SwissMAP Perspectives Issue 4 | 2019 Special Edition: Equal Opportunities 04 20 30 Simplify your life by going large Universal Optimality of E8 and Awards and Grants Leech Lattices In this article, our member Susanne Reffert In this article, our member Maryna Viazovska We are pleased to announce the awards explores how her professional path has lead discusses the E8 lattice and the Leech and grants received by our participants and her research to the subject of large-charge lattice who are among the most famous students. expansion and the exciting possibilities of mathematical objects. this relatively new direction. Contents 08 22 31 Conversation with Prof. Anna Interview with Eva Miranda New Collaborators Beliakova Anna Beliakova is a full professor of In this short interview, Eva Miranda (UPC) We continue to expand and grow thanks to mathematics at the University of Zurich. tells us about the importance of organizing a new collaborators within SwissMAP. In this interview we discuss both the past, women workshop and what she hopes it will Welcome to Alessio Figalli and Corinna present and future of her scientific career. achieve. Ulcigrai! 12 26 32 Mentoring Program for women SwissMAP member stories: The Puzzle Corner PhD and Postdocs Olga Chekeres As part of the ongoing effort of SwissMAP SwissMAP-funded PhD student, Olga Test your math and logic skills with these to address the gender gap in our field, the Chekeres, completed her thesis in April 2019. puzzles, kindly put together by some of our Equal Opportunities Committee has recently Olga’s plans are to join the University of contributors. launched the SwissMAP Mentoring Program Connecticut, USA, for the next 3 years as an for Women PhD and Postdoc members. Assistant Research Professor. 14 28 Interview with Prof. Chenchang Upcoming Events Zhu Following our Women at the Intersection A brief overview of the events organised or of Mathematics and High Energy Physics co-organised by the NCCR SwissMAP. conference, we met with Chenchang Zhu to talk about Balancing Yin and Yang in the field of Mathematics. 2 | © SwissMAP Perspectives | 2019 2019 | © SwissMAP Perspectives | 3 it often involves physics I previously a handle on strongly knew only little about. This topic was coupled problems is no exception. It is centered on the important progress. study of special sectors of three- and four-dimensional conformal field the- The approach we follow ories (CFTs). The most surprising part is quite a time-honored was that the problem had nothing to one in theoretical phys- do with string theory or even super- ics, namely making use symmetry (even though it is possible of the symmetries of Simplify your life to consider superconformal field the problem and con- theories (SCFTs)). sidering special subsec- tors of the full theory by going Conformal field theories are, as the in which simplifications name suggests, invariant under con- occur. In our case, we formal transformations. This gives consider CFTs with a rise to special features. If we know global symmetry. Such the operator dimension and spin of a symmetry has by each local operator, conformal sym- Noether’s theorem an metry fixes the two-point functions associated conserved large up to normalization. If we further- charge, which can be more know the 3-point function used to slice the Hilbert coefficients, we can solve the theory space of states of the completely, in the sense that we can theory into sectors Susanne Reffert discussing large charge with Luis Alvarez-Gaume and Domenico Orlando at the Simons Center for Geometry and Physics. Photo by Jean-François Dars. write down all higher correlation labeled by their charge. functions. We concentrate on a suppressed by inverse powers of the al and the spacetime symmetries. subsector of fixed charge, where we charge. In the problems we have Part of this breaking is explicit and CFTs play an important role in take the charge to be very large. It studied so far, we were generally left due to fixing the charge, part of it is In theoretical physics, our best tool I never actively worked on this topic, theoretical physics, as they show turns out that it is possible to write a with only a very small number of con- spontaneous and due to the ground to calculate observable quantities is it lead me to become interested in up in a variety of contexts, such as low-energy effective theory in which tributions which are not suppressed. state itself. Spontaneous symme- perturbation theory. We know very the connections between integrable critical points characterizing second the inverse of the large charge acts as In other words, working at large try breaking gives rise to massless little about strongly coupled systems. systems and supersymmetric gauge order phase transitions, fixed points a controlling parameter, bringing us charge allows us to make the step Goldstone degrees of freedom. They Any new tool to access the strongly theories. Realizing such deformed in renormalization group flows, back to a perturbative regime. from an effective action with infinite- represent the quantum fluctuations coupled regime is therefore most gauge theories appearing in these and even quantum gravity via the Wilson’s notion of the effective ly many terms to an expansion which around the classical ground state and welcome. We found that working correspondence within string theo- AdS/CFT correspondence. CFTs are action in which any term compatible captures the low-energy physics in a encode the low-energy physics in the in sectors of large charge is way of ry came next. This topic, and brane scale-free, meaning they contain no with the symmetries of the problem handful of terms. effective action. If the global symme- compensating the effects of strong realizations of supersymmetric gauge characteristic length or energy scale. must appear is conceptually very try we started from was just a U(1), coupling. theories in general kept me busy for This means also that we have no di- then things are simple and we are left quite a while through my moves to mensionful small parameter in which with a single (relativistic) Goldstone I am a string theorist by training and Japan and then to CERN. to perform a perturbative expansion. boson in terms of which we write a in the course of my career I have I am a string theorist by training and in the course The dimensionless couplings in a CFT non-linear sigma model. The action gone through what resembles a To my own surprise, I ended up add- are generically of order one. While of my career I have gone through what resembles contains all the terms compatible random walk in the space of prob- ing a quite different line of research in two dimensions the special nature with conformal symmetry which are lems in formal theoretical physics. I to my collection. This happened in a random walk in the space of problems in formal of the conformal group allows us to not suppressed by the large charge. started out in string phenomenology spring 2015, just after having started use a host of analytic techniques, in theoretical physics. If we start from a larger, non-Abelian at a time when flux compactifications my new job at the University of Bern. higher-dimensional CFTs things are global symmetry group, we need to were a hot topic. I was most at- I was in Japan, visiting my long-time much more tricky. Of course, we have first determine the symmetry-break- tracted by their most formal aspect, collaborator Simeon Hellerman some methods at our disposal, such compelling. If we don’t have a way of We approach the problem semiclas- ing pattern. Since the ground state namely the algebraic geometry of together with my collaborator (and as large-N expansions, (small) epsilon truncating the effective theory, it is sically, solving the classical equations breaks Lorentz invariance, we are the compactification manifolds. husband) Domenico Orlando. For me, expansions and the conformal boot- however of very limited practical use. of motion at fixed charge and min- generally left with both relativistic Motivated primarily by my interest every new project tends to be a jour- strap. And it is possible to run Mon- Working at fixed charge allows us to imizing in order to find the low- and non-relativistic Goldstone bos- in the (much more formal) field of ney into the unknown, not just in the te-Carlo simulations on the lattice at do exactly that. In addition to using est-energy state at fixed charge. This ons, which are distinguished by their topological string theory, I went to obvious sense that we don’t know the strong coupling. But analytic results the constraints due to symmetry, we ground state has the special feature dispersion relations (linear versus Amsterdam to work with Robbert end result of a research project when are still few and far between and any also use the fixed-charge scaling to of being time-dependent. Working at quadratic in the momentum). Dijkgraaf for my first postdoc. While we start it, but also in the sense that new approach that can help us get discard those terms which are highly fixed charge breaks both the glob- Once we have written down the 4 | © SwissMAP Perspectives | 2019 2019 | © SwissMAP Perspectives | 5 effective action in the form of a large- lar that cases with a moduli space of vors, we could compare to a super- charge expansion, we can start cal- vacua behave very differently from symmetric localization calculation culating the conformal data, namely theories with one discrete vacuum I which has again shown an amazing 4 operator dimensions and three-point described above.