Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
Today
12:45
Valentina Forini
Abstract

String sigma-models relevant in the AdS/CFT correspondence are highly non-trivial two-dimensional field theories for which predictions at finite coupling exist, assuming integrability and/or the duality itself.  I will discuss general features of the perturbative approach to these models, and present progress on how to go extract finite coupling information in the most possibly general way, namely via the use of lattice field theory techniques. I will also present new results on certain ``defect-CFT’' correlators  at strong coupling. 

  • String Theory Seminar
Today
14:15
Oscar Garcia-Prada
Abstract

It is well-known that the Teichmüller space of a compact surface can be identified with a connected component of the moduli space of representations of the fundamental group of the surface in PSL(2,R). Higher Teichmüller components are generalizations of this that exist for the moduli space of representations of the fundamental group into certain real simple Lie groups of higher rank. As for the usual Teichmüller space, these components consist entirely  of discrete and faithful representations. Several cases have been identified over the years. First, the Hitchin components for split groups, then the maximal Toledo invariant components for Hermitian groups, and more recently certain components for SO(p,q). In this talk, I will describe a general construction of (still somewhat conjecturally) all possible Teichmüller components, and a parametrization of them using Higgs bundles.

  • Geometry and Analysis Seminar
Today
14:15
NILS BERGLUND
Abstract


Stochastic processes subject to weak noise often show a metastable
behaviour, meaning that they converge to equilibrium extremely slowly;
typically, the convergence time is exponentially large in the inverse
of the variance of the noise (Arrhenius law).
  
In the case of finite-dimensional Ito stochastic differential
equations, the large-deviation theory developed in the 1970s by
Freidlin and Wentzell allows to prove such Arrhenius laws and compute
their exponent. Sharper asymptotics for relaxation times, including the
prefactor of the exponential term (Eyring–Kramers laws) are known, for
instance, if the stochastic differential equation involves a gradient
drift term and homogeneous noise. One approach that has been very
successful in proving Eyring–Kramers laws, developed by Bovier,
Eckhoff, Gayrard and Klein around 2005, relies on potential theory.
  
I will describe Eyring–Kramers laws for some parabolic stochastic PDEs
such as the Allen–Cahn equation on the torus. In dimension 1, an
Arrhenius law was obtained in the 1980s by Faris and Jona-Lasinio,
using a large-deviation principle. The potential-theoretic approach
allows us to compute the prefactor, which turns out to involve a
Fredholm determinant. In dimensions 2 and 3, the equation needs to be
renormalized, which turns the Fredholm determinant into a
Carleman–Fredholm determinant.
  
Based on joint work with Barbara Gentz (Bielefeld), and with Ajay
Chandra (Imperial College), Giacomo Di Gesù (Vienna) and Hendrik Weber
(Warwick). 

References: 
https://dx.doi.org/10.1214/EJP.v18-1802
https://dx.doi.org/10.1214/17-EJP60

  • Stochastic Analysis & Mathematical Finance Seminars
Today
15:45
YUZHAO WANG
Abstract

We will talk about some stochastic parabolic and hyperbolic partial differential equations (SPDEs), which arise naturally in the context of Liouville quantum gravity. These dynamics are proposed to preserve the Liouville measure, which has been constructed recently in the series of works by David-Kupiainen-Rhodes-Vargas. We construct global solutions to these equations under some conditions and then show the invariance of the Liouville measure under the resulting dynamics. As a by-product, we also answer an open problem proposed by Sun-Tzvetkov recently.
 

  • Stochastic Analysis & Mathematical Finance Seminars
Today
16:00
Netan Dogra
Abstract

Understanding the size of the rational points on a curve of higher genus is one of the major open problems in the theory of Diophantine equations. In this talk I will discuss the related problem of understanding how close together rational points can get. I will also discuss the relation to the subject of (generalised) Wieferich primes.

  • Junior Number Theory Seminar
Today
16:00
Federica Dragoni
Abstract

I will present a $\Gamma$-convergence for degenerate integral functionals related to homogenisation problems  in the Heisenberg group. In our  case, both the rescaling and the notion of invariance or periodicity are chosen in a way motivated by the geometry of the Heisenberg group. Without using special geometric features, these functionals would be neither coercive nor periodic, so classic results do not apply.  All the results apply to the more general case of Carnot groups. Joint with Nicolas Dirr, Paola Mannucci and Claudio Marchi.

  • Partial Differential Equations Seminar
Tomorrow
10:00
Abstract

Spatial navigation in preclinical and clinical Alzheimer’s disease - Relevance for topological data analysis?

Spatial navigation changes are one of the first symptoms of Alzheimer’s disease and also lead to significant safeguarding issues in patients after diagnosis. Despite their significant implications, spatial navigation changes in preclinical and clinical Alzheimer’s disease are still poorly understood. In the current talk, I will explain the spatial navigation processes in the brain and their relevance to Alzheimer’s disease. I will then introduce our Sea Hero Quest project, which created the first global benchmark data for spatial navigation in ~4.5 million people worldwide via a VR-based game. I will present data from the game, which has allowed to create personalised benchmark data for at-risk-of-Alzheimer’s people. The final part of my talk will explore how real-world environment & entropy impacts on dementia patients getting lost and how this has relevance for GPS technology based safeguarding and car driving in Alzheimer’s disease.

Tomorrow
12:00
Marya Bazzi
Abstract

Multilayer networks are a way to represent dependent connectivity patterns — e.g., time-dependence, multiple types of interactions, or both — that arise in many applications and which are difficult to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as communities, to discover features that lie between the microscale and the macroscale. We introduce a framework for the construction of generative models for mesoscale structure in multilayer networks.  We model dependency at the level of partitions rather than with respect to edges, and treat the process of generating a multilayer partition separately from the process of generating edges for a given multilayer partition. Our framework can admit many features of empirical multilayer networks and explicitly incorporates a user-specified interlayer dependency structure. We discuss the parameters and some properties of our framework, and illustrate an example of its use with benchmark models for multilayer community-detection tools. 

 

Tomorrow
12:00
Jan Sbierski
Abstract

A well-known theorem of Choquet-Bruhat and Geroch states that for given smooth initial data for the Einstein equations there exists a unique maximal globally hyperbolic development. In particular, time evolution of globally hyperbolic solutions is unique. This talk investigates whether the same result holds for quasilinear wave equations defined on a fixed background. After recalling the notion of global hyperbolicity, we first present an example of a quasilinear wave equation for which unique time evolution in fact fails and contrast this with the Einstein equations. We then proceed by presenting conditions on quasilinear wave equations which ensure uniqueness. This talk is based on joint work with Harvey Reall and Felicity Eperon.
 

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