Past Events

A conjecture of Erdős, Graham, Montgomery, Rothschild, Spencer and Straus states that, with the exception of equilateral triangles, any two-coloring of the plane will have a monochromatic congruent copy of every three-point configuration. In this...

Davies's efficient covering theorem states that we can cover any measurable set in the plane by lines without increasing the total measure. This result has a dual formulation, known as Falconer's digital sundial theorem, which states that we can...

The topic on the distribution of sequences saw its light with the seminal paper of Weyl. While the classical notion of equidistribution modulo one addresses the “global” behaviour of the fractional parts of a sequence, quantities such as k-point...

Mean-field game (MFG) systems provide a powerful framework for modeling the collective behavior of multi-agent systems with diverse applications. However, unknown parameters pose challenges. In this work, we tackle an inverse problem, recovering MFG...

The category of polynomial functors in one variable and natural transformations between them is incredibly rich, e.g. it has infinitely many monoidal closed structures, including cartesian closure. Its substitution comonoids are categories and the...

In 1986, Wilf posed the following question ``Which graphs have eigenvectors with entries solely -1 and +1?''. Stevanovic (2016) showed that the problem of finding such graphs is NP-Hard. Caputo, Khames, and Knippel (2019) described all graphs whose...

If A and B are two geometric progressions, we characterize all 3-term arithmetic progressions in the sumset A+B. Somewhat surprisingly, while mostly elementary, this appears to require quite deep machinery from Diophantine Approximation.

Given graphs $G$ and $H$ and a positive integer $q$, an $(H,q)$-coloring of $G$ is an edge-coloring in which each copy of $H$ receives at least $q$ colors. Erdős and Shelah raised the question of determining the minimum number of colors, $f(G,H,q)$...

In the past decade, (artificial) neural networks and machine learning tools have surfaced as game changing technologies across numerous fields, resolving an array of challenging problems. Even for the numerical solution of partial differential...

Alternating sign matrices (ASMs) were introduced by Robbins and Rumsey in the early 1980s. Together with Mills they conjectured an enumerative formula for the number of ASMs of size n×n, which was proved independently by Zeilberger and Kuperberg...