Plenary Talks

Institute of Science and Technology Austria

Tim Browning is Professor at the Institute of Science and Technology Austria (Vienna).

His work lies at the interface of analytic number theory and algebraic geometry, with recent spectacular results including proving that the Hasse principle holds for random Fano hypersurfaces (with Le Boudec and Sawin), and developing a geometric version of the classical Hardy-Littlewood circle method (with Sawin). Browning is the recipient of both the LMS Whitehead prize and the Phillip Leverhulme Prize, as well as a twice recipient of the Ferran Sunyer i Balaguer Prize for outstanding writing in a mathematical monograph.

Browning obtained his PhD at Oxford in 2002, under the supervision of Prof. Roger Heath-Brown. After postdocs at Orsay and Oxford, Browning joined the University of Bristol in 2005, where he was rapidly promoted to full professor in 2012. He moved to ISTA in 2018, which is Austria's premier research institute.

Tuesday 4th April 12:20-13:20: Integer points on cubic surfaces and a new heuristic -- LMS Lecture (Chair: Ulrike Tillmann)

Humans have been thinking about polynomial equations over the integers for millennia. Despite this, their secrets are tightly locked up and it is hard to know what to expect, even in simple looking cases. In this talk I’ll discuss recent efforts to understand the frequency of integer zeros of cubic polynomials that define affine cubic surfaces, via a new circle method heuristic. This is joint work with Florian Wilsch.

Massachusetts Institute of Technology

Pavel Etingof is Professor of Mathematics at MIT and the Chief Research Advisor of the MIT PRIMES program.

Etingof's research interests focus on the intersection between representation theory and mathematical physics.  He has co-authored over 220 journal articles and  8 books, and has collaborated with over 100 researchers across multiple disciplines of pure mathematics. He serves as chief editor of the Journal of the AMS and of Selecta Math. Awards include the Clay Mathematics Institute Prize fellowship, the Robert E. Collins Distinguished Scholar in the Mathematics Department, Frank E. Perkins Award for excellence in graduate advising. He is a Fellow of the AMS and a Fellow of the American Academy of Arts and Sciences.

Etingof received the M.S. in applied mathematics from the Moscow Oil & Gas Institute in 1989, and the Ph.D. in mathematics from Yale University in 1994, advised by Igor Frenkel. He went to Harvard as a Benjamin Peirce Assistant Professor in 1994, and joined the MIT mathematics faculty as assistant professor in 1998. He has been a professor at MIT since 2005.

In 2010, Etingof launched the Math Department's MIT PRIMES program with Dr. Slava Gerovitch. This is a free outreach program for high school students with a particular focus on increasing the representation of women and under-served minorities in mathematics research. In 2020, the AMS announced that the MIT Mathematics Department had been selected for the Award for Exemplary Program or Achievement in a Mathematics Department for its PRIMES Program.

Wednesday 5th April 12:00-13:00: Lie theory in tensor categories with applications to modular representation theory -- ICMS Distinguished Visitor Lecture (Chair: Sarah Rees)

Université Paris-Est-Créteil

Galina Perelman is Professor at the Université Paris-Est-Créteil, France.  

Her research interests focus on the asymptotic analysis of solutions to nonlinear dispersive partial differential equations with possible formation of singularities. She obtained fundamental results in the study of nonlinear Schrödinger equations, such as the construction of radial solutions for the focusing cubic NLS that blow up along contracting spheres, and the analysis of blow-up for equivariant critical Schrödinger maps. Recently she proved outstanding results on globally defined solutions for the derivative non-linear Schrödinger equations with general Cauchy data in the energy space (with H. Bahouri). She was an invited speaker at the ICM 2022.

Perelman obtained her PhD at the University of Saint Petersburg in 1993, and her habilitation thesis at the University Paris-Sud in 2004. After postdocs at the University of Paris-Sud and the University of Reims, she was a CNRS researcher and in 2010 she became Professor at the Université Paris-Est-Créteil.


Thursday 6th April 12:00-13:00: Nonlinear dispersive equations: interplay between PDE and integrable systems approaches (Chair: Kirill Cherednichenko)

The last 50 years have witnessed spectacular advances in the theory of nonlinear dispersive PDEs. To some extent, these advances were initiated and stimulated by the discovery and study of completely integrable models including the one-dimensional cubic NLS, derivative NLS, KdV and mKdV equations, for which the inverse scattering theory leads, in some cases, to a deep and detailed understanding of the dynamics. The theory of integrable PDEs is still a very active field of research and an important source of predictions of what can be expected for non-integrable equations.

 In this talk I will discuss some recent developments concerning well-posedness of integrable PDEs in Sobolev spaces, using as a model mainly the derivative NLS equation. 

University of Toronto

A specialist in probability theory, stochastic processes and partial differential equations, Jeremy Quastel has been at the University of Toronto since 1998. His research is on the large scale behaviour of interacting particle systems and stochastic partial differential equations, recently concentrating on the Kardar-Parisi-Zhang universality class.

He was a Sloan Fellow (1996-98), invited session speaker at the International Congress of Mathematicians (2010), gave the Current Developments in Mathematics (2011) and St. Flour lectures (2012), was plenary speaker at the International Congress of Mathematical Physics (2012), Fellow of the Royal Society of Canada (2016) and of the Royal Society (2021), and won the CRM-Fields-PIMS prize (2018) and the Jeffery-Williams Prize of the Canadian Mathematical Society (2019).

Wednesday 5th April 17:15-18:15: Integrable fluctuations in random growth (Chair: Antal Jarai)

In the past two decades there has been considerable progress on understanding the asymptotic fluctuations of random growing interfaces. These are often described by the Kardar-Parisi-Zhang equation, but this is a just one member of a huge universality class, and we have learned that special discretizations can have a high degree of solvability.  In the long-time, large-space limit, there is a new universal fixed point with unexpected connections to classical integrable systems. The talk will be a gentle introduction to these developments.

Trinity College Dublin

Katrin Wendland is Professor in the School of Mathematics at Trinity College Dublin.

Her main research interests are at the interface of complex algebraic geometry, differential geometry and analysis, motivated by conformal field theory, quantum field theory and string theory. In particular she studies the moduli space of two dimensional unitary conformal field theories with central charge c=6 and N=(4,4) supersymmetry, whose classical limits are described by K3 surfaces. Recent research projects deal with the algebraic geometry of elliptically fibered Calabi-Yau varieties and with topological field theories.

She received her PhD in theoretical physics in Werner Nahm's group at the University of Bonn, in 2000, and subsequently worked at UNC Chapel Hill, Warwick, Augsburg and Freiburg before moving to Dublin in 2022. She was an invited sectional speaker in Mathematical Physics at the International Congress of Mathematicians 2010 in Hyderabad and in 2009 she was awarded the Medaille für besondere Verdienste um Bayern in einem vereinten Europa by the Bavarian Minister for Federal and European Affairs.

She is an editor in chief of the Springer Monographs in Mathematics, and an editor of De Gruyter Expositions in Mathematics, the Journal de l’École polytechnique - Mathématiques, and the Annales Henri Poincaré. She is a member of EWM and was on the Committee Women in Mathematics of the EMS, 2014-2021. 

Monday 3rd April 13:30-14:30: On generic features in geometry (Chair: Gregory Sankaran)

In this talk, we will explain how generic features in geometry can provide a convenient path to the interpretation of geometric invariants in terms of 'counting'. We will showcase a number of examples, in particular the 'counting' of certain types of cohomology classes, also known as 'BPS states', on some complex surfaces.