Report 2018/2019 ETH Institute for Theoretical Studies

Home , Ivan Cherednik, Rainer Weiss

ETH-ITS

Table of Contents

Foreword 5

The ETH Institute for Theoretical Studies 6

History and aims 6

Fellows at the ITS 6

Collaborations 7

Activities 8

Meetings, talks, minicourses 8

The ITS Science Colloquium 10

Programme 2018–2019 11

Fellows’ seminar 12

Programme 2018–2019 12

Awards 13

Fellows’ report 14

Outlook 22

People at the ETH-ITS 24

Director 24

Coordinator 24

Board of Patrons 24

Advisory Committee 24

2013–2017

2017–2019

Fellows 2014–2019 25

Senior Fellows

Junior Fellows (with current affiliation of former Junior Fellows)

Contact 27 Clausiusstrasse 47, the address of the ETH Institute for Theoretical Studies.

4 Foreword

The academic year 2018/2019 was in several ways special for the Institute for Theoretical Studies. Firstly, it experimen- ted a new way of functioning, dedicating a semester to the interdisciplinary subject of «modular forms, periods and scattering amplitudes», hosting over forty physicists and mathematicians, with a school, a workshop and other events involving several young scientists and putting into contact participants with scientists of ETH. Secondly, the Institute was evaluated by an international committee, who was very positively impressed by the achievements of the Institute and gave interesting suggestions for improvement. Thirdly, on a more personal note, this was my last year as the director of the ETH-ITS; the last six years were an intense period in which I had the unique opportunity to meet scientists in a variety of subjects who are shaping their respective disciplines. I thank the donors for making this possible, the Fellows of the Institute for their excellent scientific contributions, the school board of ETH Zurich for their continuous support, the Advisory Committee for its commitment and advice, and Christina Buchmann, who is retiring this year as coordinator, for her invaluable help and competence in running the Institute. The new director Rahul Pandharipande, professor of mathematics at ETH Zurich, took office on 1 June 2019. Livia Kürsteiner is the new coordinator. I wish the new team a successful start.

Giovanni Felder, Institute’s director

The ETH Institute for Theoretical Studies is supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Foundation.

5 Ruth Britto lecturing at the school on Modular forms, periods and scattering amplitudes, organized in collaboration with SwissMAP.

The ETH Institute for Theoretical Studies

History and aims The ETH Institute for Theoretical Studies (ETH-ITS) is an interdisciplinary Institute dedicated to research in mathematics, theoretical computer science and theoretical natural sciences. It was founded on 1 June 2013 on the initiative of former ETH president Ralph Eichler, with a generous donation of Dr. Max Rössler and the Walter Haefner Foundation. The aim of the Institute is to enable top theoretical scientists to be active for an extended period of time at ETH, interact with local researchers, and establish lasting scientific collaborations in an interdisciplinary context.

Fellows at the ITS The Institute hosts up to six Senior Fellows and up to twelve Junior Fellows. Junior Fellows are talented young independent postdocs spending up to three years at ETH Zurich to work on research subjects of their choice. They are supported by a mentor, who is an ETH professor.

The Junior Fellows are selected by the director, with the assistance of the scientific Advisory Committee, by a nomination procedure: candidates are selected from a group of young researchers that are nominated by faculty members and senior researchers of universities and research institutions and are invited to apply.

6 Schedule for the selection of Junior Fellows

Mid-September Target date for nominations, eligible candidates are invited to apply

Mid-October Deadline for application of nominated candidates

November Interviews with ETH members of the Advisory Committee

December Offers are made

Senior Fellows are leading international researchers in mathematics, theoretical computer science and theoretical natural sciences, spending up to a year at the Institute on a sabbatical leave from their home institutions. They dedicate their time to research and participate in the activities of the Institute and of ETH Zurich, for example by giving a course on research topics. They are invited by the Vice-President for Research and Corporate Relations of ETH Zurich on the recommendation of the Advisory Committee. Candidates are often suggested by members of the Advisory Committee or ETH faculty, but they can also apply directly. www.ethz.ch/eth-its/fellows →

Collaborations The ETH Institute for Theoretical Studies collaborates with the Departments of ETH and their visitor programmes, such as the Forschungsinstitut für Mathematik (FIM) at the Department of mathematics and the Pauli Centre at the Department of physics. It also nurtures the relationship with other Swiss research institutions through its Fellows and by contributing to scientific activities. This year it organized a school within the thematic programme on «Modular forms, periods and scattering amplitudes» together with the National Competence Centre in Research SwissMAP – The Mathematics of Physics and contributed to the programme goMATH – Women in Mathematics of the Department of Mathematics of ETH Zurich.

