Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
In this talk we solve the exit problems for spectrally negative Lévy processes, which are exponentially killed with a killing intensity dependent on an additive functional of the Lévy process. Additionally, we study their associated resolvents. All identities are given in terms of new generalizations of scale functions. Our results generalize those for omega-killed spectrally negative processes obtained by Palmowski and Li. Finally, we apply these results to derive penalization results for spectrally negative Lévy processes with clocks driven by additive functionals. This is joint work with Kei Noba, Kouji Yano, and Kohki Ibba.
Topological phases of matter in (2+1)D should naturally form a 3-category, in which k-morphisms represent defects of codimension k. By the cobordism hypothesis, the 3-categories of (2+1)D topological order with a fixed anomaly are each equivalent to the 3-category of fusion categories enriched over a corresponding UMTC. In ongoing work with Fiona Burnell, we introduce algebraic techniques for concrete computations in 3-categories of (2+1)D topological order, including a tunneling approach to the classification of point defects which generalizes the use of braiding to identify anyon types. We then apply these techniques to compute ground state degeneracy and classify low energy excitations in a class of fracton-like (2+1)D topological defect networks.
It is known from general relativity that axisymmetric stationary black holes can be reduced to axisymmetric harmonic maps into the hyperbolic plane $H^2$, while in the Riemannian setting, 4d Ricci-flat metrics with torus symmetry can also be locally reduced to such harmonic maps satisfying a tameness condition. We study such harmonic maps. Applications include a construction of infinitely many new complete, asymptotically flat, Ricci-flat 4-manifolds with arbitrarily large $b_2$. Joint work with Song Sun.
