Past Events

Dimitroglou-Rizell-Golovko constructs a family of Legendrians in prequantization bundles by taking lifts of monotone Lagrangians. These lifted Legendrians have a Morse-Bott family of Reeb chords. We construct a version of Legendrian Contact Homology(LCH) for Rizell-Golovko's lifted Legendrians…

We care about arithmetic invariants of polynomial equations / motives e.g. conductors or L-functions, which (conjecturally) are often automorphic and related to cycles on Shimura varieties. In this talk, I will focus on L-functions of Asai motives (e.g. Rankin-Selberg motives for GL_n x GL_n)…

Ramsey and Turán numbers are both central quantities in graph theory. Both maximize some quantity — the number of edges (Turán) or independence number (Ramsey) — over n-vertex graphs containing no copy of a fixed forbidden subgraph. In this talk, I'll tell you about a quantity that combines the…

Abstract

First- and last-passage percolation are models in which weights are placed on the edges of a graph (usually Z^d), and where the objects of interest are the shortest (respectively longest) paths from the origin to various points on the graph. I'll describe both models and describe…

The well-known Adams conjecture in topology is a theorem about compactifications of real vector bundles on CW-complexes, which has important implications for analyzing stable homotopy groups of spheres. In the talk we will discuss an algebro-geometric version of this statement, which tackles…

In my talk, I will start by reviewing how various properties of characteristic zero singularities can be understood topologically by ways of the Riemann-Hilbert correspondence. After that, I will explain how similar ideas can be applied in the study of mixed characteristic singularities.…

In this talk, we follow the book ‘Fourier Integral Operators’ by Duistermaat. Fourier integral operators (FIO) are a class of operators that generalise pseudodifferential operators. While pseudodifferential operators include solution operators to elliptic problems, FIO include solution operators…

We will discuss section 3 of [FP97].

Let r_0(n) be the number of representations of n as a sum of two squares, and r_1(n) count the number of representations of n as a sum of an integer square and a prime square. The asymptotic formulas for the moments of r_0(n), with k greater than 1 summed over n up to x are well-known via…

In this paper, we find a natural four-dimensional analog of the moderate deviation results for the capacity of the random walk, which corresponds to Bass, Chen and Rosen's results concerning the volume of the random walk range for dimension 2. We find that the deviation statistics of the…