Video Lectures

Suppose that Σ⊂ℂ is compact and symmetric about the real axis and is a finite union of rectangles and real intervals with transfinite diameter dΣ greater than 1. Suppose that μ is a H older arithmetic probability distribution on Σ defined in our...

The conformal bootstrap equations in general dimension are an infinite set of coupled non-linear equations in infinitely many variables. According to the lore, the solutions of the full set of equations correspond to physical CFTs. At the same time...

I will describe the construction of a global Kuranishi chart for moduli spaces of stable pseudoholomorphic maps of any genus and explain how this allows for a straightforward definition of GW invariants. For those not convinced of its usefulness, I...

The formula introduced by Robert Lipshitz for Heegaard Floer homology is now one of the basic tools for those working with HF homology. The convenience of the formula is due to its combinatorial nature. In the talk, we will discuss the recent...

The question of whether a Symplectic manifold embeds into another is central in Symplectic topology. Since Gromov nonsqueezing theorem, it is known that this is a different problem from volume preserving embeddings. Symplectic capacities are...

This will be a discussion about large language models such as OpenAI’s GPT series, oriented towards physicists.

After a brief survey of the state of the art, we describe transformer models in detail, and discuss current ideas on how they work and...

In a recent machine learning based study, He, Lee, Oliver, and Pozdnyakov observed a striking oscillating pattern in the average value of the P-th Frobenius trace of elliptic curves of prescribed rank and conductor in an interval range. Sutherland...

Data from ESA’s Gaia mission is already revolutionizing Galactic astronomy, providing an unprecedented view of the Solar neighborhood and beyond. However, while it provides us a great opportunity to transform our understanding of the Milky Way, it...

In its dynamical formulation, the Furstenberg—Sárközy theorem states that for any invertible measure-preserving system (X,μ,T), any set A⊆X with μ(A) greater than 0, and any integer polynomial P with P(0)=0,

c(A)=limN−M→∞1N−M∑n=MN−1μ(A∩TP(n)A)>0...

We prove the existence of subspace designs with any given parameters, provided that the dimension of the underlying space is sufficiently large in terms of the other parameters of the design and satisfies the obvious necessary divisibility...