Seminar
Adelic description of principal bundles
TBA
Existence of parabolic connections
I will continue my previous talk. I will discuss the criteria for existence of a connection on a parabolic bundle.
Rank 2 connections on P^1
I will discuss rank 2 bundles with connections on P^1 with 4 regular singular points.
Generating Functions and their Applications
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.
Rank 2 parabolic bundles on P^1 and bundles with connections
I will finish my series of talks about parabolic bundles.
Stability of some Fractional function spaces
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.
Rank 2 parabolic bundles on P^1 and bundles with connections
I will continue discussing Rank 2 parabolic bundles on P^1 . Time permits, I will discuss the morphism from rank two connections with 4 regular singular points to our moduli stack of bundles.
Divisors and line bundles on toric varieties III
A new solvability condition for $L^p$ boundary value problems
Abstract: We are discussing the elliptic operator $L:=\mathrm{div}(A\nabla\cdot)$ and wonder which types of matrices $A$ yield solvability of $L^p$ boundary value problems. It is well-known that the DKP or Carleson condition implies solvability for the Dirichlet and the regularity boundary value problem. Equally, if the domain is the upper half space, independence of the transversal direction $t$ gives solvability of these boundary value problems.