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Postgraduate Seminar 2009-10

Warwick Mathematics Institute

Postgraduate Seminar

Term II, 2009-2010

Please contact Sara Maloni or if you would like to speak or suggest a speaker.

Wednesday January 20, 12:00, room MS.03

Sohail Iqbal

Title: Q-Gorenstein smoothing.

Abstract: Q-Gorenstein smoothing is a technique of construction of algebraic surfaces. An introduction followed by some constructions will be given.

Wednesday January 27, 12:00, room MS.03

Speaker 1 (h 12:00): Jorge Vitória

Speaker 2 (h 12:20): Nicholas Korpelainen

Speaker 3 (h 12:40): Andrew Ferguson

Title 1: Sequences of mutations.

Abstract 1: Quiver mutation is an interesting process with many algebraic concepts attached to it. We will mention some of these key concepts while presenting a solution to the problem of identifying when is a sequence of mutations the identity.

Title 2: How to eat a pizza greedily, how to draw a big grid in a provably inefficient way and how to make infinitely many of one's descendants incomparable.

Abstract 2: This talk will offer quick glimpses into three parallel worlds of algorithmic and structural graph theory. In particular, it will give you partial knowledge and mysterious hints on how to eat a pizza greedily, how to draw big grid in a provably inefficient way and how to make infinitely many of your descendants incomparable.

Title 3: Iterated Function Systems.

Abstract 3: Iterated functions systems provide a framework in which one may study a wide class of fractals. In this talk we give a brief overview of the theory and then discuss some of it's possible applications.

Wednesday February 3, 12:00, room MS.03

Eleonora Pinto De Moura

Title: Embeddings of finite-dimensional sets.

Abstract: In this talk, we will discuss linear embeddings of finite-dimensional subsets of Hilbert spaces into Euclidean spaces. We will then study a simple example that shows that the bound on the Hölder exponent obtained by Hunt and Kaloshin (1999) is asymptotically sharp.

Wednesday February 10, 12:00, room MS.03

Janosch Ortmann

Title: Eigenvalues of Random Matrices.

Abstract: I will give an introduction to random matrix theory, assuming no prior knowledge of probability theory, and indicate how the field was motivated by problems in physics. We will consider how the eigenvalues of certain square random matrices behave in the limit as the size of the matrix tends to infinity. We will then introduce a parameter, viewed as time, and describe the eigenvalue dynamics as the parameter varies, keeping fixed the size of the matrix.

Wednesday February 17, 12:00, room MS.03

Dr. Marj Batchelor (Cambridge University)

Title: Linyi Mathematics Summer School.

Abstract: Dr Batchelor will be talking about a project to take research and MSc students from Cambridge, Oxford and Warwick to spend three weeks from 16th August to 6th September at Linyi Normal University, Shandong Province, China. The students will each give a lecture course on an area of mathematics to the students of Linyi University. The projects goal is to raise the research potential at Linyi by exposing them - both students and staff - to effective research level seminar practise.

Wednesday February 24, 12:00, room MS.03

Andrew Ferguson

Title: An introduction to the thermodynamic formalism.

Abstract: The thermodynamic formalism has its roots in statistical mechanics with the study of systems with a large number of particles. The main ingredients of this theory; Gibbs states, entropy and pressure have since invaded dynamical systems and been used to great effect. In this talk I will give a brief overview of the theory, and time permitting, some of it's many applications.

Wednesday March 3, 12:00, room MS.03

Michele Torielli

Title: Linear free divisor and quiver representations.

Abstract: In this talk, we will first introduce the notion of linear free divisor and then of quiver representations. Moreover, we will give an idea about how to construct linear free divisor from quiver representations. Finally,we will give concrete examples of this construction.

Wednesday March 10, 12:00, room MS.03

Ben Sharp

Title: Harmonic Mappings of Riemannian Surfaces and the Harmonic Map Flow.

