Past Events
https://researchseminars.org/talk/agstanford/17/
Abstract: We are interested in G-birational equivalence of varieties where G is a finite group. Kontsevich-Tschinkel and Kresch-Tschinkel have developed…
Hermitian matrices are stable under small, additive perturbations, but this fact fails dramatically to generalize to the non-Hermitian case, as there are non-diagonalizable n x n matrices whose spectra move by O(ε^n) after an ε-perturbation. This issue is especially concerning for numerical…
A Newton-Okounkov body is a convex set associated to a projective variety, equipped with a valuation. These bodies generalize the theory of Newton polytopes. Work of Kaveh-Manon gives an explicit link between tropical geometry and Newton-Okounkov bodies. We use this link to describe a wall-…
The problem of group synchronization asks to recover states of objects
associated with group elements given possibly corrupted relative state
measurements (or group ratios) between pairs of objects. This problem
arises in important data-related tasks, such as structure from motion,…
The Mallows measure on the symmetric group gives a way to generate random permutations which are more likely to be sorted than not. There has been a lot of recent work to try and understand limiting properties of Mallows permutations. I'll discuss recent work on the joint distribution of…
I will explain how tropical degenerations and birational specialization techniques can be used in rationality problems. In particular, I will apply these techniques to study quartic fivefolds and complete intersections of a quadric and a cubic in P^6. This is joint work with Johannes Nicaise.…
The mean-field approximation is a common scheme in statistical physics to estimate the free energy of certain Gibbs measures–a key quantity on which rests many predictions of the asymptotic of the system. In this talk we will focus on rigorously justifying the mean-field approximation and…
The stochastic Burgers equation is a prototypical example of a conservation law with stochastic forcing. It is sometimes studied as a toy model for turbulence. Via the Cole–Hopf transform, it is also closely related to the KPZ equation, a model for the stochastic growth of a random surface. I…
Approximate Message Passing (AMP) algorithms are non-linear power iterations originally arising from the context of compressed sensing. In this talk, I will introduce a Lipschitizian functional iteration, as a generalization of the AMP algorithms, and discuss its universality in disorder. In…