Section 5. Geometry

Local and global differential geometry. Geometric partial differential equations and geometric flows. Geometric structures on manifolds. Riemannian and metric geometry. Kähler geometry. Geometric aspects of group theory. Symplectic and contact manifolds. Convex geometry. Discrete geometry.
Richard Bamler

UC Berkeley, USA

Jointly in sections 6, 10

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.

Robert Berman

Chalmers University of Technology, Sweden

Robert Berman is, since 2013, a Professor at the Department of Mathematical Sciences, at Chalmers University of Technology in Sweden. His research is centered around analytical aspects of complex algebraic and differential geometry, in particular the study of canonical metrics on complex algebraic varieties.

In the last years his research has focused on connections between these fields and probability, statistical mechanics and mathematical physics, as well as convex geometry and analysis.

In broad terms his research concerns, among other things, the problem of describing the emergence of coherent structures in large scale complex systems from the geometric and analytic point of view.

Danny Calegari

University of Chicago, USA

Danny Calegari is a Professor of Mathematics at the University of Chicago.

He is interested in geometry, topology and dynamics and their interaction, especially in low dimensions. He has done research on taut foliations, Kleinian groups, stable commutator length, random groups, and (most recently) has become interested in the connection between `big’ mapping class groups and complex dynamics.

He was one of the recipients of the 2009 Clay Research Award for his resolution (joint with David Gabai) of Marden’s Tameness Conjecture and the Ahlfors Measure Conjecture.

Kai Cieliebak

Universitat Augsburg, Germany

Also in section 6

Kai Cieliebak is a Professor of Mathematics at the Mathematical Institute of University of Augsburg, Germany.

His research area is symplectic geometry, in particular the theory of holomorphic curves and its applications to questions in contact and symplectic topology and Hamiltonian dynamics. He is mostly known for his contributions to the development of symplectic homology and Rabinowitz Floer homology. His other interests include interactions of symplectic geometry with adjacent fields such as Stein manifolds, string topology, celestial mechanics, and Chern-Simons theory.

David Fisher

Indiana University Bloomington, USA

Jointly in sections 6, 9

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.
Penka Georgieva

Sorbonne Université, France

Penka Georgieva is a Professor of Mathematics at the Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université.

Her work lies within the fields of Gromov-Witten theory, symplectic topology, and enumerative geometry and their interactions with mathematical physics. She has obtained important foundational results in real Gromov-Witten theory and developed effective methods for the computation of the corresponding invariants.

Peter Hintz

ETH Zürich, Switzerland

Survey lecture on recent progress in general relativity

Joint lecture with Gustav Holzegel

Jointly in sections 10, 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 10, 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).

Hiroshi Iritani

Kyoto University, Japan

Hiroshi Iritani is a Professor of Mathematics at the Department of Mathematics of Kyoto University.

His research interests include algebraic geometry, symplectic geometry, and mathematical physics. He has been working on mirror symmetry and Gromov-Witten theory and has introduced the Gamma-integral structure in quantum cohomology. He is a member of the Mathematical Society of Japan.

Bruce Kleiner

NYU, USA

Developments in 3-d Ricci flow since Perelman

Jointly in sections 6, 8, 10

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.
Chi Li

Rutgers University, USA

Also in section 4

Chi Li is an associate professor at the Department of Mathematics of Rutgers University — New Brunswick.

He worked at Purdue University between 2015-2020. His interests include canonical metrics in Kähler geometry, stability theory of algebraic varieties, and pluripotential theory.

Gang Liu

East China Normal University, China

Gang Liu is a professor at East China Normal University.

His research is in complex geometry and geometric analysis. Currently, he is interested in the interaction between Gromov-Hausdorff convergence theory and complex geometry.

Kathryn Mann

Cornell University, USA

Also in section 6

Kathryn Mann is an assistant professor of mathematics at Cornell University, working in geometric topology, geometric group theory, and low-dimensional dynamics. Her work centers on groups acting on manifolds, especially the study of rigidity and flexibility of geometrically motivated examples in low regularity.

She is a recent recipient of the Kamil Duszenko award in geometric group theory, the Joan and Joseph Birman research prize in topology, the Mary Ellen Rudin Award for young researchers as well as an NSF career award and a Sloan foundation fellowship.

Mark McLean

University of New York at Stony Brook, USA

Also in section 6

Mark McLean is an associate professor of mathematics at Stony Brook University, New York State, USA.

He is a symplectic geometer with an interest in algebraic geometry. An important tool that he has used to understand these two subject areas is pseudoholomorphic curve theory, which includes Gromov-Witten theory and Hamiltonian Floer cohomology. Recently he proved that birational Calabi-Yau manifolds have the same small quantum cohomology algebras using Floer theoretic techniques.

Richard Schwartz

Brown University, USA

Survey lecture on billiards

Jointly in sections 9, 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.

Iskander Taimanov

Novosibirsk State University, Russia

Also in section 9

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.

Lu Wang

California Institute of Technology, USA

Also in section 10

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.

Robert Young

Courant Institute, NYU, USA

Also in section 8

Robert Young is a Professor of Mathematics at the Courant Institute of Mathematical Sciences at New York University.

He obtained his Ph.D. from the University of Chicago, was a postdoc at the Institut des Hautes Études Scientifiques and an Assistant Professor at the University of Toronto.

He is interested in the relationship between geometry and complexity, in particular in geometric group theory, geometric measure theory, and quantitative geometry.

Xin Zhou

Cornell University, USA

Xin Zhouis an Associate Professor in the Department of Mathematics at Cornell University and an Associate Professor (on leave) in the Department of Mathematics at University of California Santa Barbara.

His research interests include differential geometry, calculus of variations, and general relativity. His recent work has resolved the Multiplicity One conjecture in the min-max theory of minimal surfaces. He has also established the existence theory of constant mean curvature surfaces and the existence theory of minimal surfaces with free boundary.

Xiaohua Zhu

Peking University, China

Xiaohua Zhu is a Professor of Mathematics at the School of Mathematical Sciences of Peking University. His research field is differential geometry and geometric analysis. His interests include canonical metrics in Kaehler geometry, Ricci flow and singularities, complex Monge-Ampere equation, and other topics concerning fully-linear equations arising from differential geometry. In particular, he is known for his work on the uniqueness of Kaehler-Ricci solitons, the solution of Kaehler-Ricci solitons on toric manifolds, and on the convergence theorem for the Kähler-Ricci flow.
Thu Sep 30 2021 18:28:34 GMT+0300 (Moscow Standard Time)