Past Events

The degeneracy of a graph is a measure of sparseness that gives important information about its Ramsey- and Turán-type properties. I will talk about the hypergraph extension of these problems. The typical notion of hypergraph degeneracy does not give...

The question of which nilpotent Lie algebras admit complex structures is far from being understood. In recent decades, progress has primarily focused on providing algebraic obstructions to the existence of such structures, with classification results...

Gradient flows have emerged as a powerful framework for analyzing machine learning and statistical inference algorithms. Motivated by several applications in statistical inference, generative models, generalization, and robustness of learning...

Current LLM alignment techniques use pairwise human preferences at a sample level, and as such, they do not imply an alignment on the distributional level. We propose in this paper Alignment via Optimal Transport (AOT), a novel method for...

I will introduce our recent work on parameterising OT problems with elastic costs, i.e. ground costs that mix the classic squared Euclidean distance with a regularizer (e.g. L1 norm). After highlighting the properties of OT maps that follow such...

There has been extensive study of diagonalization of matrices. Diagonalization can be viewed as using a similarity transform to concentrate the magnitude of all entries within as small a subset of entries as possible. We motivate and present results...

Let ord p ( a ) be the order of a in ( Z / p Z ) ∗ . In 1927, Artin conjectured that the set of primes p for which an integer a ≠ − 1 , ◻ is a primitive root (i.e. ord p ( a ) = p − 1 ) has a positive asymptotic density among all primes. In 1967...

Lots of problems in combinatorics and analysis are connected to upper bounds for incidences: given a set of points and tubes, how much can they intersect? This talk is about lower bounds for incidences, a topic that has received much less attention...

For a finite connected graph, the following objects have the same cardinality: the set of spanning trees, the Jacobian group, the set of equivalence classes of orientations up to cycle-cocycle reversal, the set of break divisors, the set of reduced...

Cell movement requires long-range coordination of the cytoskeletal machinery that organizes cell morphogenesis. We have found that reciprocal interactions between biochemical signals and physical forces enable this long-range signal integration...