Lirot Ofir David’s video: Researching the mathematics of billiard tables Nikita Nikolaev’s video: Abelianisation of Differential Equations. NCCR SwissMAP Hosted: SwissMAP YouTube channel Hosted: SwissMAP YouTube channel

48 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 49 2020-21 29 Jul - 07 Aug 2021 ICMP 2021 06 - 09 September Geneva 7th SwissMAP General Meeting We are happy to announce that Saanenmöser 7 - 10 June 2021 Geneva will be hosting the The program will include: The Conference in honor of J.-P. next International Congress of 2 - 7 February SwissMAP Innovator Prize Eckmann (UniGE) Mathematical Physics in 2021. Winter School in Mathematical ceremony; talks by the Innovator Geneva The event will gather world-class The conference was postponed

Events Physics - 2020 Prize winners, colloquia covering experts in the field. Les Diablerets SwissMAP research directions, from June 2020 to the following The annual Winter School in and talks by junior participants. year. This event will bring Mathematical Physics featured together students and close collab- mini-courses by Antti Kupiainen, orators of Jean-Pierre Eckmann Nicolai Reshetikhin, Jörg Tesch- on the occasion of his 50 years at ner, and a Colloquium by Victor the University of Geneva. Kac. Online Events of 2020: Due to the unusual situation the world started living in at the start of 2020, most events of the year were transfered online or postponed to a later date. During this time, SwissMAP members were able to host a number of successful regular events online. • Mathematical Physics Seminar Jan - Mar Apr - Jun Jul - Sep Oct - Dec 2 021 (UniGE) • Global Poisson Webinar (UniGE) • Ergodic Theory and Dynamical Systems Seminar (UZH) • Talks in Mathematical Physics (ETHZ) • Strings, CFT & Integrability (ETHZ) • [K-OS] KNOT online seminar January 2021 (CNRS, UNIGE) SwissMAP Research Station (SRS) 05 June Les Diablerets NCCR SwissMAP Site Visit The Station, will be based in Les Geneva Diablerets, Switzerland. The SRS The NCCR SwissMAP Review will be dedicated to the organi- Summer 2021 Panel Site Visit will take place zation of events in Mathematical Gauge/Gravity Duality 2020 online this year. 23 September Journée Georges de Rham 2020 Physics (conferences, workshops, Geneva Geneva thematic meetings). The conference was postponed The conference was postponed from July 2020 to the summer of from April to the fall of 2020. 2021. The aim of this event is This year, the invited speakers to explore all aspects of gauge/ gravity duality, both applied and For more detailed information are James Maynard (University theoretical, and to generate an please visit our Website: of Oxford) and Corinna Ulcigrai extensive exchange of ideas. https://www.nccr-swissmap.ch/ (University of Zurich). news-and-events/events

50 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 51 Awards Grants Alessio Figalli and Tudor Ratiu Alice Gasparini Shaula Fiorelli and Academia Europaea 2020 CPEP Award Pierre-Alain Cherix We are proud to announce that in 2019 two of our members, Congratulations to Alice SNSF Agora Grant Alessio Figalli and Tudor Ratiu, were elected to the Academia Gasparini (UniGE) for Congratulations to our Europaea. The object of Academia Europaea is the advance- receiving the 2020 CPEP members who received the ment and propagation of excellence in scholarship anywhere Award for: Excellence in SNSF Agora Grant which in the world for the public benefit and for the advancement of Teaching Contemporary encourages researchers the education of the public of all ages. Physics. Since 2008 Dr. to communicate to the Alessio Figalli Gasparini has been teach- general public. Their 2019 awards and distinctions ing mathematics and physics at Geneva secondary project, Leonardo in Congratulations to our member Alessio Figalli (ETH Zürich) for his different 2019 school in Switzerland, and is a scientific collabora- Perspective, was an prizes, awards and distinctions: tor at the University of Geneva. She has developed exhibition to mark the Doctor Honoris Causa Award; Foreign Member of the Academy of Sciences of Bolo- activities, a course, and a book on the subjects of 500th anniversary of gna; Gili Agostinelli Prize of the “Accademia delle Scienzedi Torino”, Knight of the general relativity and cosmology, exclusively based Leonardo Da Vinci’s death. Order of Merit of the Italian Republic. on high school mathematics and physics.

