Department of Mathematics Colloquia
The talks are relaxed and non-technical and they are accessible to all the postgraduate students. They are followed by a drinks reception.
Tuesday, 29 January 2019 at 3.30 pm
Location: K-1.56, King's Building, Strand Campus
Speaker: Professor Anna Erschler (ENS, Paris)
Title: Random walks, amenability and growth
Abstract: Random walks on groups provide numerous probabilistic invariants of the group. In case of finitely generated groups, these invariants are closely related to geometry of the corresponding Cayley graph. A challenging problem is to relate probabilistic invariants to algebraic properties of the group in question.
In my talk, I review recent results about Poisson boundaries, transition probabilities, isoperimetry and drift of the random walks, and discuss their application to amenability and growth of groups.
Tuesday, 12 March 2019 at 3.30 pm
Location: BH(S)2.03, bush House, Strand Campus
Speaker: Professor Satya Majumdar (Univerisite de Paris-Sud, France)
Title: KPZ Story
Abstract: The celebrated KPZ equation (Kardar, Parisi, Zhang, 1986) is an important milestone in statistical physics, originally introduced to describe the late time dynamics in two dimensional growth models. Over the last 30 years, the KPZ story has evolved in various interesting directions, making links on the way to different areas of physics and mathematics. This includes in particular the link to the famous Tracy-Widom distribution in random matrix theory. The story of KPZ is a very successful one, involving theoretical physics, mathematics and experiments - a fertile playground for interdisciplinary science. In this talk, I will review the evolution of the KPZ story, pointing out the important landmarks as I go along. At the very end, I will discuss some recent developments establishing a nice link between the KPZ height fluctuations and the edge physics in cold atom systems.
Tuesday, 19 March 2019 at 3.30 pm
Location: K-1.56, King's Building, Strand Campus
Speaker: Prof. Zeev Rudnick (Tel Aviv University/Israel Institute of Advanced Studies, Israel)
Title: Quantum chaos, eigenvalue statistics and the Fibonacci sequence
Abstract: One of the outstanding insights obtained by physicists working on “Quantum Chaos” is a conjectural description of local statistics of the energy levels of simple quantum systems according to crude properties of the dynamics of classical limit, such as integrability, where one expects Poisson statistics, versus chaotic dynamics, where one expects Random Matrix Theory statistics.
I will describe in general terms what these conjectures say and discuss joint work with Valentin Blomer, Jean Bourgain and Maksym Radziwill, in which we study the size of the minimal gap between the first N eigenvalues for one such simple integrable system, a rectangular billiard having irrational squared aspect ratio. For quadratic irrationalities, such as the golden ratio, we show that the minimal gap is about 1/N, consistent with Poisson statistics. In the case of the golden ratio, the problem involves some curious properties of the Fibonacci sequence.
Tuesday, 9 October 2018 at 3.30 pm
Location: Franklin-Wilkins Building 3.52, Waterloo Campus
Speaker: Professor Eugenia Malinnikova (Norwegian University of Science and Technology)
Title: An improvement of the Liouville theorem for discrete harmonic functions
Abstract: We discuss the discrete version of the Laplace operator on the standard lattice Z^2 and Z^d. On Z^2, we prove that if a harmonic function is bounded on a large portion of the lattice then it is constant. This is no longer true on Z^d, d>2. The talk is based on a joint work with L. Buhovsky, A. Logunov and M. Sodin.
Tuesday, 30 October 2018 at 3.30 pm
Location: Strand Building S-1.27, Strand Campus
Speaker: Professor Noga Alon (Princeton & Tel-Aviv Universities)
Title: Vectors, graphs and codes
Abstract: What is the maximum possible Euclidean norm of a sum of n unit vectors so that any three of them contain an orthogonal pair? What is the maximum number of binary vectors of length n so that there is no binary vector within distance (1/4+epsilon) n from more than two of them? What is the maximum number f=f(m) so that every triangle-free graph with m edges contains a bipartite subgraph with at least f edges? I will describe a construction of pseudo-random Cayley graphs with extremal spectral properties which can be used in tackling these three problems and several related ones.
Tuesday, 13th November 2018 at 3.30 pm
Location: 342 N, Norfolk Building (3rd Floor), Strand Campus
Speaker: Professor Nathanaël Berestycki, University of Vienna/University of Cambridge
Title: Picking a surface, uniformly at random
Abstract: What does a random surface look like? And what does it mean anyway to pick a surface uniformly at random? These questions and related others arise naturally in the physics of quantum gravity, and have been the subject of intense research on the mathematical side in the last few years. After discussing aspects of a canonical notion of random surface, I will discuss interesting and counter-intuitive aspects of its geometry. I will also explain some of the outstanding conjectures in this field, as well as some progress that has been made.
Information about previous colloquia can be found here.