# Upcoming Seminars & Events

## Primary tabs

##### TBA-Alex Scott

##### On the notion of genus for division algebras and algebraic groups.

Let D be a central division algebra of degree n over a field K. One defines the genus gen(D) of D as the set of classes [D'] in the Brauer group Br(K) where D' is a central division K-algebra of degree n having the same isomorphism classes of maximal subfields as D. I will review the results on gen(D) obtained in the last several years, in particular the finiteness theorem for gen(D) when K is finitely generated of characteristic not dividing n.

##### Nonlinear stability of Minkowski spacetime for self-gravitating massive fields

I will discuss the global evolution problem for self-gravitating massive matter in the context of Einstein's theory and, more generally, of the f(R)-theory of gravity. In collaboration with Yue Ma (Xian), by analyzing the Einstein equations in wave gauge coupled to Klein-Gordon equations, I have established that Minkowski spacetime is globally nonlinearly stable in presence of massive fields. This extends fundamental works by Christodoulou and Klainerman and by Lindblad and Rodnianski, who were concerned with vacuum spacetimes and massless fields.

##### Symmetry methods for quantum variational principles and expectation value dynamics

Inspired by previous works by Kramer & Saraceno and Shi & Rabitz, this talk exploits symmetry methods for the variational formulation of different problems in physics and chemistry. First, I will use symmetry methods to provide new variational principles for the description of mixed quantum states, in various pictures including Schrödinger, Heisenberg, Dirac (interaction) and Wigner-Moyal. Then, after discussing Ehrenfest's mean-field model, I will modify its symmetry properties to provide a new variational principle for expectation value dynamics in general situations.

##### Dominating varieties by liftable ones.

Given a smooth projective variety over an algebraically closed field of positive characteristic, can we dominate it by another smooth projective variety that lifts to characteristic 0? We give a negative answer to this question.

##### Hydrodynamics of integrable classical and quantum systems

Discussed is the Euler-type hydrodynamics for one-dimensional integrable quantum systems, as the Lieb-Liniger delta Bose gas and the XXZ chain. Of particular interest are domain wall initial states. We will use classical hard rods as an illustration of the underlying structure.

##### Provably good convex methods for mapping problems

Computing mappings or correspondences between surfaces is an important tool for many applications in computer graphics, computer vision, medical imaging, morphology and related fields. Mappings of least angle distortion (conformal) and distance distortion (isometric) are of particular interest. The problem of finding conformal/isometric mappings between surfaces is typically formulated as a difficult non-convex optimization problem. Convex methods relax the non-convex optimization problem to a convex problem which can then be solved globally.

##### TBA-Congling Qiu

##### Hadamard well-posedness of the gravity water waves equations

The gravity water waves equations consist of the incompressible Euler equations and an evolution equation for the free boundary of the fluid domain. Assuming the flow is irrotational, Alazard-Burq-Zuily (Invent. Math, 2014) proved that for any initial data in Sobolev space $H^s$, the problem has a unique solution lying in the same space, here s is the smallest index required to ensure that the fluid velocity is spatially Lipschitz. We will discuss the strategy of a proof of the fact that the flow map is continuous in the strong topology of H^s.

##### TBA-Nancy Hingston

##### TBA-Jingjun Han

##### Peculiar modules for 4-ended tangles

A peculiar module is a certain algebraic invariant of 4-ended tangles that I developed in my PhD thesis as a tool for studying the local behaviour of Heegaard Floer homology for knots and links. I will briefly explain its construction and describe its classification in terms of immersed curves on a 4-punctured sphere as well as a glueing formula. Finally, I will discuss some applications, such as rational tangle detection, skein relations and mutation symmetries.

##### TAB-Massimiliano Berti

##### Recent developments in dimensional free estimates in harmonic analysis

**Please note the different time.**

We will discuss some recent developments in dimensional-free bounds for the Hardy--Littlewood averaging operators defined over convex symmetric bodies in $\mathbb R^d$. Specifically we will

##### TBA-Li-Sheng Tseng

##### Lecture 1: The games of Steiner and Poncelet and algebraic group schemes

We shall briefly present in very elementary terms the `games' of Steiner and Poncelet, amusing mathematical solitaires of the XIX Century, also related to elliptic billiards. We shall recall that the finiteness of the game is related to torsion in tori or elliptic curves.

##### Lecture 2: Torsion values for sections in abelian schemes and the Betti map

We shall consider variations in the games, related to the so-called `Betti-map', which we shall describe. We shall also illustrate some links of the Betti map with several other contexts and state some theorems on torsion values, both of existence type and finiteness type (obtained mainly in joint work with David Masser).