The 2022-23 Chern Lectures - Yakov Eliashberg

The Department of Mathematics will host two 2022-23 Chern Lecturers during the Spring '23 semester: Professor Peter Sarnak, Professor, Princeton University and Institute for Advanced Study (January-February) and Yakov Eliashberg, Professor, Stanford University (April).

Prof. Yakov Eliashberg

The second series of Chern Lecturers in 2022-23 will be given by Professor Yakov Eliashbergthe Herald L. and Caroline L. Ritch Professor of Mathematics at Stanford University (April 18, April 20, April 25, and April 26, 2023). The title of the series is "Flexible Mathematics".  The overall abstract for the series is: Flexible mathematics was born in the work of Hassler Whitney in 1930s-1940s, Stephen Smale and John Nash in 1950s, and then greatly developed by Mikhail Gromov in the late 1960s-early 1970s under the name of the h-principle. In recent years the area went through a period of renaissance. In the lectures there will be discussed the evolution of notions and methods of the h-principle and consider a few recent examples from complex, symplectic and contact geometries. Please join us for a reception in 1015 Evans after the first lecture on April 18 beginning around 5:15pm.

Lecture 1 of 4 (April 18, 2023 @ 4:10–5:00 pm, UC Berkeley Campus, Location: Sibley Auditorium - Bechtel): "h-principle and its evolution". ABSTRACT: Our understanding which problem belongs to the domain of the h-principle has evolved since the inception of the subject. We will explore the development of basic methods and ideas on various examples.

Lecture 2 of 4: (April 20, 2023 @ 4:10–5:00 pm, Location: 60 Evans Hall): "Flavors of convexity in complex geometry". ABSTRACT: We will discuss two instances of h-principle in complex geometry and analysis: the Oka principle in the theory of holomorphic functions on Stein manifolds and  the theory of complex convexity in its various flavors, such as pseudo-convexity, holomorphic, rational and polynomial convexity.  Complex convexity has  counterparts in symplectic and contact geometry, and this interplay turned out to be useful for all sides of the story. 

Lecture 3 of 4 (April 25, 2023 @ 4:10–5:00 pm, UC Berkeley Campus, Location: Valley Life Science Building 2060): "Wienstein manifolds: on the frontier of symplectic flexibility". ABSTRACT: In symplectic and contact geometry flexible and rigid results come in a striking proximity. We consider a few examples in the theory of Weinstein manifolds, which are symplectic counterparts of Stein complex manifolds. 

Lecture 4 of 4: (April 26, 2023 @ 4:10-5:00 pm, UC Berkeley Campus, Location: Valley Life Science Building 2060): "Convexity in contact geometry". ABSTRACT: Recently Ko Honda and Yang Huang discovered a new flexibility phenomenon related to contact convexity. We will discuss their results and some further development in this direction.