Section 9. Dynamics

Topological and symbolic dynamics. Smooth dynamical systems, including those derived from ordinary differential equations. Hamiltonian systems and dynamical systems of geometric origin. One-dimensional, holomorphic and arithmetic dynamics. Dynamics on moduli spaces. Ergodic theory, including applications to combinatorics and combinatorial number theory. Actions of discrete groups and rigidity theory. Homogenous dynamics, including applications to number theory. Infinite dimensional dynamical systems and partial differential equations.
Miklos Abert

Renyi Institute, Hungary

Miklos Abert is a Senior Researcher at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. His research interests include measured and asymptotic group theory, in particular, spectral theory of graphs and groups, weak sampling convergence of graphs and locally symmetric spaces, stochastic processes on groups, rank gradient, homology growth, and invariant random subgroups.
Aaron Brown

Northwestern University, USA

Aaron Brown is an Associate Professor of Mathematics at Northwestern University in Evanston, Illinois.

His research interests include smooth dynamical systems and ergodic theory with application to group actions on manifolds.

Jon Chaika

University of Utah, USA

Joint lecture with Barak Weiss

Jon Chaika is an Associate Professor of Mathematics at the University of Utah. He works in ergodic theory and is particularly interested in systems related to flows on translation surfaces.
Mark Demers

Fairfield University, USA

Mark Demers is a Professor of Mathematics at Fairfield University in Connecticut.

His research interests include measure-theoretic and statistical properties of dynamical systems exhibiting some degree of hyperbolicity. He has worked extensively on open systems and on mathematical billiards, with a particular emphasis on constructing anisotropic Banach spaces for associated transfer operators. In addition to postdoctoral positions at Georgia Tech and MSRI Berkeley, he has held several visiting positions, including ENS Paris, the University of Rome, the University of Toulon, and SNS Pisa.

Romain Dujardin

Sorbonne Universite, France

Romain Dujardin is a Professor of Mathematics at Sorbonne Université.

He previously held appointments in Université Paris Diderot, École Polytechnique and Université Paris-Est.

His main field of research is holomorphic dynamics in one and several complex variables, with notable contributions to 2-dimensional polynomial dynamics and bifurcation theory.

His work also features interactions with geometric measure theory, arithmetic dynamics and probability.

Semyon Dyatlov

Massachusetts Institute of Technology, USA

Also in section 10

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.

David Fisher

Indiana University Bloomington, USA

Jointly in sections 5, 6

David Fisher is the Ruth N Halls Distin­guished Professor of Mathematics at Indiana University Bloomington. His interests center on rigidity in geometry and dynamics and include actions of large groups, large scale geometry and structure of locally symmetric spaces. He is particularly well known for his work in the Zimmer program, particularly his solution of many cases Zimmer’s conjecture with Brown and Hurtado. He is also known for his work with Eskin and Whyte on quasi-­isometries of solvable groups and his work with Bader, Miller and Stover on totally geodesic manifolds and arithmeticity. He is a Fellow of the American Mathematical Society and has held two fellowships from the Simons Foun­dation, a Fellowship at the Radcliffe Institute at Harvard, a Miller Profes­sorship at Berkeley and has been a member of the School of Mathematics at the Institute for Advanced Study.
Mariusz Lemanczyk

University Nicolaus Copernicus, Poland

Mariusz Lemańczyk is a Professor at the Faculty of Mathematics and Computer Science of Nicolaus Copernicus University in Toruń (Poland). His interests include ergodic theory and dynamical systems, in particular, theory of joinings, spectral theory, systems of probabilistic origin, topological dynamics, parabolic systems, and information theory.

Over the past decade, his interests have shifted towards interactions between ergodic theory and analytic number theory, and he published several works on Sarnak’s conjecture on Moebius disjointness. He received the Kuratowski Prize in 1987 and the Banach Prize in 1998 of the Polish Mathematical Society. He was a holder of the Jean-Morlet Chair (CIRM, Marseille) in 2016. Since 2006 he has been an editor of Studia Mathematica.

Amir Mohammadi

University of California, San Diego, USA

Also in section 7

Amir Mohammadi is a Professor of Mathematics at The University of California, San Diego.

His research interests include Lie groups and ergodic theory,in particular, he is interested in the interplay between dynamical systems and other areas of mathematics, such as number theory and geometry. He is a recipient of the Alfred P. Sloan Research Fellowship and the von Neumann Fellowship.

Michela Procesi

University of Roma Tre, Italy

Michela Procesi is a professor of Mathematics at the Department of Mathematics and Physics of the University of Roma Tre.

