Seminar

We will review Klyachko's classification of torus equivariant vector bundles on toric varieties.

TBA

I will continue my previous talk. I will discuss the criteria for existence of a connection on a parabolic bundle.

I will discuss rank 2 bundles with connections on P^1 with 4 regular singular points. 

Generating functions are a simple but powerful mathematical tool for encoding and manipulating sequences. In this talk, I will give a basic description of ordinary, exponential, and Dirichlet generating functions. I will show how these different types of generating functions have applications many different areas of math including probability, combinatorics, and abstract algebra.

I will finish my series of talks about parabolic bundles.

Fractional Sobolev spaces, which generalize the concept of classical Sobolev spaces, have been a central tool in harmonic analysis, variation problems, and PDE for several decades. One of the main issues of these spaces is that they are unstable as the fractional parameter s goes to 1. In this talk, I will share some of the new results that I've obtained regarding stabilizing these spaces, and how these results compare to the classical Bourgain-Brezis- Mironescu formula.