A ��������t Hooft loop is a typical disorder operator defined in any gauge theory that can be studied by a combination of holography, localization and integrability. After reviewing the quantum mechanics magnetic monopoles, I will describe how integrability and Bethe ansatz can help to study ��������t Hooft loops in the N=4 super-Yang-Mills theory.

Gaussian Processes and the Kullback-Leibler divergence have been deeply studied in Statistics and Machine Learning. This paper marries these two concepts and introduce the local Kullback-Leibler divergence to learn about intervals where two Gaussian Processes differ the most. We address subtleties entailed in the estimation of local divergences and the corresponding interval of local maximum divergence as well. The estimation performance and the numerical efficiency of the proposed method are showcased via a Monte Carlo simulation study. In a medical research context, we assess the potential of the devised tools in the analysis of electrocardiogram signals.

I will discuss sharp estimates for the norm of the operator ���identity minus conditional expectation���. They allow one to find the optimal constant in the bounded compact approximation property of Lp([0, 1]), 1 < p < infty. I will also discuss related open problems. The talk is based on a joint paper with T. Sharia.

Kreck and Su have recently described, almost completely, the mapping class group of a smooth hypersurface in CP^4. There is a "monodromy" map from the fundamental group of the space of all smooth hypersurfaces in CP^4 to this mapping class group, and I will explain how the image of this map can be described. I will then give some idea of the differential topology methods which go into the proof.

Let X be a simple random walk in \mathbb{Z}_n^d with d\geq 3 and let t_{\rm{cov}} be the expected time it takes for X to visit all vertices of the torus. In joint work with Pr��vost and Rodriguez we study the set \mathcal{L}_\alpha of points that have not been visited by time \alpha t_{\rm{cov}} and prove that it exhibits a phase transition: there exists \alpha_* so that for all \alpha>\alpha_* and all \epsilon>0 there exists a coupling between \mathcal{L}_\alpha and two i.i.d. Bernoulli sets \mathcal{B}^{\pm} on the torus with parameters n^{-(a\pm\epsilon)d}with the property that \mathcal{B}^-\subseteq \mathcal{L}_\alpha\subseteq \mathcal{B}^+ with probability tending to 1 as n\to\infty. When \alpha\leq \alpha_*, we prove that there is no such coupling.

In these lectures we will provide a basic introduction to Supergravity as it arises in String Theory and M-Theory. We will start by introducing vielbeins and spin connections in order to construct supergravity actions. In the second lecture we will briefly introduce the maximal supergravity theories in ten and eleven-dimensions. We will briefly discuss special holonomy manifolds, explicitly construct BPS p-brane solutions and prove their non-perturbative stability. Time permitting we will discuss toroidal compactifications and U-duality.

I will assume basic MSc level material (Riemannian geometry, fermions and rigid supersymmetry). The lecture notes that will be provided are largely self-contained but the text book �������Supergravity������� by Freedman and van Proeyen contains more details.

This time, there will be two lectures (one in the morning and one in the afternoon), with pizza lunch in between them.

An elliptic curve over a characteristic zero field is said to have complex multiplication when its endomorphism ring is larger than Z ("E has extra endomorphisms"). Generic elliptic curves don't have complex multiplication. Often one tries to understand elliptic curves via their Tate modules. When the Tate module of E has extra endomorphisms we say E has formal complex multiplication. Over a number field, E has formal complex multiplication if and only if it has complex multiplication. Over a local field this need not be the case. How often does this happen?

The two-stage examination method is a variant on exam taking whereby students are asked to take the same exam twice --- once in the 'usual' way, and the second time in small groups of three to four. It has been used in mathematics, physics and engineering since its inception 20 years ago at UBC in Vancouver, but is normally used in basic modules in the first or second year.

I will talk about a trial I am running on two-stage exams in a Masters level class. Here, the focus will be a bit different: I use the second part, in groups, to ask the students slightly more open-ended questions. In this talk I will talk about the concept, my observations, and the challenges that were faces in the first implementation.

The geometry and topology of negatively curved manifolds are subtly reflected in a geometric bound for the Laplace eigenvalues, a connection that has been explored since the 1980s. Building upon these foundational studies in the case of the Laplacian, we investigate the Steklov eigenvalues of pinched negatively curved manifolds with totally geodesic boundary. These eigenvalues are associated with a first-order elliptic pseudodifferential operator known as the Dirichlet-to-Neumann operator. We discuss how the results for Laplace eigenvalues can be extended to Steklov eigenvalues. In particular, we show a spectral gap for the Steklov eigenvalue problem in negatively curved manifolds with dimensions of at least three. This talk is based on joint work with Ara Basjmaian, Jade Brisson, and Antoine M��tras.