Renato Renner Qingtao Chen AHP Prize ICCM Best Paper Alessandro Congratulations to Marius Junge, Renato Renner, David Sutter, Mark M. Wilde, and Award Sfondrini Congratulations to our Andreas Winter, who were awarded the AHP Prize for the paper: Universal Recovery SNSF “Spark” Grant alumnus Qingtao Chen Maps and Approximate Sufficiency of Quantum Relative Entropy. Each year a prize Congratulations to our (ETH Zurich, Felder founded by Birkhäuser is awarded for the most remarkable paper published in the member Alessandro Group), for winning the journal Annales Henri Poincaré. Sfondrini (ETH Zurich Best Paper Award at the - Gaberdiel Group) and International Consortium Burkhard Eden (ETH Corinna Ulcigrai of Chinese Mathematicians (ICCM). His paper was Zurich) for receiving 2020 Brin Prize for Dynamical Systems entitled “Volume conjectures for the reshetikhin– the SNSF Spark Grant for their project: Exact Congratulations to our member Corinna Ulcigrai (UZH) who is the recipient of the turaev and the turaev–viro invariants”. Qingtao correlation functions in AdS/CFT. 2020 Brin Prize for Dynamical Systems for her fundamental work on the ergodic Chen is now Assistant Professor at the New York theory of locally Hamiltonian flows on surfaces, of translation flows on periodic sur- University Abu Dhabi. faces and wind-tree models, and her seminal work on higher genus generalizations of Vincent Tassion Markov and Lagrange spectra. ERC Starting Grant Avelio Sepulveda Our member Vincent 2019 Francisco Aran- Tassion was awarded an Maryna Viazovska da-Ordaz Prize ERC Starting Grant for 2020 European Mathematical Society Prize & 2019 Fermat Prize Congratulations to our his project Critical and Congratulations to our member Maryna Viazovska (EPFL) who was amongst the 10 Alumnus Avelio Sepul- supercritical percolation. outstanding young researchers who received the 2020 EMS prize. The EMS Prizes veda (ETH Zurich, W. Vincent is focusing on are awarded every four years in recognition of excellent contributions in mathema- Werner Group) who the mathematical study tics. Maryna Viazovska also won the 2019 Fermat Prize for research in Mathematics received the 2019 Fran- of models arising in statistical mechanics. These for her solution to the famous sphere packing problems in dimensions 8 and 24. cisco Aranda-Ordaz Prize models describe different mechanisms that give rise for his PhD research: “Exit sets of the continuum to phase transitions in physics. Such models include Wendelin Werner Gaussian free field in two dimensions and related percolation processes, which are the main topic of Elected to the Royal Society questions”. This prize is awarded by SLAPEM and his ERC project. A number of groundbreaking The renowned Royal Society has elected Wendelin Werner as its member. The ETH co-sponsored by the Bernoulli Society. It is awarded results have improved the understanding of mathematician now officially belongs to the “Foreign Members of the Royal Society every 2-3 years to one PhD in Probability and one percolation. As some fundamental questions remain (ForMemRS)”. The traditional British learned society has existed since 1660 and only PhD in Statistics, written by students from Latin unanswered, Vincent aims to answer some of admits scientists as its members who have made an “outstanding contribution to sci- America regardless of the country of the university them by establishing new connections between entific understanding and its use for the benefit of humanity”. offering the degree. percolation theory and other fields of mathematics or theoretical computer science.