7 Participants at the workshop on Modular forms, periods and scattering amplitudes.

Activities

Meetings, talks, minicourses In the spring semester 2019 a thematic programme on «Modular forms, periods and scattering amplitudes» took place at the ETH-ITS. It was organized by Babis Anastasiou (ETH Zurich), Claude Duhr (CERN), Giovanni Felder (ETH Zurich) and Eric Panzer (University of Oxford). Over the last few years, the calculations of scattering amplitudes in particle physics and string theory led to the development of sophisticated mathematical methods and brought new questions in the classical area of mathematics of modular forms. The aim of the programme was to bring together experts on these integrals and related objects, both in physics and in mathematics, with the grand goal of advancing the field via a cross-fertilisation between disciplines. The programme started with a school with minicourses by Ruth Britto (Dublin), Claude Duhr (CERN), Javier Fresán (Ecole Polytechnique) and Nils Matthes (Oxford), with talks accessible to both mathematicians and physicists and ended with a workshop. There were a number of visitors and further activities throughout the programme.

8 The fourth edition of the European-Japanese Symposium on Symplectic Varieties and Moduli Spaces took place at ETH with the support of the ETH-ITS. It was organised by Junior Fellow Ulrike Rieß together with Chiara Camere (Università degli Studi di Milano), Daisuke Matsushita (Hokkaido University), Giovanni Mongardi (Università di Bologna), Hisanori Ohashi (Tokyo University of Science). It included minicourses of Claire Voisin and Yoshinori Namikawa and talks by participants. In addition, Senior Fellows Sandu Popescu and Gilles Brassard gave series of lectures on topics related to quantum information theory and foundation of quantum mechanics, see the Fellows’ report below for more details.

9 Former Senior Fellow Robert Brandenberger (left) discusses with Philippe Jetzer and ITS Colloquium Speaker Rainer Weiss (right).

The ITS Science Colloquium

The ITS Science Colloquium aims at exposing students and researchers in mathematics, theoretical computer science and theoretical natural sciences to new questions and research subjects of common interest to different disciplines.

The first talk was by ETH physicist Renato Renner who asked whether quantum mechanics can be used to describe a physicist who herself uses quantum mechanics, a question based on the much discussed thought experiment recently proposed by Renner with Daniela Frauchiger. In another well-attended talk Nobel prize laureate Rainer Weiss, of the Massachusetts Institute of Technology, co-founder of the LIGO project, told us about the exploration of the Universe through gravitational waves. The third speaker of the academic year was Ranit Aharonov, of IBM Research, manager of Project Debater, an AI system that can engage humans in debates on complex topics. In her talk she addressed the question «How persuasive can a computer be?» Finally, Miranda Cheng, of the University of Amsterdam, told us the story of the 17 mysterious formulae written by Ramanujan in a 1920 letter, that marked the beginning of a theory that has recent application to various research areas, including the moonshine theory in mathematics and black holes in theoretical physics.

10 The audience at Renato Renner’s talk «Beyond Schrödinger’s cat».

Programme 2018/2019

25.10.2018 Renato Renner, ETH Zurich Beyond Schrödinger’s cat

28.02.2019 Rainer Weiss, MIT and LIGO Exploring the universe with gravitational waves

07.03.2019 Ranit Aharonov, IBM research Project Debater – How persuasive can a computer be?

14.03.2019 Miranda Cheng, Amsterdam Mock modular forms are everywhere

Videos of selected talks can be viewed on www.ethz.ch/eth-its/activities →

11 Fellows’ seminar

The aim of the Fellows’ seminar, organized by Junior Fellows Johannes Noller and Ulrike Rieß, is to present the research of the Fellows of the ETH-ITS. It is open to all interested and the rule is that talks should be accessible to other Fellows, which are typically from a different field.

Programme 2018/2019

09.10.2018 Sandu Popescu On conservation laws in quantum mechanics

16.10.2018 Pierrick Bousseau Quivers and curves

06.11.2018 Nina Holden Schramm-Loewner evolutions and Liouville quantum gravity

Generalization property of machine learning models in theory 20.11.2018 Fanny Yang and practice

12 Senior Fellow Gilles Brassard.

Awards

Senior Fellow Gilles Brassard was awarded the 2018 Wolf Prize for Physics. Professor Brassard, of the Université de Montréal, shares the prize with Charles H. Bennett, of the IBM Research Center, Yorktown Heights, «for founding and advancing the fields of Quantum Cryptography and Quantum Teleportation». Professor Brassard was at the ETH-ITS for a first stay in 2014 and is back as a Senior Fellow in the Spring of 2019.

