Submit your nominations for staff and students in MPLS who have gone above and beyond in their efforts to advance Equality, Diversity and Inclusion within your communities. These awards are an opportunity to celebrate individuals and teams that have accomplished amazing things to make our workplaces a better place for all of us. Self-nominations are accepted. Deadline: 4pm on Tuesday 24 September 2024.
14:15
Machine learning detects terminal singularities
Abstract
In this talk, I will describe recent work in the application of machine learning to explore questions in algebraic geometry, specifically in the context of the study of Q-Fano varieties. These are Q-factorial terminal Fano varieties, and they are the key players in the Minimal Model Program. In this work, we ask and answer if machine learning can determine if a toric Fano variety has terminal singularities. We build a high-accuracy neural network that detects this, which has two consequences. Firstly, it inspires the formulation and proof of a new global, combinatorial criterion to determine if a toric variety of Picard rank two has terminal singularities. Secondly, the machine learning model is used directly to give the first sketch of the landscape of Q-Fano varieties in dimension eight. This is joint work with Tom Coates and Al Kasprzyk.
11:00
Probabilistic Schwarzian Field Theory
Abstract
Schwarzian Theory is a quantum field theory which has attracted a lot of attention in the physics literature in the context of two-dimensional quantum gravity, black holes and AdS/CFT correspondence. It is predicted to be universal and arise in many systems with emerging conformal symmetry, most notably in Sachdev--Ye--Kitaev random matrix model and Jackie--Teitelboim gravity.
In this talk we will discuss our recent progress on developing rigorous mathematical foundations of the Schwarzian Field Theory, including rigorous construction of the corresponding measure, calculation of both the partition function and a natural class of correlation functions, and a large deviation principle.
15:30
Statistical Inference for weakly interacting diffusions and their mean field limit
Abstract
We consider the problem of parametric and non-parametric statistical inference for systems of weakly interacting diffusions and of their mean field limit. We present several parametric inference methodologies, based on stochastic gradient descent in continuous time, spectral methods and the method of moments. We also show how one can perform fully nonparametric Bayesian inference for the mean field McKean-Vlasov PDE. The effect of non-uniqueness of stationary states of the mean field dynamics on the inference problem is elucidated.