Section 10. Partial Differential Equations

Solvability, regularity, stability and other qualitative and quantitative properties of linear and non-linear equations and systems. Asymptotics. Spectral theory, scattering, inverse problems, deterministic and stochastic control theory, stochastic differential equations. Nonlocal equations, free boundary problems, calculus of variations, kinetic equations. Optimal transportation. Homogenization and multi-scale problems. Approximate solutions and perturbation problems. Relations to many applications.
Keith Ball

University of Warwick, UK

Survey lecture on convex analysis and its connections to other areas of mathematics

Jointly in sections 8, 12, 13

Keith Ball is a professor at the University of Warwick. His interests are in high-dimensional and discrete geometry, information theory and (more recently) analytic number theory. He was scientific director of the International Centre for Mathematical Sciences in Edinburgh from 2010 to 2014 and holds honorary professorships from the University of Edinburgh and Heriot-Watt University.

Towards the end of his tenure at ICMS he was chair of ERCOM, the umbrella organisation for European mathematics research centres.

He is a Fellow of the Royal Society of London and the Royal Society of Edinburgh and was on the governing council of the Royal Society during 2018-2019.

Among other things his research demonstrated that the central limit theorem of probability is driven by an analogue of the second law of thermodynamics: namely, that entropy increases along the central limit process. He is also known for a popular book on mathematics entitled «Strange Curves, Counting Rabbits...»

Richard Bamler

UC Berkeley, USA

Jointly in sections 5, 6

Richard Bamler is a Professor at the Department of Mathematics at UC Berkeley.

He received his undergraduate education at the University of Munich, where he was mentored by Prof. Bernhard Leeb. In 2011, he obtained his Ph.D. under the supervision of Prof. Gang Tian at Princeton, and between 2011-2014 he was a postdoc at Stanford University.

His field of research is geometric analysis and he is particularly interested in Ricci flows.

Some of his work --- in part with Bruce Kleiner --- is aimed at studying geometric-analytic aspects of Ricci flows (with surgery) in dimension 3. This has led to a number of topological applications, such as the resolution of the Generalized Smale Conjecture. More recently, he has devised a new theory that allows the study of singularity formation in higher dimensional Ricci flows.

Pierre Cardaliaguet

Paris Dauphine University, France

Joint lecture with François-Delarue

Also in section 12

Pierre Cardaliaguet is a Professor of Mathematics at Paris Dauphine PSL University. His research interests include partial differential equations, calculus of variations, optimal control and games theory.
François Delarue

Université Côte d’Azur, Nice, France

Joint lecture with Pierre Cardaliaguet

Also in section 12

François-Delarue is a Professor of Mathematics at Laboratoire Jean-Alexandre Dieudonné of Université Côte d’Azur in Nice, France. His interests include probability theory, stochastic analysis and connections with partial differential equations. He has been working for several years on mean field models and on the related theory of mean field games. Together with René Carmona, he is the winner of the 2020 AMS Doob prize for the two-volume book they wrote on the subject. He was a co-editor in chief of the Annals of Applied Probability from 2019 to 2021. He is also interested in the rough path theory.
Semyon Dyatlov

Massachusetts Institute of Technology, USA

Also in section 9

Semyon Dyatlov is an Associate Professor of Mathematics at the Massachusetts Institute of Technology.

His interests include microlocal analysis and its applications to mathematical physics (quantum chaos, scattering theory) and to dynamical systems. He is known in particular for introducing the Fractal Uncertainty Principle, a statement in harmonic analysis which applies to problems in quantum chaos, and for his work on dynamical zeta functions. He received the IAMP Early Career Award in 2018.

Irene Fonseca

Carnegie Mellon University, USA

Also in section 18

Irene Fonseca is the Kavčić-Moura University Professor of Mathematics and is the Director of the Center for Nonlinear Analysis of the Mathematical Sciences Department at Carnegie Mellon University in Pittsburgh, USA.

