Past Events

In practice, L-functions appear as generating functions encapsulating information about various objects, such as Galois representations, elliptic curves, arithmetic functions, modular forms, Maass forms, etc. Studying L-functions is therefore of...

Let G = (V, E) be a simple graph of order n. The adjacency matrix of G is denoted by A(G) = [a_ij], where a_ij=1 if {v_i ,v_j} ∈ E and a_ij=0, otherwise. The diagonal matrix of degrees of G, D(G) = [d_ij], is defined by d_ii=d(v_i), and d_ij=0, ∀ i...

Automorphic representations, which provide a vast generalization of modular forms, are are grouped together into so-called L-packets according to the L-functions they produce. From this point of view, automorphic representations give a kind of fine...

Bregman proximal-type algorithms, such as mirror descent, are popular in optimization and data science for effectively exploiting problem structures and optimizing them under tailored geometries. However, most of existing convergence results rely on...

Grothendieck's duality theory relies on the notion of a dualizing complex. In the non-commutative setting such dualizing complexes were studied in the 90s beginning with work by Yekutieli. Since these complexes are not unique (for example, one can...

The quadratically regularized optimal transport problem (QOT) has emerged in the literature as a sparse alternative to entropic regularization (EOT). Unlike EOT, whose solutions always have full support—even for small regularization parameters—QOT...

A classical question in extremal (hyper)graph theory asks for tight minimum degree conditions which force the existence of certain spanning structures in large graphs, generalising Dirac's theorem from 1952. One aspect of this concerns tiling graphs...

An (m, n)-mixed graph consists of a set of vertices, any two of which may be joined by either an edge of one of m colours or an arc of one of n colours, or not be joined at all. The operation of switching at a vertex v of an (m, n)-mixed graph with...

The q , t -Catalan numbers can be described elegantly in terms of pairs of statistics on Dyck paths: area and bounce, or area and dinv. Using bijective and recursive methods, we prove new expressions of the q , t -Catalan numbers in terms of pairs of...

We discuss the Bunkbed Conjecture, a long-standing conjecture about connection probabilities in percolation. We describe a recent counterexample to this conjecture, a graph on 7772 vertices, and describe its structure.