Department of Mathematics
Department of Mathematics

# Seminar Series 2012-13

DateSpeakerRoom
02/10/2012 Evgeny Sklyanin (York) CG04
09/10/2012 Roland Frederick (Humboldt)

Title: Novel algebraic directions in Free Probability Theory

Abstract: Free probability theory, a species of non-commutative probability theory, is amazing for several reasons. Not only has it nice combinatorial features underlying it but also profound connections with other fields, in particular physics. Recently, we established a priori unexpected relations with some very prominent algebraic objects, in particular Hopf algebras. In this talk we will carefully introduce some of the basic features and give a glance at future directions.
CG04

Title: On Hochschild cohomology of algebras

Abstract: Hochschild cohomology is a sophisticated invariant which can be associated with any algebra over a commutative ring. The structural connections between an algebra and its Hochschild cohomology are far from being well understood. We describe some aspects of this relationship, with a particular view to applications in modular representation theory.
CG04
23/10/2012 Andrey Morozov (Leicester) CG04
30/10/2012 Jerome Gauntlett (Imperial)

Title: Holography, black holes and superconductors

Abstract: The AdS/CFT correspondence in string theory is a powerful holographic" tool to study strongly coupled quantum systems using weakly coupled gravitational techniques. It is possible that it can provide valuable insight into poorly understood systems arising in condensed matter such as high temperature superconductors. We will explain how superconducting phases can be described using holography via the construction of novel black hole solutions. We also describe the dynamical evolution of holographic superconductor via the construction of dynamical black holes. This reveals a new emergent temperature scale in the superconducting phase that also exists outside of the context of holography and could be experimentally tested.
CG04
31/10/2012 Tamara Rogers (Arizona) CG04
13/11/2012 Tina Davies (Leeds)

Title: Short-wavelength magnetic buoyancy instability

Abstract: We consider the magnetic buoyancy instability in the short-wavelength limit of Gilman (1970). In this limit the perturbation equations (a system of coupled ODEs) can be reduced to a single algebraic dispersion relation, with coefficients depending on height. Put otherwise it seems that, in this limit, a problem that would have been treated as an eigenvalue problem requiring a set of boundary conditions can be reduced to a single equation for which the boundary conditions are unimportant. Here I present asymptotics and numerical calculations to illustrate the link between the two systems, which can be viewed as being analogous to the more familiar problem of the quantum harmonic oscillator.
CG04
20/11/2012 Gerard Watts (King's) CG04
27/11/2012 David B Penman (Essex)

Title: Sums, Restricted Sums and Differences

Abstract: Given a (nonempty) set $A$ of integers, two of the most obvious things to do with it are to form the sumset $A+A=\{a+b:\,a,b\in A\}$ and the difference set $A-A=\{a-b:\,a,b\in A\}$. One might also wish to consider the restricted sumset $A\hat{+}A=\{a+b:\,a,b\in A,\,a\neq b\}$. One can then ask various obvious questions about the relationships between the sizes of various of these sets and what this implies about structure, and I shall discuss some known results on this, including generalisations to more general contexts, e.g. in group theory. An intuition one might have is that the sumset/restricted sumset will be smaller than the difference set as addition is commutative but subtraction isn't: I shall survey various known results showing that this intuition is non-trivially wrong. At the end I shall discuss some recent constructions of sets $A$ which give new record large values of $\log(|A+A|)/\log(|A-A|)$. The original part of the talk is based on joint work with my research student Matthew Wells.
CG04
04/12/2012 Nick Dorey (DAMTP) CG04
11/12/2012 Anne Kandler (City)

Title: Modelling cultural evolution: A differential equation-based framework

Abstract: Over the last three decades, cultural evolution has evolved from a useful metaphor to a legitimate scientific field. Going hand in hand with the emergence of this new field of study, mathematical and computational modelling approaches have been developed to describe the phenomenon of cultural evolution. In this talk I will show on the examples of (i) the application of the concept of neutral evolution to the archeological record and (ii) the process of language shift how such models can be constructed and how they can enhance our understanding of the process of cultural evolution
CG04
29/01/2013 David Tong (DAMTP) CG04
12/02/2013 Chris Hull (Imperial) CG04
19/02/2013 Friedrich Lenz (QMUL) CG04
26/02/2013 Alexander Veselov (Loughborough University)

Title: Universal formulae in Lie algebras and Chern-Simons theory

Abstract: In 1990s Vogel introduced an interesting parametrisation of simple Lie algebras by 3 parameters defined up to common multiple and permutations. Numerical characteristic of Lie algebra is universal if it can be expressed rationally in terms of Vogel's parameters (example - dimension of Lie algebra). I will present new universal formulae for certain Casimir eigenvalues as well as for some quantities in Chern-Simons theory on a 3D sphere, found jointly with Mkrtchyan and Sergeev.
CG04
12/03/2013 Alessandro de-Martino (City)

Title: A short trip in carbon flatland

Abstract: The exceptional properties of graphene, a new two-dimensional carbon crystal first isolated in 2004, have triggered an extraordinary amount of experimental and theoretical research. One of the reasons for the popularity of graphene is that its electronic properties are very different from those of conventional two-dimensional electronic systems and very intriguing from a fundamental point of view. In this talk I will give an introduction to the electronic properties of graphene and illustrate some of my work in this field.
CG04
18/03/2013 Inna Polichtchouk

Title: Intercomparison of General Circulation Models for Hot Extrasolar Planets

Abstract: We compare five general circulation models (GCMs), which have been recently used to study hot extrasolar planet atmospheres, under three test cases useful for assessing model convergence and accuracy. The models considered all solve the traditional primitive equations, but employ different numerical algorithms or grids. The test cases are chosen to cleanly address specific aspects of the behaviours typically reported in hot extrasolar planet simulations: 1) steady-state, 2) non-linearly evolving baroclinic wave and 3) response to fast thermal relaxation. When initialised with a steady jet, all models maintain the steadiness - except MITgcm in cubed-sphere grid. A very good agreement is obtained for a baroclinic wave evolving from an initial instability in spectral models only (see Figure 1). However, exact numerical convergence is not achieved across the spectral models: amplitudes and phases are observably different. When subject to a typical 'hot-Jupiter'-like forcing, all five models show quantitatively different behaviour - although qualitatively similar, time-variable, quadrupole-dominated flows are produced. Overall, in the tests considered here, spectral models in pressure coordinate (BOB and PEQMOD) perform the best and MITgcm in cubed-sphere grid with Shapiro filter performs the worst.
CG04
20/03/2013 Shigeo Koshitani (Chiba University)

Title: Source algebras version of Z*-theorem for odd primes
CG03
26/03/2013 Benjamin Favier (DAMTP)

Titile: Large-scale dynamos in compressible convection
CG04
09/04/2013 Andrei Bytsko (Geneva) CG04

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