Past Events

We consider neural networks (NN) as discretizations of continuous dynamical systems. There are two relevant systems: the NN architecture on one side and the gradient flow for optimizing the parameters on the other. In both cases, stability properties...

There is now an expansive collection of mathematical work on building models for the transport of intracellular cargo by molecular motors. Commonly studied cargo undergo “saltatory” motion (bidirectional ballistic motion, intermixed with periods of...

Varieties that fail to have rational points despite having local points for each prime are said to fail the Hasse principle. A systematic tool accounting for these failures uses the Brauer group to define an obstruction set known as the Brauer-Manin...

A set { a 1 , a 2 , … , a m } of distinct positive integers is a Diophantine m -tuple if the product of any two distinct elements in the set is one less than a square. In this talk, I will discuss some recent results related to Diophantine tuples and...

A sequence of tournaments is said to be quasirandom if it behaves as a sequence of random tournaments would. In 1991, Chung, Graham, and Wilson provided a list of equivalent properties that any sequence of random tournaments satisfies with high...

Talk Abstract The orthogonally projected shadows of a dispersed set in the plane carry much of the information about the shape of the set. The average size of the shadow, known as the Favard length, can be used to study density, structure...

In two independent papers, Aizenman and Fröhlich argued that every scaling limit of the critical Ising model in dimensions d > 4 is trivial (or Gaussian). This qualitative result can be reformulated as follows: the Schwinger functions of any...

Mathematical modeling, when combined with diverse epidemiological datasets, provides valuable insights for understanding and controlling infectious diseases. In this talk, I will present a series of case studies demonstrating how the synergy between...

This talk will discuss two inference problems in dynamical systems, both motivated by applications in mathematical biology. First, we will discuss the classical gene regulatory network inference problem for time-stamped single-cell datasets and...

Given a graph G, its genus distribution is the sequence whose k-th term is the number of 2-cell embeddings of G in the orientable surface of genus k. The Log-Concavity Genus Distribution (LCGD) Conjecture states that the genus distribution of every...