Section 6. Topology

Algebraic, differential and geometric topology. Surgery and diffeomorphism groups of manifolds. Homotopy theory, including motivic homotopy and K-theory. Operads and higher categories. Floer and gauge theories. Low-dimensional manifolds including knot theory. Moduli spaces. Symplectic and contact manifolds. Aspects of quantum field theory.
Richard Bamler

UC Berkeley, USA

Jointly in sections 5, 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.

Kai Cieliebak

Universitat Augsburg, Germany

Also in section 5

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 5, 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.
Jennifer Hom

Georgia Tech, USA

Jennifer Hom is an Associate Professor in the School of Mathematics at Georgia Tech.

Her research focuses on applications of Heegaard Floer homology to low-dimensional topology. She was a Sloan Fellow and earned an NSF CAREER award. Her other interests include board games and long distance running.

Bruce Kleiner


Developments in 3-d Ricci flow since Perelman

Jointly in sections 5, 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.
Marc Levine

The University of Duisburg-Essen, Germany

Survey lecture on motivic cohomology

Jointly in sections 2, 3, 4

Marc Levine was born in Detroit, Michigan.

He is a Senior Professor in the Faculty of Mathematics at the University of Duisburg-Essen.

He works in algebraic geometry and algebraic topology, specialising in motivic cohomology, algebraic K-theory, algebraic cobordism, motives and motivic homotopy theory, with an interest in applications to basic problems in algebraic geometry and arithmetics.

He is a member of the Leopoldina-German National Academy of Science and the Academia Europaea, and is a recipient of the Wolfgang Paul Award (2001) and the Senior Berwick Prize (2018). He also held a Humboldt Professorship at the University of Duisburg-Essen (2009-2014).

Yi Liu

Peking University, China

Yi Liu is a professor at Beijing International Center for Mathematical Research (BICMR) at Peking University.

His research interests include low dimensional topology and hyperbolic geometry. In particular, he studies the topology of 3-dimensional manifolds and their finite covers, very often from the perspective of geometrization.

Kathryn Mann

Cornell University, USA

Also in section 5

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 5

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.

Roman Mikhailov

St. Petersburg State University/St. Petersburg branch of Steklov Mathematical Institute, Russia

Roman Mikhailov is a leading researcher at St. Petersburg State University and St. Petersburg branch of Steklov Mathematical Institute and a professor of the Russian Academy of Sciences.

His interests include group theory, homotopy theory, and homological algebra. In particular, he is known as an author of solutions to a series of problems in algebra and topology.

Thomas Nikolaus

University of Münster, Germany

Thomas Nikolaus is a Professor of Mathematics at the University of Münster.

His research is mostly focused on homotopy theory and algebraic topology, but also concerns arithmetic and mathematical physics. More specifically, he works on (algebraic) K-theory, topological cyclic homology, and various related aspects. He has pioneered the use of higher categorical methods to attack and solve various problems in the area. His earlier work also concerns differential cohomology theories, operads, topological field theories, and mathematical physics.

Oscar Randal-Williams

University of Cambridge, UK

Oscar Randal-Williams is a Professor of Mathematics at the Department of Pure Mathematics and Mathematical Statistics of the University of Cambridge. He is interested in algebraic and geometric topology, in particular, the topology of moduli spaces, automorphism groups of manifolds, and applications of homotopy theory to geometry. He has been awarded the Whitehead Prize, the Philip Leverhulme Prize, the Dannie Heineman Prize, and the Oberwolfach Prize.
Jacob Rasmussen

University of Cambridge, UK

Jacob Rasmussen is a Professor of Mathematics in the Department of Pure Mathematics at the University of Cambridge.

His interests include the topology of knots, three-manifolds, and four-manifolds, and the tools for their study, such as Floer homology and categorification. He is known for his work on knot Floer homology and Khovanov homology.

Nathalie Wahl

University of Copenhagen, Denmark

Nathalie Wahl is a Professor of Mathematics at the University of Copenhagen.

Her research lies at the crossroads of algebraic topology, geometric topology and homotopy theory, with interests including loop spaces, field theories, homological stability, mapping class groups, and higher structures.

She is a Belgian citizen and obtained her Ph.D. from Oxford in 2001.

Guozhen Wang

Fudan University, China

Joint lecture with Zhouli Xu

Guozhen Wang is working in modern homotopy theory, focusing on the stable and unstable homotopy groups of spheres, equivariant homotopy theory, and topological cyclic homology theory.

His research accomplishments include his joint work with collaborators in proving that the 61-dimensional sphere has a unique smooth structure, developing the motivic deformation method and Chow t-structures, and computing the classical and motivic stable homotopy groups of spheres in the previously unknown range of dimensions.

He is an Associate Professor at Shanghai Center for Mathematical Sciences, at Fudan University.

Zhouli Xu

University of California/ San Diego, USA

Joint lecture with Guozhen Wang

Zhouli Xu is an Assistant Professor at the University of California, San Diego since 2020. He works in algebraic topology and focuses on classical, motivic and equivariant homotopy groups of spheres, with connections and applications to chromatic homotopy theory and geometric topology. His research accomplishments include his joint works with collaborators in proving that the 61-dimensional sphere has a unique smooth structure, proving a «10/8 + 4»-theorem on the geography problem in 4-dimensional topology, developing the motivic deformation method and the Chow t-structure, and computing the classical and motivic stable homotopy groups of spheres in the previously unknown range of dimensions. Dr. Xu received his Ph.D. in Mathematics from the University of Chicago in 2017, mentored by Peter May, Dan Isaksen and Mark Mahowald, and was a C.L.E. Moore Instructor at the Massachusetts Institute of Technology between 2017 and 2020, mentored by Haynes Miller. During his time at the University of Chicago, he received a Plotnick Fellowship in 2015 and the Harper Dissertation Fellowship in 2016.
Peter Zograf

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

Jointly in sections 4, 9

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.
Tue Oct 05 2021 16:05:00 GMT+0300 (Moscow Standard Time)