Irene Fonseca is a Fellow of the American Mathematical Society (AMS), and a Fellow of the Society for Industrial and Applied Mathematics (SIAM). She was SIAM President in 2013 and 2014. She is a Grand Officer of the Military Order of Saint James of the Sword (Grande Oficial da Ordem Militar de Sant’Iago da Espada, Portuguese Decoration). She serves in 20 Editorial Boards, including Advances in Calculus of Variations, Archive for Rational Mechanics and Analysis, Communications of the American Mathematical Society (CAMS), ESAIM:COCV (SMAI), Journal of Nonlinear Science, M3AS, and SIAM Journal on Mathematical Analysis.

Irene Fonseca’s main contributions have been on the variational study of ferroelectric and magnetic materials, composites, thin structures, phase transitions, and on the mathematical analysis of image segmentation, denoising, detexturing, registration and recolorization in computer vision. Her research program continues to explore modern methods in the calculus of variations motivated by problems emerging from materials science and imaging science.

Rupert Frank

LMU Munich/ CalTech, Germany/ USA

Rupert Frank is working on problems in analysis, calculus of variations and mathematical physics. He received his PhD degree in 2007 from the Royal Institute of Technology in Stockholm under the supervision of Ari Laptev. After a post-doctoral stay and an assistant professorship at Princeton, in 2013 he became a Professor at Caltech and in 2016 at LMU Munich.
Peter Hintz

ETH Zürich, Switzerland

Survey lecture on recent progress in general relativity

Joint lecture with Gustav Holzegel

Jointly in sections 5, 11

Peter Hintz is a Professor of Mathematics and Physics at the Department of Mathematics at ETH Zürich. His research focuses on partial differential equations arising in the theory of general relativity. In particular, he is known for his proof, joint with András Vasy, of the global nonlinear stability of rotating Kerr-de Sitter black holes. His awards include a Clay Research Fellowship and a Sloan Research Fellowship. His research has also been featured in popular science media including Quanta Magazine, Live Science, and New Scientist.
Gustav Holzegel

University of Münster, Germany

Survey lecture on recent progress in general relativity

Joint lecture with Peter Hintz

Jointly in sections 5, 11

Gustav Holzegel is a member of the Institute of Mathematics in Muenster (Germany), where he holds a Humboldt Professorship. He is also affiliated with

Imperial College London, where he has been a member of staff since 2012. Holzegel’s main interests are the partial differential equations of general relativity.

He is mainly known for his work on black holes and spacetimes with a negative cosmological constant.

His notable distinctions include an ERC Consolidator Grant (2017) and the Whitehead Prize (2016).

Alexandru Ionescu

Princeton University, USA

Alexandru Ionescu is a Professor of Mathematics at Princeton University. His main interests include partial differential equations, fluid mechanics, general relativity, and harmonic analysis. His recent work is on stability properties of solutions of various evolution models, such as the water waves system, the Euler equations in 2D, and the Einstein equations of general relativity. He is a Fellow of the American Mathematical Society, a former Sloan Research Fellow, and a former Packard Fellow.
Bruce Kleiner

NYU, USA

Developments in 3-d Ricci flow since Perelman

Jointly in sections 5, 6, 8

Bruce Kleiner is a Silver Professor of mathematics as well as the chair of the mathematics department at the Courant Institute of Mathematical Sciences at New York University. His interests include geometric analysis (especially geometric flows), analysis on metric spaces, and geometric group theory. He has given an invited sectional lecture at the 2006 ICM and invited plenary lectures at the annual meeting of the AMS and the International Congress of Mathematical Physics. He received the National Academy of Sciences Award for Scientific Reviewing and has been a Clay Institute Scholar and a Sloan fellow.
Mathieu Lewin

Paris Dauphine University, France

Mathieu Lewinis a CNRS Research Director at the University of Paris-Dauphine. His research focuses on the application of variational and spectral methods to quantum physics and chemistry. He won an EMS Prize in 2012 and was awarded successively a Starting and a Consolidator grant from the European Research Council.
Kenji Nakanishi

