Department of Mathematics
  1. Representation Theory
  2. Mathematical Physics
  3. Mathematical Biology
  4. Events
  5. Research Grants
  1. Seminar Series 2013-14
Department of Mathematics

Seminar Series 2013-14

Date Speaker Room
01/10/2013 Andrea Baronchelli (City)

Title: Unconsciously rational: optimal strategies in human mental searches in online auctions

Abstract: Characterizing how we explore abstract spaces is key to understand our (ir)rational behavior and decision making. While some light has been shed on the navigation of semantic networks, however, little is known about the mental exploration of metric spaces, such as the one dimensional line of numbers, prices, etc. Here we address this issue by investigating the behavior of users exploring the "bid space" in online auctions. We find that they systematically perform Lévy flights, i.e., random walks whose step lengths follow a power-law distribution. Interestingly, this is the best strategy that can be adopted by a random searcher looking for a target in an unknown environment, and has been observed in the foraging patterns of many species. In the case of online auctions, we measure the power-law scaling over several decades, providing the neatest observation of Lévy flights reported so far. We also show that the histogram describing single individual exponents is well peaked, pointing out the existence of an almost universal behaviour. Furthermore, a simple model reveals that the observed exponents are nearly optimal, and represent a Nash equilibrium. We rationalize these findings through a simple evolutionary process, showing that the observed behavior is robust against invasion of alternative strategies. Our results show that humans share with the other animals universal patterns in general searching processes, and raise fundamental issues in cognitive, behavioural and evolutionary sciences.
08/10/2013 L. Mason (Oxford University)

Title: Scattering amplitudes and holomorphic Wilson loops

Abstract: Scattering amplitudes and correlation functions can be reformulated in twistor space in terms of holomorphic objects. I'll explain how the amplitude Wilson-loop correspondence for planar N=4 super Yang-Mills can be reformulated in twistor space and proved at the level of the loop integrand. If I have time I will discuss more recent work that shows that this leads to a simple representation of all-loop integrand in dlog form and how it can for examples be directly integrated without Feynman parameters.
15/10/2013 J. Simon (Edinburgh University)

Title: Typicality in black hole physics

Abstract : In this talk we will review the connection between black holes and thermodynamics, motivating the need for a quantum theory of gravity as the corresponding quantum statistical mechanics behind its thermodynamical behaviour. Using this perspective, we will explore the idea of quantum entanglement being responsible for the origin of thermalization. We will use our results on typicality, which are based on geometrical properties of large dimensional spheres, in quantum mechanics and 2d CFTs to give a further twist on the explanation for why Hawking's calculation is so robust.
22/10/2013 K. Sharkey (Liverpool University)

Title: Exact representations of Susceptible-Infectious-Removed (SIR) epidemic dynamics on networks

Abstract: The majority of epidemic models fall into two categories: 1) deterministic models represented by differential equations and 2) stochastic models which can be evaluated by simulation. In this presentation I will discuss the precise connection between these models. Until recently, exact correspondence was only established in situations exhibiting large degrees of symmetry or for infinite populations.

I will consider SIR dynamics on finite static contact networks. I will give an overview of two provably exact deterministic representations of the underlying stochastic model for tree-like networks. These are the message passing description of Karrer and Newman and my pair-based moment closure representation. I will discuss the relationship between the two representations and the relative merits of both.
29/10/2013 A. Tseytlin (Imperial College London)

Title: On conformal higher spin models
12/11/2013 B Vicedo (Hertfordshire) cancelled CG04
19/11/2013 A.-C. Davis (DAMTP, Cambridge) cancelled

Title: The Cosmological Chameleon

Abstract: Observations suggest the Universe is undergoing accelerated expansion today. One possible explanation for this acceleration is modified gravity. The chameleon mechanism is one such theory of modified gravity whereby potential deviations from standard can be screened in denseenvironments. I will first discuss the accelerating Universe before introducing the chameleon mechanism. I will end with ways of detecting chameleon theories and some recent work on black holes in screened, modified gravity theories.
26/11/2013 Reinhold Egger (Düsseldorf University)

Title: Majorana fermions in mesoscopic quantum transport

Abstract: Recent experiments have provided the first signatures of localized Majorana fermions through peculiar zero-bias anomalies in the conductance of semiconductor nanowires. In this talk, from a theory perspective, a broad introduction to the physics of Majorana fermion induced quantum transport will be given. After a discussion of the mathematical properties of Majorana fermions and the physical conditions for their realization, the zero bias anomaly will be traced to the phenomenon of resonant Andreev reflection. In the final part of the talk, it will be shown that in settings where Coulomb interactions are pronounced, a novel topological Kondo effect characterized by the orthogonal symmetry group, and leading to non-Fermi liquid physics, can be realized.
27/11/2013 Eirik Eik Svanes (Oxford University)

Manifolds with SU(3) structure
29/11/2013 Andrew Mathas (University of Sydney)

Title: Cyclotomic quiver Hecke algebras of type A

Abstract: Brundan and Kleshchev have shown that the cyclotomic Hecke algebras of type A are isomorphic to the cyclotomic quiver Hecke algebras of type A, which arose out of work of Khovanov and Lauda, and Rouquier. As a result these algebras, which include as special cases the group algebras of the symmetric groups, are Z-graded algebras. I will describe some of the recent developments in the graded representation theory of these algebras and show how the grading is already implicit in their classical (ungraded) representation theory.
04/12/2013 Chis Braun (City)