Her main research interests are in nonlinear analysis and dynamical systems. In her undergraduate thesis she contributed to the discovery of what is now known as the Degasperis Procesi equation. Her current research focuses on KAM theory for PDEs and Normal Forms, in particular,the search for special stable and unstable global solutions for nonlinear Hamiltonian PDEs on tori. Typically the main difficulties arise from the presence of resonances and small divisors. From 2012 to 2018 she has been the principal investigator of the ERC Starting Grant HamPDEs.

Richard Schwartz

Brown University, USA

Survey lecture on billiards

Jointly in sections 5, 11

Richard Schwartz is the Chancellor’s Professor of Mathematics in the Department of Mathematics at Brown University. His research interests lie in geometry and dynamical systems, especially in the computer-assisted exploration of these topics. In particular, he is known for the proof of quasi-isometric rigidity of rank one lattices, the proof of the Goldman-Parker Conjecture about complex hyperbolic ideal triangle groups, the solution of the Moser-Neumann problem about unbounded orbits of outer billiards, and the solution of Thomson’s 5-electron problem. He was an Invited Speaker at the 2002 International Congress of Mathematicians inBeijing, and has held Sloan, Guggenheim, Clay, and Simons Fellowships. Hisresearch has long been supported by the U.S. National Science Foundation.

His other interests include computer programming, writing children’s books, cycling, yoga, tennis, weight-lifting, and spending time with his family.

Joseph H. Silverman

Brown University, USA

Survey lecture on arithmetic dynamics

Also in section 3

Joseph H. Silverman is a Professor of Mathematics at Brown University.

His interests include elliptic curves, arithmetic geometry, arithmetic dynamics, and cryptography.

In particular, he is known for his numerous books on these subjects, and for being one of the founders of the field of arithmetic dynamics, a subject in which number theory and dynamical systems on algebraic varieties are intertwined. He is also a co-inventor, with Jeffrey Hoffstein and Jill Pipher, of NTRU, the first practical lattice-based public key cryptosystem.

He is a Fellow of the American Mathematical Society and a recipient of the AMS Steele prize.

Iskander Taimanov

Novosibirsk State University, Russia

Also in section 5

Iskander Taimanov is a Principal Research Fellow at Sobolev Institute of Mathematics of Siberian Branch of Russian Academy of Sciences and the Head of the chair of geometry and topology in Novosibirsk State University.

His interests include geometry, topology, and integrable systems. In particular, his results concern topological obstructions to integrability of geodesic flows, the existence theorems of closed magnetic geodesics, and applications of integrable systems to surface theory. He is a member of the Russian Academy of Sciences.

Corinna Ulcigrai

University of Zurich, Switzerland

Corinna Ulcigrai is a Full Professor in Pure Mathematics at the Institute for Mathematics of the University of Zurich. She grew up in Italy, where she studied at Scuola Normale Superiore, received her Ph.D. from Princeton University and was a Professor at the University of Bristol.

Her research interests are mainly in dynamical systems and ergodic theory, with a particular focus on parabolic dynamics, or systems that display a «slow» form of chaotic evolution. In particular, she is known for her works motivated by Arnol’d conjecture on the Novikov model, classifying chaotic properties of locally Hamiltonian flows on surfaces of higher genus. She is currently a member of the Italian ’Accademia Nazionale delle Scienze, detta dei XL’ and her achievements have been recognized by several awards, including the European Mathematical Society Prize, an ERC Starting Grant, the LMS Whitehead Prize and recently the 9th Brin Prize for Dynamical Systems.

Barak Weiss

Tel Aviv University, Israel

Joint lecture with Jon Chaika

Barak Weiss is a Professor of Mathematics at Tel Aviv University.

He completed his doctoral dissertation in Jerusalem under the supervision of Hillel Furstenberg. After a postdoc at SUNY Stony Brook, he held a position at Ben Gurion University before moving to Tel Aviv in 2013. He studies dynamics of Lie group actions, focusing on dynamics on homogeneous spaces and moduli spaces of translation surfaces. He is also interested in applications to Diophantine approximation, rational billiards, geometry of numbers, and large scale geometry of discrete sets.

Peter Zograf

St. Petersburg Department of the Steklov Mathematical Institute and St. Petersburg University, Russia

Jointly in sections 4, 6

Peter Zograf is a Leading Researcher at St.Petersburg Department of the Steklov Mathematical Institute and a Chief Researcher at the Chebyshev Laboratory of St.Petersburg University. His research interests include mathematical physics, geometry of moduli spaces, and enumerative combinatorics.
Thu Sep 16 2021 18:10:46 GMT+0300 (Moscow Standard Time)