13 Fellows’ report Senior Fellows

Sandu Popescu is Professor of Physics at the University mixed states: In quantum mechanics it is possible to have of Bristol. He joined ITS as Senior Fellow on a year-long completely different physical situations which nevertheless Sabbatical, October 2017–November 2018. The activities in cannot be distinguished from one another by any obser- first part of his visit have been reported in the 2017–2018 vation. This is the case of various ensembles of systems Annual Report; here the activities in the second part are prepared in ways corresponding to the same mixed state. described. When information is also given about how these different situations were prepared, we can tell them apart, but as Professor Popescu is a theoretical physicist, whose re- long as we only have the systems themselves, no obser- search centres on conceptual and fundamental problems vation can differentiate them. What Popescu found out is in quantum mechanics. In his view, the fact that so often that a particular, very limited, type of knowledge about one discovers seemingly paradoxical new quantum effects the preparation of physical systems, which apparently is is a signature that a deep and intuitive understanding of completely useless and has been hitherto completely ig- quantum mechanics is still missing. Professor Popescu’s nored, has physical consequences. A consequence of this main goal is to reach such an understanding. A major fo- is the need to introduce in quantum mechanics a new type cus of his research has been quantum entanglement and of quantum state, intermediary between pure and mixed non-locality. More recently he became interested in the states, which were considered until now to be the only two foundations of statistical mechanics and thermodynamics. existing types of quantum states. One of Popescu’s main results during this time is the discovery of a subtle interplay between quantum states, Other results obtained in this period concern quantum re- in particular the so called «mixed states» or «density ference frames and their applications to thermodynamics. matrices», and the knowledge about their preparation. New collaborative projects have also been initiated with Quantum mechanics presents many crucial differences Professor Renato Renner from ETH and Professor Nicolas from the classical world that we know in our daily life. One Gisin and Professor Nicolas Brunner from the University of the most dramatic of them is, arguably, the one related to of Geneva.

14 Senior Fellow Sandu Popescu.

During this second part of his visit at ITS, Professor Popes- Computer scientist Gilles Brassard is professor at the cu gave a seminar on «Conservation laws in quantum me- University of Montreal Université de Montréal and Cana- chanics». In his talk Popescu raised fundamental questions da Research Chair in Quantum Information Science. He about the very meaning of conservation laws in quantum investigates novel uses of quantum mechanics for the mechanics and argued that the standard way of defining enhancement of our information processing capabilities, conservation laws, while perfectly valid as far as it goes, covering the whole range of research from pure theory to misses essential features of nature and has to be revisited actual experiments. and extended. He spent the spring of 2019 as a Senior Fellow at the ETH At the end of his stay at ITS, the Pauli Centre for Theo- Institute for Theoretical Studies and gave a series of lec- retical Studies at ETH invited Professor Popescu to join tures on «Local realistic and non-signalling theories» at as the Erwin Schrödinger Distinguished Visiting Professor the Institute for Theoretical Physics of ETH Zurich. He also 2018–2019. Apart from his research there, Popescu conti- gave several talks in Switzerland during his stay, including nued his very popular lectures series on Quantum Parado- «Could Einstein have been right after all?» at the Università xes, started at ITS, aimed at advanced undergraduate and della Svizzera italiana, «Cryptography in a quantum world» graduate students as well as staff interested in quantum at the Paul Scherrer Institute, and the public lecture «Could mechanics, further contributing to the strong activity ETH Einstein have been right? Quantum theory can be local- has in this area. realistic!» at the Summer School «Solstice of Foundations» on foundations of quantum mechanics held at ETH Zurich in June 2019.