Title: Noncommutative localisation of algebras and modules

Abstract: Localisation is, in its simplest form, a method of adding multiplicative inverses, for example constructing the rational numbers from the integers. Localisation permeates mathematics in increasingly sophisticated guises and lies at the centre of homotopy theory. In this talk I will provide an introduction to these ideas and discuss a result connecting the localisation of an algebraic structure to the localisation of its representations. This general abstract result has a range of concrete applications, including the group completion theorem, characteristic classes of A-infinity algebras and a derived Riemann-Hilbert correspondence. This is joint work in progress with Joe Chuang and Andrey Lazarev.
10/12/2013 Toby Wood (Leeds University)

Title: No lights, no music: The pseudo-incompressible MHD equations

Abstract: Most fluid flows of interest in engineering, geophysics, and even astrophysics can be regarded as "pseudo-incompressible", in the sense that acoustic waves carry only a tiny fraction of the total energy. Numerical simulations of such flows therefore often use "wave-filtered" equations (e.g. incompressible, Boussinesq, anelastic, etc.) that are based on approximations to the fully compressible equations. Such equations are always derived under very specific physical assumptions, but are often applied in situations where these assumptions are not appropriate. In this talk, we will describe how these approximations can be improved, and generalized, by using concepts from Lagrangian mechanics.
14/01/2014 Carl M. Bender (Washington University in St. Louis and City)

Title: Nonlinear eigenvalue problems

Abstract: We present an asymptotic study of the nonlinear differential equation y'(x)=cos[\pi xy(x)] subject to the initial condition y=y(0) at x=0. Although the differential equation is nonlinear, the solutions to this initial-value problem are strikingly similar to solutions to the time-independent Schroedinger eigenvalue problem. As x increases from 0, y(x) oscillates and thus resembles a quantum wave function in a classically allowed region. At a critical value that depends on the initial condition y(0) the solution y(x) undergoes a transition; the oscillations abruptly cease and y(x) decays to 0 monotonically for large x. This transition resembles the transition in a wave function that occurs at a turning point as one enters the classically forbidden region. The initial conditions y(0) fall into discrete classes; in the nth class of initial conditions, a_{n-1}<y(0)<a_n (n=1, 2, 3, ...), y(x) exhibits exactly n maxima in the oscillatory region. The boundaries a_n of these classes are the analogs of quantum-mechanical eigenvalues. We give an asymptotic calculation of a_n for large n; this calculation corresponds to a semiclassical (WKB) calculation in quantum mechanics of high-energy eigenvalues. Our principal result is that for large n, a_n is asymptotic to A n^{1/2}$, where A=2^{1/3}. The work presented here was done by C. M. Bender, A. Fring, and J. Komijani.
28/01/2014 Chris Bowman (City)

Title: The Partition algebra and the Kronecker Problem

Abstract: The Kronecker problem asks for a combinatorial understanding of the tensor products of simple modules for the symmetric group. We shall introduce the partition algebra as a natural setting in which to study this problem and discuss new results concerning its representation theory. This is based on joint work with M. De Visscher, O. King, and R. Orellana.
04/02/2014 Ginestra Bianconi (QMUL)

Title: Statistical mechanics of multiplex networks

Abstract: A large variety of complex systems, from the brain to the weather networks and complex infrastructures, are formed by several networks that coexist, interact and coevolve forming a "network of networks". Modeling such multilayer structures and characterizing the rich interplay between their structure and their dynamical behavior is crucial in order to understand and predict complex phenomena. In this talk I will present recent works on statistical mechanics of multiplex networks. Multiplex networks are formed by N nodes linked in different layers by different networks. I will present models that generate multiplexes with different types of correlations between the layers, and characterize new percolation phenomena on multiplex networks, showing first order phase transitions, bistability or a complex phase diagram with tricriticals points and higher order critical points.
11/02/2014 Tobias Galla (University of Manchester) POSTPONED CG04
18/02/2014 Steven Donkin (University of York)

Title: Some Remarks on Gill's Theorems On Young Modules.

Abstract: In a recent paper C. Gill proves some results on the tensor product of Young modules for symmetric groups. Gill uses methods from the modular representation theory of finite groups. We here take a different point of view by first working in the context of representations of general linear groups and then applying the Schur functor (a point of view pioneered by J. A. Green). Our results are valid too (and no more difficult to obtain) in the quantised situation (of representation of quantum general linear groups and Hecke algebras). For the purposes of exposition we shall describe the situation in the classical context and then compare and contrast with the quantised context if time permits.
25/02/2014 Paul Martin (Leeds University)

Title: "Fun with partition categories"

Abstract: The Brauer category sits inside the partition category - both having elementary set-theoretic constructions. The Temperley-Lieb category sits inside these categories (in at least two different ways), but it's construction has a more geometrical flavour. We will consider geometrically defined extensions of the TL category in the Brauer and partition categories. These constructions are motivated in part by applications in computational physics, but here we will consider them from a representation theory perspective.)
11/03/2014 Giuseppe Mussardo (Sissa) CG04
18/03/2014 Anne Davis (Cambridge) CG04
25/03/2014 John McNamara (Bristol) CG04
01/04/2014 Peter Hydon (Surrey)

Title: "Difference equations by differential equation methods"

Abstract: Around twenty years ago, I heard an eminent numerical analyst say, "Any problem involving difference equations is an order of magnitude harder than the corresponding problem for differential equations." Research since that time has transformed our understanding of difference equations and their solutions. The basic geometric structures that underpin difference equations are now known. From these, it has been possible to develop systematic techniques for finding solutions, first integrals or conservation laws of a given difference equation. These look a little different to their counterparts for differential equations, mainly because the solutions of difference equations are not continuous. However, they are widely applicable and most of them do not require the equation to have special properties such as linearizability or integrability.

Find us

City, University of London

Northampton Square

London EC1V 0HB

United Kingdom

Back to top

City, University of London is an independent member institution of the University of London. Established by Royal Charter in 1836, the University of London consists of 18 independent member institutions with outstanding global reputations and several prestigious central academic bodies and activities.