Fall Semester 2025-2026
Abstract: Modular forms arise in many areas of mathematics, and most prominently in modern number theory. They appear in the proof of Fermat's last theorem, a key ingredient in Viasovska's solution to the packing problem in dimension 8, have a remarkable connection to the Monstrous Moonshine correspondence, and have far-reaching applications in arithmetic and analytic number theory (partitions, Congruences, L-functions, and more).
I will give an introduction to the theory of elliptic modular forms and present an elegant connection to the theory of integral quadratic forms.
If time permits, I will discuss recent results of mine regarding the zeros of modular forms.
No previous knowledge is assumed.
Abstract: In this talk, we address the recovery of point sources (modeled as diracs) from bandlimited and noisy Fourier measurements, known as the super-resolution problem. We show how the geometry of the sources affects the stability of reconstruction and present our recent results on optimal error bounds for the super-resolution problem in high dimensions. These bounds are crucial for establishing the optimality of widely used algorithms such as Matrix Pencil and Prony's method.
Abstract: Extremal combinatorics studies how large/small a finite set of objects can be if it has to satisfy some certain restrictions. For instance, one may ask: how many edges can a graph on $n$ vertices have if it contains no triangles?
In 1959, Erdős and Rényi introduced a fundamental model of random graphs on $n$ vertices, in which each pair of vertices is joined by an edge independently with probability $p$.
In this talk, we will first discuss some classical results in extremal combinatorics. We will then explore how these ideas interact with random graphs. Finally, if time permits, we will look at what is known about the largest bipartite subgraphs (max-cuts) of random graphs.
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