15 Junior Fellows

In her third year as a Junior Fellow, Shoham Letzter col- In November, he posted on arxiv a preprint exploring some laborated with several computer scientists – Omri Ben- aspects of the connection between enumerative geometry, Eliezer from Tel Aviv University, Clément Cannone from more precisely Gromov-Witten theory, and representation Stanford, and Erik Waingarten from Columbia – on a pro- theory, more precisely topological invariants of moduli perty testing project. Property testing is a general name for spaces of quiver representations. This paper includes in a collection of problems where one is given a large object particular a construction of a quiver for a large number of – say a graph, a permutation, or a sequence – and the goal algebraic surfaces, generalizing previously known isolated is to determine (with high probability) whether or not a cer- examples. tain property holds for the graph, by sampling (randomly) a relatively small part of the object. In the aforementioned In April, he posted on arxiv.org a preprint extending the project, the large object in question is a sequence of real known relation between tropical geometry, more precisely numbers, and the property is the containment of an incre- refined floor diagrams, and relative Gromov-Witten inva- asing subsequence of length k. This property is a special riants. The results of this paper give in particular a geo- case of a more general one, of forbidding any given order metric proof of some previously conjectured combinatorial pattern; for example, forbidding the order pattern (132) relations between refined tropical invariants. means that there is no subsequence of three elements, whose first element has the smallest value of the three The main project recently pursued by Pierrick Bousseau and the second has the largest. However, it is known that will appear soon and involves moduli spaces of coherent increasing (and, equivalently, decreasing) order patterns sheaves on the projective plane. The result is a new al- exhibit different behaviour than other order patterns, and gorithm computing topological invariants of these very thus it is interesting to study them separately. Roughly classical objects in complex algebraic geometry. This al- speaking, the group solves the following question, up to a gorithm is of tropical flavour and its proof relies on recent constant factor: suppose that a given sequence of length n advances on spaces of Bridgeland stability conditions, contains many disjoint increasing subsequences of length and on the Kontsevich-Soibelman wall-crossing formula k; how many samples are needed to find an increasing in Donaldson-Thomas theory. A remarkable fact is that this subsequence of order k, with high probability? In order to algorithm was previously known to compute completely obtain the right answer, the group improves on both best different invariants in Gromov-Witten theory. Using know- known lower and upper bounds for this problem; for the ledge on the sheaf side, this gives a proof of Takahashi’s upper bound, they obtain a structural result that could be conjecture in Gromov-Witten theory, a question open since useful in future research. roughly 15 years.

Pierrick Bousseau started as ITS Junior Fellow in Sep- In a current work in progress joint with Longting Wu, post- tember 2018. He has been working on various aspects doc at ETH, Pierrick Bousseau studies some new version of algebraic geometry, including tropical geometry, of the holomorphic anomaly equation for relative Gromov- Gromov-Witten theory, moduli spaces of coherent she- Witten invariants, motivated by the refined holomorphic aves, and connections with representation theory and anomaly equation introduced in theoretical physics for the theoretical physics. refined topological string.

16 Junior Fellow Nina Holden.

In some work in progress joint with Michel van Garrel and Nina Holden arrived at the ITS as a Junior Fellow in Sep- Andrea Brini, he uses some tropical techniques to study tember 2018 after completing her Ph.D. studies at MIT in Gromov-Witten invariants of some non-compact Calabi-Yau spring of the same year. 4-folds. One of her current research projects is about conformal In February, Pierrick Bousseau gave, as part of the Algeb- embedding of random planar maps (RPM). A RPM is a na- raic geometry and moduli seminar at ETH, a minicourse on tural model for a discrete random surface studied in com- tropical geometry, logarithmic geometry and applications binatorics, probability, theoretical physics, and geometry. to Gromov-Witten theory. The lectures were focused on In string theory and conformal field theory, RPM are viewed tropical geometry and logarithmic geometry as practical as discrete versions of the continuum random surfaces tools to study normal crossings compactifications and known as Liouville quantum gravity (LQG) surfaces. In re- degenerations in algebraic geometry. cent years there have been a large interest among proba- bilists in establishing rigorous relationships between these Pierrick Bousseau spoke about his research at various two natural models for random surfaces. In series of works international conferences: in Nantes for a European con- with Xin Sun and other coauthors, she proves that uniformly ference on tropical geometry, in Miami for an annual con- sampled RPM converge to LQG in a conformal sense. ference on mirror symmetry, in Budapest for a conference on moduli spaces, and in Oberwolfach for a workshop on Another line of research is critical LQG. Duplantier, Miller, new directions in tropical geometry. In addition, he spoke and Sheffield (2014) proved that a so-called subcritical LQG at regular research seminars at Hebrew University Jeru- surface can be encoded in terms of a correlated planar salem, University Paris 11, University Paris 6, University of Brownian motion. This encoding is a useful tool for the Texas Austin, and University of California Berkeley. study of LQG, e.g. since Brownian motion is a more studied and well-understood object than LQG, and since it allows for establishing rigorous links between LQG and RPM. Together with Aru, Powell, and Sun, Nina has started to investigate whether one can obtain a similar encoding for the case of critical LQG.