Abstract: In this talk we will define what it means for a map between Riemannian manifolds to be harmonic and give some examples of such maps. We can then talk about the harmonic map flow of Riemannian surfaces, and how solutions to this flow give exitence of harmonic maps, and in some cases, exitence of harmonic maps in every homotopy class. If there is time we will talk in a bit more detail about the bubbling phenomenon and in particular bubbling at infinity.

Wednesday March 17, 12:00, room MS.03

Bing Kwan So

Title: Singular objects needs singular differential calculus -- Pseudo-differential calculus defined by groupoids.

Abstract: In this talk, I shall introduce the notion of Lie groupoids, and explain how they are used to define interesting classes of pseudo-differential operators that are adapted to singular objects. The discussion would be based on examples, most importantly that of manifolds with boundary and the Bruhat sphere. In particular, the Fredholmness problem and index theory of these examples will be outlined.

Warwick Mathematics Institute

Postgraduate Seminar

Term III, 2009-2010

Wednesday March 31, 12:00, room B3.03

Barinder Banwait

Title: The Birch and Swinnerton-Dyer Conjecture.

Abstract: I shall explain this remarkable conjecture, and why it is important.

Wednesday April 7, 12:00, room B3.03

Thomas Kempton

Title: Ergodic Optimisation.

Abstract: We will state an interesting problem in ergodic optimisation and use it as impetus for a gentle discussion of some key concepts in ergodic theory which have been applied to dynamical systems, number theory and hyperbolic geometry. We will also mention a couple of open problems in the area which are extremely simple to state but seem rather more difficult to solve.

Wednesday April 21, 12:00, room B3.03

Jorge Vitória

Title: A leisurely walk in noncommutative algebraic geometry.

Abstract: It is said that there are "more noncommutative geometries than noncommutative geometers". In this talk I will outline the general ideas behind some algebraic approaches to noncommutative geometry.

Wednesday April 28, 12:00, room B3.03

David Howden

Title: Word reduction in Coxeter groups.

Abstract: We begin by introducing Coxeter groups and derive some basic word length properties. We then explore some basic theory of regular languages and their connection to finite Automata. Combining these ideas we construct an Automaton which recognises minimal length expressions for Coxeter groups and outline a procedure for determining the minimal representation for a given word.

Wednesday May 12, 12:00, room B3.03

Mikolaj Sierzega

Title: The business of evolution PDEs.

Abstract: Evolutionary equations are equations determining temporal change of a given system. Among those, evolution PDEs play a special role as they encode physical laws in mathematical framework. In this talk I will briefly explain why and how we study evolution PDEs.

Wednesday May 19, 12:00, room B3.03

Neha Gupta

Title: A journey into Frobenius World.

Abstract: Starting from an ordinary notion of a Frobenius algebra lifting the concept to a general monoidal category, I take you one level higher where monoidal categories themselves can be examples. I will also discuss how these Frobenius structures give rise to topological Quantum Field theories in dimension 2.

Wednesday May 26, 12:00, room B3.03

Yuxin Yang

Title: Hodge decomposition in infinite dimensions.

Abstract: I will talk about some of the attempts to extend the classical Hodge theory to infinite dimensions and the difficulties involved.

Wednesday June 2, 12:00, room B3.03

Sarah Davis

Title: Resolution of singularities.

Abstract: In this talk I will explain how to resolve quotient singularities by blow-ups. I will introduce the famous ADE singularities, which have particularly nice representations. I will go on to discuss how toric geometry gives a nice method for blowing-up singularities. No prior knowledge of algebraic geometry will be assumed.

Wednesday June 9, 12:00, room B3.03

Damon McDougall

Title: Bayesian data assimilation for a toy model.

Abstract: I will talk about what data assimilation is and make a few links to climate science. I will start with the very basics and build a data assimilation problem from a very toy model and mention two approaches that scientists take in solving these problems. I will then talk about some difficult issues that arise in climate science and end with a nice video. The talk will be pitched pretty low and should be accessible to almost anyone who wishes to come. No advanced or technical knowledge should be needed.