Seminários, para a disseminação informal de resultados de investigação, trabalho exploratório de equipas de investigação, actividades de difusão, etc., constituem a forma mais simples de encontros num centro de investigação de matemática.
O CAMGSD regista e publica o calendário dos seus seminários há bastante tempo, servindo páginas como esta não só como um método de anúncio dessas actividades mas também como um registo histórico.
We consider the near-critical dimer model on isoradial graphs, with Temperleyan boundary conditions. We show that the centered height function converges as the mesh size tends to zero to a limiting field which agrees with the (electromagnetically tilted) sine-Gordon model at the free fermion point. This answers a longstanding question in the field. A crucial part of the work is to develop a theory of massive holomorphicity both in the continuum and at the discrete level.
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.
