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.

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.

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

Quitting Games are among the simplest example of schotastic games to describe, yet many of their properties, namely the existence of uniform equilibria, remain open. In this talk, we present the game as well as various approaches from recent years to solve it as well as to find the structure of the equilibria.

No prior knowledge is required, although some familiarity with concepts in game theory will be useful.

I will introduce the concept of Zero-Knowledge Proofs through classical examples, illustrating how a "prover" can prove knowledge of information to a "verifier", without revealing the information. I will then present the modern STARK protocol, which enables the verification of arbitrary computational statements efficiently.

We'll discuss basic concepts in classical mechanics motivating the definition of a symplectic manifold - the central object of study in symplectic geometry.

I will present the Gowers inverse problem, which is a central problem in the field of additive combinatorics. We will discuss some motivation, and see old and new results.

The talk will be at an elemantary level (no prior knowledge is assumed).

Classical model theory explains meaning via structures and satisfaction: a sentence is true in a model because its interpretation is globally well-defined and compositional. Semantic paradoxes (liar-type and their relatives) stress-test this picture: locally compelling inferential steps force globally inconsistent truth assignments. In this talk, I present a geometric perspective on logical phenomena according to which the “paradox” is not primarily a defect of language, but an obstruction to gluing, a relatively common and well-known occurrence in algebraic topology and, as we will see, also in quantum mechanics.

In this talk, I outline how we can start with propositional logic and model it using algebraic-topological tools such as simplicial complexes, chain complexes, presheaves, and Čech-style cohomology, in order to provide invariants that witness these failures of gluing. The payoff is a unifying framework that clarifies why different “resolutions” of paradox (non-classical logics, restricted compositionality, semantic revision, etc.) can be compared as distinct ways of modifying the underlying site, the presheaf, or the gluing conditions, so as to restore or intentionally relax global logical consistency in a tractable way.

In this talk, we study the convergence rate of learning pairwise interactions in single-layer attention-style models, where tokens interact through a weight matrix and a non-linear activation function. I'll present results showing that the minimax rate is M^{-\frac{2\beta}{2\beta+1}} with M being the sample size, depending only on the smoothness \beta of the activation, and crucially independent of token count, ambient dimension, or rank of the weight matrix.

These results highlight a fundamental dimension-free statistical efficiency of attention-style nonlocal models, even when the weight matrix and activation are not separately identifiable, and provide a theoretical understanding of the attention mechanism and its training.

I will talk about convex polytopes (i.e. higher-dimensional analogues of polygons), their faces, and their combinatorics. I'll recall Kalai's 3^d conjecture and talk about a result of Sanyal and Winter, which proves it for a special class of polytopes.