Past Events
384I
Abstract: (Joint with Jacob Fox and Matthew Kwan) The classical Erdős-Littlewood-Offord theorem says that for any n nonzero vectors in R^d, a random signed sum concentrates on any point with probability at most O(n^{1/2}). Combining tools from probability theory, additive…
Motivated by applications to wireless communication, we consider the propagation of waves transmitted by ambient noise sources and interacting with metamaterials. We discuss a generalized Helmholtz-Kirchhoff identity that is valid in dissipative and dispersive media and we characterize the…
Macdonald often included in his talks the “specialization square” for symmetric Macdonald polynomials, which has monomial symmetric functions on the top edge, elementary symmetric functions on the right edge, Hall-…
Abstract: Given a compact surface, F, and K in {0,1,-1}, the following are equivalent.
- There is a metric of constant curvature K on F…
Large deviations of nonlinear functions of adjacency matrices of sparse random graphs have gained considerable interest over the last decade. This includes popular examples like subgraph count, or the extreme eigenvalues. For the first half of the talk, we will discuss how the upper tail large…
We give an asymptotic lower bound on the number of field extensions generated by algebraic points on superelliptic curves over $\mathbb{Q}$ with fixed degree $n$, discriminant bounded by $X$, and Galois closure $S_n$. For $C$ a fixed curve given by an affine equation $y^m = f(x)$ where $m \geq 2…
A brief introduction to the construction of Lagrangian Floer homology and its application to a case of Arnold’s conjecture concerning intersections between Hamiltonian isotopic Lagrangian submanifolds.
Abstract: Given a polynomial $P$ of constant degree in $d$ variables and consider the oscillatory integral $$I_P = \int_{[0,1]^d} e(P(\xi)) \mathrm{d}\xi.$$ Assuming $d$ is also fixed, what is a good upper bound of $|I_P|$? In this talk, I will introduce a ``stationary set'' method that gives an…