Kyoto University, Japan

Kenji Nakanishi is a Professor at the Research Institute for Mathematical Sciences, Kyoto University. He has been studying partial differential equations, mainly of nonlinear dispersive waves. In recent years, the ultimate goal of his research is to grasp the entire picture of all general solutions for some equations. He is particularly interested in understanding and describing possible transitions in time among various types of solutions, as well as in the intermediate or threshold solutions in the phase space.
Alexander I. Nazarov

Saint Petersburg State University, Russia

Also in section 12

Alexander I. Nazarov graduated from Leningrad State University in 1985 and defended his Ph.D. thesis in 1988 under the supervision of Nina N. Uraltseva. Now he is a Leading Researcher in the Laboratory of Mathematical Physics, St. Petersburg Branch of Steklov Mathematical Institute, and a Full Professor (part-time) in the Department of Mathematical Physics, St. Petersburg State University.

The main fields of his research are elliptic and parabolic PDEs, calculus of variations, spectral theory, their applications in probability and statistics, and history of mathematics. He is the editor and one of the authors of the monograph «Mathematical Petersburg». His other interests include giveaway checkers. He is a winner of many tournaments and a holder of the title ‘Master of Sports of Russia’.

Galina Perelman

Paris-Est Créteil University, France

Galina Perelman is a Professor at the Department of Mathematics of Paris-Est-Créteil University. Her research centers on partial differential equations, mainly on nonlinear dispersive equations, and aims in particular at understanding qualitative properties of solutions, including long time asymptotics, dynamics of coherent structures, formation of singularities.
Charles Smart

Yale University, USA

Charles Smart is a Professor of Mathematics at Yale University. He wrote his Ph.D. in 2010 at UC Berkeley under the supervision of Lawrence C Evans and Leo Harrington. He has held positions at Courant, MIT, Cornell, and the University of Chicago. He was awarded a Sloan Fellowship in 2014.

Charles Smart is interested in analysis, probability, and mathematical physics. He is known for his work on stochastic homogenization, the Abelian sandpile, and Anderson localization.

Gabriella Tarantello

University of Rome Tor Vergata, Italy

Gabriella Tarantello is a Full Professor at the Department of Mathematics of the Universita’ di Roma «Tor Vergata» in Italy. Her research interests include nonlinear differential problems of interest in physics and geometry. In particular, she has contributed to the study of self-dual gauge field vortices, surfaces with conical singularities, minimal immersions and the Donaldson functional in Teichmuller theory, as well as related analytical, variational and topological aspects.
Vlad Vicol

Courant Institute of Mathematical Sciences, New York University, USA

Also in section 18

Vlad Vicol is a Professor of Mathematics at the Courant Institute of Mathematical Sciences, New York University. He received his Ph.D. in 2010 from the University of Southern California, under the supervision of Igor Kukavica. His research focuses on the analysis of partial differential equations arising in fluid dynamics, with an emphasis on problems motivated by hydrodynamic turbulence. He was awarded an Alfred P Sloan Research Fellowship (2015), the MCA Prize by the Mathematical Congress of the Americas (2017), and shared a Clay Research Award (2019).
Lu Wang

California Institute of Technology, USA

Also in section 5

Lu Wang is a Professor of Mathematics at the Department of Mathematics of Yale University.

Her interests include geometric flows (mean curvature flow and Ricci flow) and related topics, including minimal surfaces and geometric topology. She was awarded a Sloan Fellowship in 2016.

Zhifei Zhang

Peking University, China

Zhifei Zhang is a Professor of Mathematics at the School of Mathematical Sciences, Peking University.

His research interests include the interface problem of the incompressible fluids, mathematical theory of the liquid crystal, hydrodynamic stability at high Reynolds number, and other topics such as the well-posedness of the hydrodynamic equations.

He was awarded the National Science Fund for Distinguished Young Scholars in 2014.

Tue Oct 05 2021 16:06:05 GMT+0300 (Moscow Standard Time)