We will be joined by Frances Kirwan to talk about the various careers available for Mathematicians and how to be a successful applicant.

We will be joined by Charlotte Turner-Smith to discuss issues surrounding harassment and mental health, and how the department is helping to tackle these.

Come along for free pizza and to hear about the Mathematrix events this term.

Electric 1-form symmetries are generically broken in gauge theories with Chern-Simons terms. In this talk we discuss how infinite subsets of these symmetries become non-invertible topological defects. Time permitting we will also discuss generalizations and applications to the Swampland program in relation to the completeness hypothesis.

Given a cover U of a family of smooth complex algebraic varieties, we associate with it a class C of structures locally definable in an o-minimal expansion of the reals, containing the cover U.  We prove that the class is ℵ0-homogeneous over submodels and stable. It follows that C is categorical in cardinality ℵ1. In the one-dimensional case we prove that a slight modification of C is an abstract elementary class categorical in all uncountable cardinals.
 

Conformal Field Theories (CFT) are believed to be exactly solvable once their primary scaling fields and their 3-point functions are known. This input is called the spectrum and structure constants of the CFT respectively. I will review recent work where this conformal bootstrap program can be rigorously carried out for the case of Liouville CFT, a theory that plays a fundamental role in 2d random surface theory and many other fields in physics and mathematics. Liouville CFT has a probabilistic formulation on an arbitrary Riemann surface and the bootstrap formula can be seen as a "quantization" of the plumbing construction of surfaces with marked points axiomatically discussed earlier by Graeme Segal. Joint work with Colin Guillarmou, Remi Rhodes and Vincent Vargas

This talk is motivated by computing correlations for domino tilings of the Aztec diamond.  It is inspired by two of the three distinct methods that have recently been used in the simplest case of a doubly periodic weighting, that is the two-periodic Aztec diamond. This model is of particular probabilistic interest due to being one of the few models having a boundary between polynomially and exponentially decaying macroscopic regions in the limit. One of the methods to compute correlations, powered by the domino shuffle, involves inverting the Kasteleyn matrix giving correlations through the local statistics formula. Another of the methods, driven by a Wiener-Hopf factorization for two- by-two matrix valued functions, involves the Eynard-Mehta theorem. For arbitrary weights the Wiener-Hopf factorization can be replaced by an LU- and UL-decomposition, based on a matrix refactorization, for the product of the transition matrices. In this talk, we present results to say that the evolution of the face weights under the domino shuffle and the matrix refactorization is the same. This is based on joint work with Maurice Duits (Royal Institute of Technology KTH).  

I will present two examples of log-correlated fields in 2 dimensions. It is well known that the log-characteristic polynomial of a uniform unitary matrix converges toward a 1 dimensional log-correlated field, and our first example will be obtained from a dynamical version of this model. The second example will be obtained from a radically different construction, based on the Brownian loop soup that we will introduce. It will lead to a whole family of log-correlated fields. We will focus on the description of the behaviour of these objects, more than on rigorous details.

Conformal blocks appear in several areas of mathematical physics from random geometry to black hole physics. A probabilistic notion of conformal blocks using gaussian multiplicative chaos measures was recently formulated by Promit Ghosal, Guillaume Remy, Xin Sun, Yi Sun (arxiv:2003.03802). In this talk, I will show that the semiclassical limit of the probabilistic conformal blocks recovers a special case of the elliptic form of Painlevé VI equation, thereby proving a conjecture by Zamolodchikov. This talk is based on an upcoming paper with Promit Ghosal and Andrei Prokhorov.

I will present recent results on the growth of entanglement between two adjacent regions in a tripartite, one-dimensional many-body system after a quantum quench. Combining a replica trick with a space-time duality transformation a universal relation between the entanglement negativity and Renyi-1/2 mutual information can be derived, which holds at times shorter than the sizes of all subsystems. The proof is directly applicable to any local quantum circuit, i.e., any lattice system in discrete time characterised by local interactions, irrespective of the nature of its dynamics. The derivation indicates that such a relation can be directly extended to any system where information spreads with a finite maximal velocity. The talk is based on Phys. Rev. Lett. 129, 140503 (2022).