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, I will present recent results on the contact process on two specific types of scale-free, inhomogeneous random networks that evolve either through edge resampling or by resampling entire neighborhoods of vertices. Depending on the type of graph, the selected stationary dynamic, the tail exponent of the degree distribution, and the updating rate, we identify parameter regimes that result in either fast or slow extinction. In the latter case, we determine metastable exponents that exhibit first-order phase transitions. This is joint work with Emmanuel Jacob (ENS Lyon) and Peter Mörters (Universitat zu Köln).
We present a systematic study of kinematic formulas in convex geometry. We first give a classical presentation of kinematic formulas for integration with respect to the rotation group $SO(n)$, where Steiner's Formula, the intrinsic volumes and Hadwiger's Characterization Theorem play a crucial role. Then we will show a new extension to integration along the general linear group $GL(n)$. Using the bijection of matrix polar decomposition and a Gaussian measure to integrate along positive definite matrices, a new formula is obtained, for which the classical $SO(n)$ formula is a particular case. We also reference the unitary group $U(n)$ case and its corresponding extension to the symplectic group $Sp(2n,\mathbb{R})$.
