Past Events
In this talk, we consider the strict convexity of energy functions
of harmonic maps at its critical points from…
In this talk, we will investigate the emergence of geometric patterns in well-trained deep learning models by making use of a layer-peeled model and the law of equi-separation. The former is a nonconvex optimization program that models the last-layer features and weights. We use the model to…
This seminar will go into some detail into a proof of the central limit theorem for the values of the Estermann function D(x) at rationals x ordered by denominators, which we worked out with Sandro Bettin (Genova) in 2018. Here D(x) is the values at s=1/2 of the analytic continuation of the…
Fintushel-Stern's knot surgery construction on elliptic surfaces has been a central source of exotic, smooth four-manifolds since its introduction in the 1990's. The construction associates a homotopy elliptic surface to a classical knot. These homotopy elliptic surfaces are non-diffeomorphic if…
We consider the binary perceptron model, a simple model of neural networks that has gathered significant attention in the statistical physics, information theory, and probability theory communities. We show that at low constraint density (m=n^{1-epsilon}), the model exhibits a strong freezing…
Abstract: Kac’s celebrated inverse spectral question “Can one hear the shape of a drum?” consists in recovering a metric from the knowledge of the spectrum of its Laplacian. I will discuss a very similar question on negatively-curved manifolds, where the word “metric” is now replaced by “…
Abstract: The issue of the stability of the Kerr family $\KK(a,m)$ has been at the center of attention of GR physics and mathematical relativity ever since their discovery by R.Kerr in 1963. Roughly the problem here is to show that all spacetime developments of initial data sets…
We study the fine distribution of lattice points lying on expanding circles in the hyperbolic plane. The angles of lattice points arising from the orbit of the modular group and lying on hyperbolic circles are shown to be equidistributed for generic radii. However, the angles fail to…
Abstract: G_2-monopoles are special solutions to the Yang–Mills–Higgs equation on G_2-manifolds, similar to 3-dimensional BPS monopoles.
Donaldson and Segal proposed that these gauge theoretic objects have a close relationship to the geometry of the underlying manifolds.…