17 In the past year, Nina has also worked on LQG with central from cosmology and from gravitational waves, in the past charge in the interval (1,25) (with Gwynne, Pfeffer, and year, together with Andrina Nicola, he has also derived Remy) and on the communication cost for consensus pro- highly complementary bounds on gravitational physics tocols where the nodes have limited memory (with Fanti, from radiative stability (arXiv:1811.03082) and, together Peres, and Ranade). with his former student Scott Melville, from so-called positivity bounds (arXiv:1904.05874). These are basic theoretical Nina is an active member of the probability group at ETH. constraints any known, well-defined quantum field theory A new activity of the group this year is a weekly pizza lunch needs to satisfy: Radiative stability ensures the theory is at ITS, where one member of the group presents recent indeed predictive and the additional requirements of unita- work or a topic of interest for the rest. In addition, the group rity, locality and causality encoded in positivity bounds are had a reading group (jointly with UZH) about Yang-Mills additional fundamental features that known UV completi- theory in fall. ons of quantum field theories share. In the above papers Johannes was able to show that such bounds together Nina has presented her work at several occasions, inclu- with present-day observational constraints can drastically ding seminars at ETH, IST Austria, Marseille, Paris Nord, improve the constraints on gravitational physics, ruling out Columbia, Shanghai, and Warwick, and a colloquium talk as much as 99% of the previously allowed parameter space at Courant. She has also given conference talks at Institut for deviations from General Relativity. This amounts to a Henri Poincare, Stanford, UCLA, and Fondation des Treilles. significant improvement in our understanding of gravity and In summer she will give a mini-course on Schramm-Lo- the associated new approach will therefore also be key in ewner evolutions in Montreal, participate in a workshop at extracting maximal constricting power from the upcoming Porquerolles, and give a talk at the 12th Seasonal Institute wealth of new experimental data in cosmology in the next of the Math Society of Japan. decade.

Nina has accepted a position as tenured Associate Profes- Within Professor Alexandre Refregier’s cosmology group at sor at Courant Institute for Mathematical Sciences from the IPA, Johannes has also been supervising the master’s fall 2020. She will still be at ETH-ITS in the next academic thesis of Rafaela Gsponer and has been lecturing parts of year 2019/2020. the (MSc in Physics) masters course on «Early Universe Cosmology», related to the fundamental physics leading During his second year at the ETH-ITS, Johannes Noller to the observed cosmic microwave background radiation. established new links with the Institute for Particle Physics Back at the ETH-ITS, together with Junior Fellow Ulrike and Astrophysics (IPA), culminating in the publication of Rieß, Johannes has been organising the Fellows’ seminars. the current state-of-the-art constraints on (and tests of) In the past year, Johannes has also started a number of new General Relativity from observational data sets on the very collaborations, both at ETH Zurich and further afield, and largest scales (arXiv:1811.12928) in collaboration with An- presented his work at a number of workshops/conferences drina Nicola. This forms part of Johannes’ long-term effort and seminars, including at the Max Planck Institute for to establish a program fully integrating observational and Astrophysics, Garching, at the University of Geneva and at theoretical constraints on gravitational physics for the first the European Einstein Toolkit Workshop in Lisbon. time. In addition to incorporating observational constraints

18 Recently, Johannes has been awarded an Ernest Ruther- Grégoire Menet (Université de Bourgogne) she works on a ford Fellowship by the UK-based STFC research council generalization of parts of the theory for irreducible symple- (https://stfc.ukri.org/news/next-generation-of-research- ctic varieties to singular irreducible symplectic orbifolds, leaders-given-funding-boost/) and will be starting this at thus extending previous work of Grégoire Menet. During a the University of Cambridge during the upcoming year. visit to Strasbourg for a talk in the research seminar, Ulrike started a cooperation with Robert Laterveer (IRMA, Stras- In 2018/2019 Ulrike Rieß spent her second year as a Junior bourg), where they study certain phenomena concerning the Fellow at the ETH-ITS. She works in the field of complex Chow ring of irreducible symplectic varieties. algebraic geometry. The focus of her research are irreducible symplectic varieties. This class of varieties occurs In addition, Ulrike is involved in ongoing projects together naturally in the classification of algebraic varieties and has with Giovanni Mongardi (Università di Bologna) and Daniele been subject to vivid research since the 1980’s. Agostini (Humboldt-Universität Berlin) on alternative ap- proaches towards a characterization of base loci of ample As an ongoing project, Ulrike analyzes base loci of ample line bundles on irreducible symplectic varieties. line bundles on irreducible symplectic varieties. The two- dimensional irreducible symplectic varieties are exactly Recently, Ulrike started working with Johannes Schmitt K3 surfaces – a class of surfaces with a very rich geometry (ETH) on tautological points in the moduli spaces of curves. which has been studied in great detail. For K3 surfaces, the Apart from her research projects, Ulrike was supervising behaviour of base loci of ample line bundles is very special: two students during the last year: One student who wrote The occurrence of base divisors for ample line bundles is his Bachelor’s thesis on Riemannian surfaces with her, very well-understood and base loci in higher codimension and a second student who started working on a semester cannot occur. During the last year, Ulrike completed two project in preparation to his Master’s thesis. articles on corresponding statements on higher dimensi- Throughout the year, Ulrike attended several conferences onal irreducible symplectic varieties. The first one gives and promoted her work in invited research talks. a complete characterization of the base divisors of ample line bundles under mild conditions. Ulrike is an organizer for the Japanese-European Sympo- sium on Symplectic Varieties and Moduli spaces. This mee- The second article is a first approach towards base loci ting has an emphasis on irreducible symplectic varieties of higher codimension for ample line bundles on irredu- and the related field of moduli spaces. There are many peo- cible symplectic varieties. While this cannot appear for ple around the world studying these topics – in particular in K3 surfaces, there exist examples already in dimension Europe and in Japan. However, the exchange between these four. Furthermore, this article contains a statement on regions is still rather limited. With the annual meeting, the generic behaviour of base loci. Ulrike is currently con- which recurrently brings together young researchers from ducting research towards a better understanding of these the different regions, exchange and cooperation is encoura- phenomena. ged. The third edition of the symposium took place in Tokyo. Supported by the ETH-ITS, Ulrike could bring this year’s Furthermore, Ulrike is involved in several cooperation pro- edition of the Japanese-European Symposium to Zurich, jects with other international researchers. In a project with where it took place from 3–7 June 2019.

