**Feb 15**

**Algebra Seminar- Raul Gomez (Cornell University)**

A GIT approach to Stiefel Harmonics

4:00PM, Mon Feb 15 2016, Math 250

In 1974, Stephen Gelbart developed a theory of Stiefel harmonics for the Stiefel manifolds $SO(n)/SO(n-m)$ generalizing, in this way, the theory of spherical harmonics. (That is, the case $m=1$.) This theory has been further extended to include compact Stiefel manifolds of Unitary and Symplectic type. In this talk we describe a new, unified, approach to Stiefel harmonics using Geometric Invariant Theory. Time permitting, I will also explain some directions of further research that can be taken with this approach.

This is an outgrowth of the Cornell SPUR summer program.

**Feb 16**

**Graduate Mentoring Seminar- Dr. Joseph Hundley**

Representation theoretic methods in automorphic forms

5:00PM, Tue Feb 16 2016, Math 250

We give a brief introduction to the subject of automorphic forms, representations, and L-functions, beginning with the simplest examples (holomorphic modular forms on the upper half plane) and progressing to computational aspects of pushing classical ideas into exceptional groups.

**Feb 18**

**Colloquium- Erkao Bao (UCLA)**

An invitation to contact homology.

4:00PM, Thu Feb 18 2016, Math 250

Contact homology is an invariant of a contact structure. In this talk, we will start with the definition of a contact structure, then build up our way by looking at the Morse homology, and finally we will have a gentle definition of contact homology, which can be viewed as an infinite dimensional Morse homology.

**Feb 19**

**Geometry/Topology Seminar- Erkao Bao (UCLA)**

Semi-global Kuranishi structures and contact homology.

4:00PM, Fri Feb 19 2016, Math 122

Contact homology was proposed and studied by Eliashbergy, Givental and Hofer 16 years ago. It is a very powerful tool to distinguish different contact structures. However, the rigorous definition did not come out until last year.

In this talk, we will first see that the naive definition does not work because the spaces of "trajectories" that we count to define the differential of contact homology are not transversally cut out. Then we will construct a finite dimensional space K around the spaces of "trajectories" in a systematical way, and inside K we perturb the "trajectories" so that now they are transversally cut out. The space K together with the perturbation is called a semi-global Kuranishi structure.

**Feb 24**

**Analysis Seminar**

Lewis Coburn (SUNY at Buffalo)

4:00PM, Wed Feb 24 2016, Math 250

**Mar 2**

**Analysis Seminar**

Zhengxin Lian (University of Science and Technology of China and SUNY at Buffalo)

Sequences realized by noncommutative toral automorphisms with zero entropy and Sarnak conjecture

4:00PM, Wed Mar 2 2016, SUNY at Buffalo

http://www.math.buffalo.edu/~hfli/abstract-Spring 2016-Lian.pdf