Video Lectures

Matrix powering, and more generally iterated matrix multiplication, is a fundamental linear algebraic primitive with myriad applications in computer science. Of particular interest is the problem’s space  complexity as it constitutes the main route...

While conducting a series of number-theoretic machine learning experiments, He, Lee, Oliver, and Pozdnyakov noticed a curious oscillation in the averages of Frobenius traces of elliptic curves over Q.  If one computes the average value of a_p(E) for...

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 work...

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...

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...

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 conditions...

Contact homology is a Floer-type invariant for contact manifolds, and is a part of Symplectic Field Theory. One of its first applications was the existence of exotic contact structures on spheres. Originally, contact homology was defined only for...