Termine

We invite all early career researchers who have started their position at Mathematics Münster since January 2026 to join us for this MM Welcome Event. Learn more about the Cluster, its research topics and opportunities. Get to know your fellow new colleagues.

Shrinking gradient Kähler-Ricci solitons model finite-time singularities of the Kähler-Ricci flow on compact Kähler manifolds. I will discuss the existence problem for shrinking gradient Kähler-Ricci solitons in the non-compact toric setting. This talk is based on joint work with Ivin Babu and Alix Deruelle.

Let $G$ be an even orthogonal group over a $p$-adic local field. Given a parahoric subgroup $K_p$ of $G$ and a minuscule geometric cocharacter $\mu$, one can associate a canonical local model, which is a projective scheme over the ring of $p$-adic integers whose generic fiber is the flag variety attached to $\mu$. When $p>2$ and the triple $(G,K_p,\mu)$ arises from a global Shimura datum, it is known that the local model is étale locally isomorphic to the canonical integral model of the corresponding Shimura variety. In this talk, we focus on the case of PEL type D. We prove that the spin local models introduced by Pappas-Rapoport are isomorphic to the corresponding canonical local models. This confirms a conjecture of Pappas-Rapoport. As a corollary, we obtain an explicit moduli interpretation for flat integral moduli spaces of PEL type D. This talk is partly based on joint work with Ioannis Zachos and Zhihao Zhao.

Vaughan Jones and I showed in the late 1990's that whenever a subfactor has an intermediate subfactor, the fundamental subfactor symmetries are captured by what we called the ``Fuss-Catalan algebras''. If the subfactor has two intermediate subfactors in general position, i.e. we are given a quadrilateral of subfactors, describing the quantum symmetries is more complicated and not much progress had been made since the work of Grossman, Izumi and Jones some 20 years ago. I will discuss recent work with Junhwi Lim in which we determine the quantum symmetries of a quadrilateral of subfactors when the four algebras form a co-commuting square and satisfy some additional conditions. The subfactor symmetries we find are related to partition algebras and Bell numbers.