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.
Since the groundbreaking work of M. Gromov in the 1980s many tools have been developed for distinguishing open symplectic domains. However, until recently, similar questions in the contact geometric setup were largely open. For instance, it was not known whether there are open domains in the standard contact vector space of dimension $>3$ which are diffeomorphic but not contactomorphic to it (in dimension $3$ it is known that all of them are). In my lecture I will discuss Floer theoretic tools for answering this type of questions. As one application I will construct a continuous family of pairwise non-contactomorphic open balls in the standard contact ${\mathbb R}^5$. The lecture is based on a joint work in progress with K. Ajij, Mahan Mj, Dishant Pancholi and L. Polterovich.
Bartnik introduced a notion of quasi-local mass based on a minimization procedure over asymptotically flat extensions. After reviewing the fundamental ideas behind Bartnik's approach, I will introduce a spacetime version of a Bartnik-type quasi-local mass and establish its positivity and monotonicity in time for two classes of domains associated with black holes. This is joint work with L. Andersson, M. Khuri and W. Simon.
Let us consider two notions of concentration for homogeneous polynomials in $d$ complex variables on the unit sphere: a local notion measuring the fraction of the $L^2$-norm supported on a measurable subset and a global notion given by the generalized Wehrl entropy. Lieb and Solovej proved that the extremizers in both cases are monomials up to a unitary rotation. Their result generalizes the one by Lieb in 1978 on the Wehrl entropy conjecture for coherent states in representations of the Heisenberg group to symmetric representations of the groups $\operatorname{SU}(d)$.
In this talk, we will focus on the stability of the previous inequalities. Namely, if the concentration is close to the optimal one, we will quantify how close the polynomial is to the extremizers. This is obtained in full generality in the case $d=2$, while in the case of higher dimensions restrictions on the size of the subset or on the degree of the polynomials arise. We will finally recover analogous stability results in the Bargmann–Fock space.
This is a joint work with Joaquim Ortega-Cerdà (UB-CRM).
There are many works on geometric representation theory of quiver varieties and their relation to quantum loop algebras and Yangians. Recently, I have been interested in their variants, where quiver varieties are replaced by σ-quiver varieties, the fixed point loci of involutions on quiver varieties. I will explain my recent work on geometric representation theory of σ-quiver varieties and twisted Yangian, focusing on the special case of cotangent bundles of l-step isotropic flag varieties.
