Members Seminar

Lie algebras and homotopy theory

Jacob Lurie
Professor, School of Mathematics
November 11, 2019

In this talk, I'll discuss the role that Lie algebras play in algebraic topology and motivate the development of a "homotopy coherent" version of the theory. I'll also explain an "equation-free" formulation of the classical theory of Lie algebras, which emerges as a concrete byproduct.

Pseudoholomorphic curves with boundary: Can you count them? Can you really?

Sara Tukachinsky
Member, School of Mathematics
November 4, 2019

Open Gromov-Witten (OGW) invariants should count pseudoholomorphic maps from curves with boundary to a symplectic manifold, with various constraints on boundary and interior marked points. The presence of boundary poses an obstacle to invariance. In a joint work with J. Solomon (2016-2017), we defined genus zero OGW invariants under cohomological conditions.

Logarithmic concavity of Schur polynomials

June Huh
Visiting Professor, School of Mathematics
October 7, 2019

Schur polynomials are the characters of finite-dimensional irreducible representations of the general linear group. We will discuss both continuous and discrete concavity property of Schur polynomials. There will be one theorem and eight conjectures. No background beyond basic representation theory will be necessary to enjoy the talk. Based on joint work with Jacob Matherne, Karola Mészáros, and Avery St. Dizier.

Etale and crystalline companions

Kiran Kedlaya
University of California, San Diego; Visiting Professor, School of Mathematics
April 15, 2019

Deligne's "Weil II" paper includes a far-reaching conjecture to the
effect that for a smooth variety on a finite field of characteristic p,
for any prime l distinct from p, l-adic representations of the etale
fundamental group do not occur in isolation: they always exist in
compatible families that vary across l, including a somewhat more
mysterious counterpart for l=p (the "petit camarade cristallin"). We
explain in more detail what this all means, indicate some key

A recent perspective on invariant theory

Viswambhara Makam
Member, School of Mathematics
April 1, 2019

Invariant theory is a fundamental subject in mathematics, and is potentially applicable whenever there is symmetry at hand (group actions). In recent years, new problems and conjectures inspired by complexity have come to light. In this talk, I will describe some of these new problems, and discuss some positive and negative results regarding them.