19 Fanny Yang arrived at the ITS in September 2018. In her first year she explored how distribution shifts between different training can be exploited for robust model prediction and shifts between train and test data can be accounted for. An important sufficient desired property for learning systems to perform well under such shifts are invariance properties that allow robustness against (adversarial) worst-case perturbations and interventions. Following this line of thought, Fanny has worked on several collaborations: one paper with researchers at Caltech on correcting label distribution shift using regularized importance weights has been presented at one of the major machine learning conferences (Inter- national Conference for Representation Learning) in New Orleans in May 2019.

In two other projects of the Seminar for Statistics in the D-MATH at ETH Zurich, the goal is to bring together research from invariant causal prediction and modern machine learning methods to (1) achieve robustness using invariance-inducing regularization and (2) using variational auto-encoders to determine non-linear causal effects on a large scale efficiently. She has launched another on-going collaboration with researchers at Stanford University exploring the question of characterizing distributional conditions under which adversarially robust training leads to an improvement or deterioration of generalization.

20 Junior Fellows Ulrike Rieß and Johannes Noller (second row) at the ITS Science Colloquium.

In particular, Fanny showed that invariance-inducing re- serves better to gain understanding for adversarial learning gularizers can increase predictive accuracy for worst-case in practice. For their setting based on one-dimensional spatial transformations (spatial robustness). Evaluated B-spline regression, she characterizes properties of the on these adversarially transformed examples, standard marginal covariate distribution, true underlying function and adversarial training with such regularizers achieves a and model class as well as regime of sample size as a func- relative error reduction of 20% for CIFAR10 with the same tion of these quantities, for which robust training helps or computational budget compared to the corresponding hurts generalization. The hope is that a high-dimensional unregularized variants. This even surpasses handcrafted version of this setting could be transferred to gain insights spatial-equivariant networks. Furthermore, she observed for neural network function classes and shed some light on with collaborators that for SVHN, known to have inherent the regime on which the image data manifold actually lies variance in orientation, that robust training also improves in high-dimensional space. Furthermore, the fact that this standard accuracy on the test set. Her work provides a proof problem is convex reveals a rather fundamental tension that this no-trade-off phenomenon holds for adversarial between robustness and generalization independent of examples from transformation groups. optimization procedures.

In her work with Stanford collaborators, her goal is to un- The aforementioned works have been submitted to ma- derstand the root cause and characteristics of machine jor conferences in May and, together with two other on- learning models which exhibit a lack of robustness against going projects on generalization properties of interpola- l-infinity perturbations. For this purpose, she studies the ting functions, will be extended to involve a more subs- trade-off between standard and robust accuracy in the tantive amount of theoretical results during the rest of the finite data setting for l-infinity perturbation sets based on year. Since September, Fanny has been invited to speak a convex example where the robust classifier is consistent about her work at several conferences and workshops, as with the standard loss minimizer in the infinite data limit. well as institute seminars. Fanny will leave ITS and join This latter property holds for their example which hence the Department of Computer Science ETH Zurich in aligns much better with problems observed for popular January 2020 to start her position as a tenure-track models and real-world image and NLP datasets and thus assistant professor.

