Past Events

A new computational task has been defined and solved over the past 15 years for extended material systems: the analytic fitting of the Born-Oppenheimer potential energy surface as a function of nuclear coordinates. The resulting potentials ("force...

Hopf algebras are algebras for which one can form the tensor product of two representations. In more abstract terms, this means that their representation category is a tensor category, and all additional required properties of this tensor category...

Every group admits a faithful unitary representation on some Hilbert space. In other words, every group can be realized concretely as symmetries on a Hilbert space. From these representations we can construct certain operator algebras known as C*...

The classical theory of hypergeometric functions, developed by generations of mathematicians including Gauss, Kummer, and Riemann, has been used substantially in the ensuing years within number theory, geometry, and the intersection thereof. In more...

Motivated by a conjecture of Maglione–Voll from group theory, we introduce and study the Poincaré-extended ab-index. This polynomial generalizes both the ab-index and the Poincaré polynomial. For posets admitting R-labelings (a relaxation of EL...

Percolation on a graph is a random process that divides the edges into two groups: open and closed. Events such as "vertices v and w are connected via a path of open edges" occur within this process. We investigate the dependencies between these...

"Double dipping" is the practice of using the same data to fit and validate a model. Problems typically arise when standard statistical procedures are applied in settings involving double dipping. To avoid the challenges surrounding double dipping, a...

Coalgebraic modal logic is a set of approached to modal semantics that defines frames and models as coalgebras for a functor. This approach has captured the traditional notions of Kripke and Neighbourhood frames, as well as many other types of...

In 1909, Thue proved that when $F(x,y)$ is an irreducible, homogeneous, polynomial with integer coefficients and degree at least 3, the inequality $\left\| F(x,y) \right\| \leq h$ has finitely many integer-pair solutions for any positive $h$. Because...

The generic representations of p-adic groups are used in different contexts but still carry a touch of mystery. I will explain their use, and some central results about them. Further, I will give an account on a recent work with Cunningham, Fiori and...