52 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 53 New Members Artur Avila University of Zurich Renato Renner Artur Avila is a professor ETH Zurich at the Institute of Mikaela Iacobelli We would like to Mathematics of the welcome Renato Renner Juhan Aru ETH Zurich University of Zurich. We would like to welcome as a new SwissMAP EPFL He will be joining our Mikaela Iacobelli as a member. He will be We welcome Juhan Statistical Mechanics new SwissMAP member. joining our Quantum Aru will be joining our research project. His She will be joining our Systems research project. Statistical Mechanics main research interests lie Statistical Mechanics Renato is a Professor research project. He was primarily in dynamical systems research project. Mikaela for Theoretical Physics and previously a SwissMAP and spectral theory. He is one of is a professor at the head of the research group for postdoc member in the winners of the 2014 Fields Department of Mathematics at Quantum Information Theory Wendelin Werner’s Medal, being the first Latin ETH Zürich. Her research is at the ETH Zurich. His research group (ETH Zurich). His American to win such an award. focused on the study of problems interests are in the area of research interests include how Avila is known for proving the arising from the wide context quantum information science, to mathematically describe and “conjecture of the ten martinis” of statistical mechanics. More quantum thermodynamics, and the study systems where geometric along with mathematician precisely, she is interested in the foundations of quantum physics. structure and randomness Svetlana Jitomirskaya. He also analysis of partial differential interact. The mathematical field proved the Zorich–Kontsevich equations in kinetic theory. Part studying such phenomena lies at conjecture together with Marcelo of her work concerns the analysis the interface of probability theory, Alexander Viana. of singular limits for Vlasov-type analysis and mathematical physics. Zhiboedov equations. She makes extensive He works on random curves CERN use of PDEs techniques, optimal (SLE curves), height functions We welcome Alexander transport, probability, calculus (Gaussian free field) and other Zhiboedov who will be of variations, and Riemannian random geometric structures (e.g. joining our Field Theory Nicolas Brunner geometry. Gaussian multiplicative chaos), and String Theory University of Geneva often with roots in the phenomena research projects. We would like to welcome of statistical physics. Alexander is interested Nicolas Brunner as a in understanding the space of new SwissMAP member. Chiara Saffirio quantum field theories (QFTs), He will be joining our University of Basel especially the strongly coupled Quantum Systems We welcome Chiara models. He applies and develops Nicolas Gisin research project. Saffirio as a new nonperturbative methods of the Nicolas is an associate University of Geneva SwissMAP member. conformal and S-matrix bootstrap professor in the group of applied We would like to welcome She will be joining which rely on general principles, physics at the University of Nicolas Gisin as a new our Quantum Systems such as symmetry and quantum Geneva. His research interests SwissMAP member. research project. mechanics. One motivation for are quantum information He will be joining our Her research focuses this work is holography which theory, foundations of quantum Quantum Systems mainly on the rigorous derivation relates QFTs to quantum gravity mechanics and quantum research project. of effective evolution equations in spacetimes with one extra thermodynamics. His research interests from the dynamics of many- dimension. By understanding lie in: quantum physics - from body classical and quantum the space of consistent QFTs foundation to application in systems, with special emphasis via bootstrap methods one hopes quantum information science, on the Boltzmann equation. The to understand nonperturbative quantum communication, open tools she uses come mostly from aspects of quantum gravity and quantum systems, indeterminism kinetic theory, functional analysis, string theory, which are hard to and non-locality. semiclassical analysis, statistical mechanics and probability.

3. Problem in the dark You enter a room. On a table there are some counters, each of which has a red side and a blue side. Twenty of these counters have their blue side facing up while the others have red facing up.

Your task is to separate the counters into two piles, not necessarily of the same size, but so that each pile contains exactly the same number of Corner counters with blue side up. To do this, you can turn over as many counters as you like.

Here’s the catch: the room is in total darkness. 1. Infected Grid Initially, 9 of the 100 squares in a 10 x 10 grid are infected. At a given How would you separate the counters into two piles so that each pile instant, a square becomes infected if at least two of its neighbors (sharing contains the same number of counters with blue side up? a side) already are. Can the infection spread across the entire grid?

4. The Circle inside the Triangle Can you caluclate the area of the small circle inside this triangle? Puzzle

5cm

3cm

4cm

5. Without Head nor Tail On a distant island, a valiant knight must face dragons with several heads and tails. With a sword, the knight can cut off either: one head, two heads, one tail or two tails.

