Mon, 08 Jun 2026
15:30 -
16:30
L3
Thu, 30 Apr 2026
17:00
17:00
L3
Large fields, Galois groups, and NIP fields
Will Johnson
(Fudan University)
Abstract
A field K is "large" if every smooth curve over K with at least one K-rational point has infinitely many K-rational points. In this talk, I'll discuss what we know about the relations between the arithmetic condition of largeness and the model-theoretic conditions of stability and NIP. Stable large fields are separably closed. For NIP large fields, we know something much weaker: there is a canonical field topology satisfying a weak form of the implicit function theorem for polynomials. Conjecturally, any stable or NIP infinite field should be large. I will discuss these results, as well as the following conjecture: if K is a field and p is a prime and every separable extension of K has degree prime to p, then K is large. This conjecture would imply that NIP fields of positive characteristic are large, and would classify stable fields of positive characteristic. I will present some (very weak) evidence for this conjecture.
Thu, 26 Mar 2026
15:00 -
17:00
L3
Renormalisation group on Lorentzian manifolds using (p)AQFT
Kasia Rejzner
(University of York)
Abstract
I will start the talk by discussing renormlisation group in perturbative algebraic quantum field theory (pAQFT) and its non-perturbative incarnation acting on the Buchholz-Fredenhagen dynamical C*-algebra. I will also explain how pAQFT can be used to derive functional renormlisation group (FRG) equations that generalize Wetterich equations to globally hyperbolic Lorentzian manifolds and arbitrary states (beyond the usual FRG in the vacuum).
Thu, 26 Mar 2026
11:00 -
13:00
L3
Mathematics behind perturbative quantisation of gauge theories on curved spacetimes
Kasia Rejzner
(University of York)
Abstract
In this talk I will briefly introduce the framework of perturbative algebraic quantum field theory (pAQFT), which is a mathematically rigorous formulation of perturbative QFT that works on a large class of Lorentzian manifolds (globally hyperbolic ones). Then I will focus on the problem of quantisation of gauge theories, which is performed using the Batalin-Vilkovisky (BV) framework. I will also discuss the connection to the factorization algebras framework of Costello and Gwilliam.
Mon, 11 May 2026
15:30 -
16:30
L3
Formation of clusters and coarsening in weakly interacting diffusions
Prof. Greg Pavliotis
(Imperial)
Abstract
We study the clustering behavior of weakly interacting diffusions under the influence of sufficiently localized attractive interaction potentials on the one-dimensional torus. We describe how this clustering behavior is closely related to the presence of discontinuous phase transitions in the mean-field PDE. For local attractive interactions, we employ a new variant of the strict Riesz rearrangement inequality to prove that all global minimizers of the free energy are either uniform or single-cluster states, in the sense that they are symmetrically decreasing. We analyze different timescales for the particle system and the mean-field (McKean-Vlasov) PDE, arguing that while the particle system can exhibit coarsening by both coalescence and diffusive mass exchange between clusters, the clusters in the mean-field PDE are unable to move and coarsening occurs via the mass exchange of clusters. By introducing a new model for this mass exchange, we argue that the PDE exhibits dynamical metastability. We conclude by presenting careful numerical experiments that demonstrate the validity of our model.
Mon, 27 Apr 2026
15:30 -
16:30
L3
Fractional Black-Scholes model and Girsanov transform for sub-diffusions
Prof. Zhen-Qing Chen
(University of Washington)
Abstract
We propose a novel Black-Scholes model under which the stock price processes are modeled by stochastic differential equations driven by sub-diffusions. The new framework can capture the less financial activity phenomenon during the bear markets while having the classical Black-Scholes model as its special case. The sub-diffusive spot market is arbitrage-free but is in general incomplete. We investigate the pricing for European-style contingent claims under this new model. For this, we study the Girsanov transform for sub-diffusions and use it to find risk-neutral probability measures for the new Black-Scholes model. Finally, we derive the explicit formula for the price of European call options and show that it can be determined by a partial differential equation (PDE) involving a fractional derivative in time, which we coin a time-fractional Black-Scholes PDE.