21 1 2 3

Outlook Three new Junior Fellows are joining the ETH-ITS in the summer 2019:

1 Yi-Jun Chang received his Ph.D. in Computer Science and Engineering from the University of Michigan in May 2019 under the supervision of Seth Pettie. He is broadly interested in theoretical computer science, with a focus on local distributed graph algorithms. His dissertation addressed fundamental questions on the LOCAL model of distributed computing, such as «How much does random- ness help?» and «Can we solve more problems given more time?». (Photo: Yi-Jun Chang)

2 Stefan Glock received his Ph.D. in mathematics from the University of Birmingham in July 2018 under the supervision of Daniela Kühn and Deryk Osthus. He studies (random) discrete objects, such as graphs and hypergraphs, and investigates their extremal and typical properties. His thesis contains a new proof of the Existence conjecture on combinatorial designs (dating back to a question of Jakob Steiner from 1853) based on combinatorial and probabili- stic methods. (Photo: Stefan Glock)

3 Dominik Schröder received his Ph.D. in mathematics from IST Austria in 2019 under the supervision of László Erdős. His research interests are in probability theory. More specifically, he explored universal spectral properties of large random matrices and quantum spin glasses. He is also interested in applications to the analysis of algorithms in machine learning. (Photo: Dominik Schröder)

22 4 5 6 7 8

Six Senior Fellows are joining the ETH-ITS in the acade- His research interests lie at the interface of mathema- mic year 2019/2020: tical physics, geometry and representation theory, more specifically in quantum field theory, statistical mechanics, 4 Ivan Cherednik is the Austin M. Carr Distinguished geometry and low-dimensional topology, and representa- Professor of Mathematics at the University of North Ca- tion theory of quantum groups. He was a plenary speaker rolina at Chapel Hill. He obtained his Ph.D. from Moscow at the International Congress of Mathematians in 2010. He State University in 1976. Cherednik works in combinatorics, joined the ETH Institute for Theoretical Studies on 1 July representation theory, and mathematical physics. Among 2019. He will teach a course on quantum integrable models his many contributions are his introduction of double af- in the cycle of ETH Nachdiplom Lectures in Mathematics fine Hecke algebras (Cherednik algebras) and his proof of in the spring 2020. (Photo: Nicolai Reshetikhin) Macdonald’s constant term conjecture. He was an invited speaker at the ICM 1998 in Berlin. He arrived on 1 July and 7 Number theorist Kannan Soundararajan is professor of will spend the full academic year 2019/2020 at the ETH mathematics at Stanford University. He obtained his Ph.D. Institute for Theoretical Studies. (Photo: Ivan Cherednik) in 1998 from Princeton University His research is in analytic number theory, especially L-functions and multiplicative 5 Yakov Eliashberg, professor of mathematics at Stan- number theory. He is the recipient of several awards, most ford University, obtained his Ph.D. in 1972 from Leningrad recently the Ostrowski prize in 2011. He is Senior Fellow at University. He is a specialist in symplectic, contact topology the ETH-ITS since 1 July 2019 and will give a Nachdiplom and complex geometry. Among other awards, he received Lecture in the spring 2020. (Photo: Kannan Soundararajan) the Hopf prize in 2013 and the Crafoord Prize in Mathema- tics in 2016. He is a member of the National Academy of 8 Ming Yuan got his Ph.D. in 2004 in Statistics from the Science and gave a plenary talk at the ICM 2006 in Madrid. University of Wisconsin-Madison. He is currently professor He will be at the ETH Institute for Theoretical Studies in of Statistics at Columbia University. His is developing novel the summer 2019 and again in the spring 2020. statistical methods and efficient computational algorithms (Photo: Yakov Eliashberg) to analyse high-dimensional data sets with applications to finance, sparse signal detection and the analysis of gene 6 Nicolai Reshetikhin is professor of mathematics at the expression data. Among other awards he received the 2016 University of California, Berkeley. He obtained his Ph.D. in Leo Breiman Junior Award. He will join the ETH-ITS as a 1984 from the Steklov Mathematical Institute in Leningrad. Senior Fellow in January 2020. (Photo: Bryce Richter)

23 People at the ETH-ITS

Director Giovanni Felder (from 1 June 2019: Rahul Pandharipande)

Coordinator Christina Buchmann (from 1 June 2019: Livia Kürsteiner)

Board of Patrons Martin Haefner, Walter Haefner Foundation Dr. Max Rössler Prof. Dr. Ralph Eichler