But these dragons have magical powers: cut off one head, and he will in- 2. The Strawberry Tart stantly regrow another one; cut off one tail, and he will regrow back two! Luke: How old are your 3 children? On the other hand, if you cut off two heads with a single sword strike, Eva: The product of their ages equals 36 nothing grows back... but two tails cut off at once are replaced by a new Luke: I need more information head. Of course, a dragon is only completely dead when it has no head or Eva: The sum of their ages is the house number you can see on the tail left. other side of the street Luke: I’m sorry, but in hindsight I still can’t determine the age of your How do you kill a magical dragon with 5 heads and 7 tails? kids yet Are there any immortal dragons? Which ones? Eva: The oldest one loves strawberry tarts Luke: Ah, now it’s clear! I know how old your children are

Can you determine the ages of the 3 children? 6. Positive integers Does there exist a set M of positive integers with the following property: each positive integer outside of M is the average of two dierent elements of M, while no positive integer in M has this property?

56 | © SwissMAP Perspectives | 2020 2020 | © SwissMAP Perspectives | 57 4. The Circle inside the Triangle Answers 1. Infected Grid No. The total perimeter of the infected region never increases.

Initially, it is at most 36, so it cannot reach 40.

2. The Strawberry Tart The children are 2, 2 and 9 years old respectively. Eva’s first answer, allows you to find 8 possibilities (hence Luke’s need for more information). 1-1-36 1-2-18 1-3-12 1-4-9 1-6-6 2-2-9 2-3-6 3-3-4

Luke’s second request for information (“I’m sorry, but...”), indicates that at least two of the possibilities have the same sum. 1+6+6=13 2+2+9=13

Since both possibilities indicate that two of the children are twins, Eva’s last clue (“The oldest one loves strawberry tarts”) allows you to find the right answer: where the oldest child is not one of the twins. 5. Without Head nor Tail To kill a dragon with 5 heads (H) and 7 tails (T): 3. Problem in the dark 1. Cut off 2 x 2H and 3 x 2T (two at a time). You are left with 4H and 1T Divide the counters into two piles: one consisting of a randomly selected 2. Cut off 3 x 1T (one T at a time). You are left with 4H and 4T 20 counters and the other containing the rest. Now turn over each coun- 3. Cut off 2 x 2T (two T at a time). You are left with 6H ter in the pile of 20. 4. Cut off 3 x 2H (two H at a time). You have defeated the dragon!

Suppose that the pile of 20 contains n blue counters. Then, since there Immortal dragons are those with an odd number of heads and no tail. If are 20 blue counters in total, the other pile has 20 - n blue counters. Since you have tails you can always cut them off and make heads to get an even the pile of 20 has n blue counters, it must have 20 - n red ones. By turning number of heads. each counter over, we are left with a pile having n red counters and 20 - n blue ones - exactly the same number of blues as in the other pile.

6. Positive integers Yes. Let M be the set of positive integers whose expansion in base 3 contains only 0’s and 1’s. If x \in N–M, then 2x (just as any positive inte- Puzzle contributors: ger) can be writen as the sum of two elements of M; use that 2=1+1, 1=1+0, No 3: Mathscope & RTSdécouverte | Monthly maths problem | https://scienscope.unige.ch/mathscope/ and 0=0+0. If x \in M, then 2x consists of only 0’s and 2’s, so it cannot be No 1, 6: ETH Math Youth Academy | https://people.math.ethz.ch/~kslavov/ written as the sum of two distinct elements of M (there can be no carry No 2, 4, 5: Alice Gasparini | University of Geneva operations).

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Contributors: Fathi Ben Aribi; Lucia Camenisch; Alice Gasparini; Shaula Fiorelli; Maria Kondratieva; Mayra Lirot; Joana Mailler; Elise Raphael; Kaloyan Slavov; Terence Wenger;

Original illustrations by Varia Timchenko. All other design elements licensed under the designcuts.com extended license.

Copyright ©2020 NCCR SwissMAP and all Contributors as identified. SwissMAP Perspectives (images excepted) is made available for non-commercial re-use with proper attribution under the terms of the Creative Commons Attribu- tion-NonCommercial-ShareAlike 4.0 International License. To view a copy of this license, please visit http://creativecommons.org/licenses/by-nc-sa/4.0/ For further information please contact: Produced by Amrin Design. ©2020 NCCR SwissMAP Cover photo: Maria Kondratieva, Les Diablerets UNIGE, Math Department 2-4 rue du Lièvre, CP 64 1211 Genève 4

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