Seminars and Colloquia Schedule

Linear and rational factorization of tropical polynomials

Series
Algebra Seminar
Time
Monday, March 30, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bo LinGeorgia Tech

Already for bivariate tropical polynomials, factorization is an NP-Complete problem.In this talk, we will introduce a rich class of tropical polynomials in n variables, which admit factorization and rational factorization into well-behaved factors. We present efficient algorithms of their factorizations with examples. Special families of these polynomials have appeared in economics,discrete convex analysis, and combinatorics. Our theorems rely on an intrinsic characterization of regular mixed subdivisions of integral polytopes, and lead to open problems of interest in discrete geometry.

The talk will be held online via Bluejeans. Use the following link to join the meeting.

Hopf Algebras and Cohomology of Lie Groups

Series
Geometry Topology Student Seminar
Time
Wednesday, April 1, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Online
Speaker
Tao YuGeorgia Tech

In 1941, Hopf gave a proof of the fact that the rational cohomology of a compact connected Lie group is isomorphic to the cohomology of a product of odd dimensional spheres. The proof is natural in the sense that instead of using the classification of Lie groups, it utilizes the extra algebraic structures, now known as Hopf algebras. In this talk, we will discuss the algebraic background and the proof of the theorem.

Eigenvectors' overlaps for integrable models of non-Hermitian random matrices

Series
Stochastics Seminar
Time
Thursday, April 2, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Guillaume Dubach

Right and left eigenvectors of non-Hermitian matrices form a bi-orthogonal system to which one can associate homogeneous quantities known as overlaps. The matrix of overlaps quantifies the stability of the spectrum and characterizes the joint eigenvalues increments under Dyson-type dynamics. Overlaps first appeared in the physics literature: Chalker and Mehlig calculated their conditional expectation for complex Ginibre matrices (1998). For the same model, we extend their results by deriving the distribution of the overlaps and their correlations (joint work with P. Bourgade). Similar results can be obtained for quaternionic Gaussian matrices, as well as matrices from the spherical and truncated-unitary ensembles.