Advisory Committee

2013–2017

ETH members Gianni Blatter, Matthias Gaberdiel, Rahul Pandharipande, Tristan Rivière, Angelika Steger, Nicola Spalding* External members Noga Alon (Tel Aviv and Princeton), Luis Alvarez-Gaumé (CERN), Artur Ekert (Oxford), Shafira Goldwasser (MIT and Weizmann Institute), Gerhard Huisken (MFO), Elon Lindenstrauss (Hebrew University), Martin Hairer (Warwick) *replaced by Ueli Maurer in 2015

2017–2019

ETH members Alessio Figalli, Matthias Gaberdiel, Ueli Maurer, Rahul Pandharipande, Manfred Sigrist, Angelika Steger External members Noga Alon (Tel Aviv and Princeton), Robert Brandenberger (McGill), Artur Ekert (Oxford), Gerhard Huisken (MFO), Elon Lindenstrauss (Hebrew University), Martin Hairer (Imperial College), Claire Voisin (Collège de France)

24 Fellows 2014–2019

Senior Fellows

Terry Hwa, UC San Diego 02.2014 – 09.2014 and 04.2015 – 08.2015 Gilles Brassard, Université de Montréal 06.2014 – 12.2014 and 04.2019 – 06.2019 Henryk Iwaniec, Rutgers University 08.2014 – 05.2015 and 06.2016 – 07.2016 Dmitry Chelkak, St. Petersburg 09.2014 – 08.2015 Alex Lubotzky, Hebrew University 02.2015 – 07.2015 and 02.2016 – 08.2016 Adi Shamir, Weizmann Institute 02.2015 – 07.2015 and 02.2016 – 07.2016 Eugene Demler, Harvard University 05.2015 – 06.2015 and 09.2015 – 12.2015 Robert Brandenberger, McGill University 08.2015 – 07.2016 Walter Schachermayer, University of Vienna 08.2015 – 08.2016 Riccardo Barbieri, SNS Pisa 11.2015 – 10.2016 Alexander Balatsky, Nordita and LANL 02.2016 – 04.2016 and 07.2016 – 03.2017 Eitan Tadmor, University of Maryland 08.2016 – 07.2017 Vadim Kaloshin, University of Maryland 09.2016 – 08.2017 Jean-Michel Coron, Université Pierre et Marie Curie 01.2017 – 12.2017 Claire Voisin, Collège de France 01.2017 – 12.2017 Gerhard Huisken, MFO 02.2017 – 09.2017 Leonid Glazman, Yale University 05.2017 – 12.2017 and 05.2018 – 08.2018 Sandu Popescu, University of Bristol 10.2017 – 12.2017 and 03.2018 – 12.2018 Yakov Eliashberg, Stanford University 06.2019 – 09.2019 and 03.2020 – 06.2020 Ivan Cherednik, University of North Carolina at Chapel Hill 07.2019 – 06.2020 Nicolai Reshetikhin, UC Berkeley 07.2019 – 06.2020 Kannan Soundararajan, Stanford University 09.2019 – 07.2020 Ming Yuan, Columbia University 01.2020 – 08.2020

Junior Fellows (with current affiliation of former Junior Fellows)

Emily Clader, University of San Francisco 09.2014 – 07.2016 Zur Luria, Azrieli College of Engineering 09.2014 – 09.2017 Alessandro Carlotto, ETH Zurich 09.2015 – 08.2016 Maria Colombo, EPF Lausanne 09.2015 – 08.2018 Lavinia Heisenberg, ETH Zurich 09.2015 – 09.2018 Titus Lupu, CNRS, U. Paris 11, Orsay 09.2015 – 12.2017 Aline Ramires, ICTP-SAIFR, Sao Paulo 09.2015 – 08.2018 Ran Tessler, Weizmann Institute 09.2015 – 10.2018 Shoham Letzter 09.2016 – 12.2019 William Sawin, Columbia University 09.2016 – 07.2018 Ulrike Rieß 09.2017 – 08.2020 Johannes Noller 09.2017 – 03.2020 Pierrick Bousseau 09.2018 – 08.2021 Nina Holden 09.2018 – 08.2021 Fanny Yang 09.2018 – 09.2019 Yi-Jun Chang 07.2019 – 07.2022 Stefan Glock 09.2019 – 08.2022 Dominik Schröder 09.2019 – 08.2022

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Publisher: ETH Institute for Theoretical Studies Editor: Giovanni Felder Photos: Christina Buchmann (Titel, S. 4, 6, 8, 10, 11, 13, 15, 21), Nina Holden (S. 17) Layout: grafikvonfrauschubert Print: ETH Druckzentrum