School of Mathematics

Statistical mechanics models undergoing a phase transition often exhibit rich, fractal-like behaviour at their critical points, which are described in part by critical exponents, the indices governing the power-law growth or decay of various...

The Loewner energy is a Möbius invariant quantity that measures the roundness of Jordan curves on the Riemann sphere. It arises from large deviation deviations of SLE0+ and is also a Kähler potential on the Weil-Petersson Teichmüller space...

Donaldson-Thomas (DT) invariants of a quiver with potential can be expressed in terms of simpler attractor DT invariants by a universal formula. The coefficients in this formula are calculated combinatorially using attractor flow trees. In joint...

This lecture is devoted to a survey on explicit stability results in Gagliardo-Nirenberg-Sobolev and logarithmic Sobolev inequalities. Generalized entropy methods based on carré du champ computations and nonlinear diffusion flows can be used for...

Given any bounded multiplicative function a deep conjecture of Elliott predicts

cancellations of the form for all distinct shifts unless it is ``close" to the modulated Dirichlet character in an

appropriate sense. Partial progress towards this...

The Lipschitz extension problem is the following basic “meta question” in metric geometry:  Suppose that X and Y are metric spaces and A is a subset of X. What is the smallest K such that every Lipschitz function f:A\to Y has an extension F:X\to Y...

How do we describe the topology of the space of all nonconstant holomorphic (respectively, algebraic) maps F: X--- greater than Y  from one complex manifold (respectively, variety) to another? What is, for example, its cohomology? Such problems are...

A CSS quantum code C=(W1,W2) is a pair of orthogonal subspaces in 𝔽n2. The distance of C is the smallest hamming weight of a vector in W⊥1−W2 or W⊥2−W1. A large distance roughly means that the quantum code can correct many errors that affect the...

Hives, as defined by Knutson and Tao, are discrete concave functions on a triangular grid on an equilateral triangle of side n. It is known through the work of Knutson and Tao that the probability distribution of the spectrum of the sum of two...

We consider the Schramm-Loewner evolution (SLE_{kappa}) for kappa in (4,8), which is the regime that the curve is self-intersecting but not space-filling. We let K be the set of kappa in (4,8) for which the adjacency graph of connected components of...