Forthcoming events in this series


Thu, 29 May 2014

16:00 - 17:00
C6

Topological Insulators and K-theory

Thomas Wasserman
(Oxford University)
Abstract

Topological insulators are a type of system in condensed matter physics that exhibit a robustness that physicists like to call topological. In this talk I will give a definition of a subclass of such systems: gapped, free fermions. We will look at how such systems, as shown by Kitaev, can be classified in terms of topological K-groups by using the Clifford module model for K-theory as introduced by Atiyah, Bott and Shapiro. I will be using results from Wednesday's JTGT, where I'll give a quick introduction to topological K-theory.

Thu, 22 May 2014

16:00 - 17:00
C6

Cancelled

TBA
Thu, 15 May 2014

16:00 - 17:00
C6

Cancelled

Cancelled
Thu, 08 May 2014

16:00 - 17:00
C6

Moment maps in gauge theory

Lucas Branco
Abstract

Since their introduction in the context of symplectic geometry, moment maps and symplectic quotients have been generalized in many different directions. In this talk I plan to give an introduction to the notions of hyperkähler moment map and hyperkähler quotient through two examples, apparently very different, but related by the so called ADHM construction of instantons; the moduli space of instantons and a space of complex matrices arising from monads.

Thu, 01 May 2014

16:00 - 17:00
C6

A Fourier--Mukai transform for Higgs bundles

Jakob Blaavand
Abstract

The first half of this talk will be an introduction to the wonderful world of Higgs bundles. The last half concerns Fourier--Mukai transforms, and we will discuss how to merge the two concepts by constructing a Fourier--Mukai transform for Higgs bundles. Finally we will discuss some properties of this transform. We will along the way discuss why you would want to transform Higgs bundles.

Thu, 13 Mar 2014

16:00 - 17:00
C6

Harmonic Maps and Heat Flows

Roland Grinis
Abstract

I plan to give a non technical introduction (i.e. no prerequisites required apart basic differential geometry) to some analytic aspects of the theory of harmonic maps between Riemannian manifolds, motivate it by briefly discussing some relations to other areas of geometry (like minimal submanifolds, string topology, symplectic geometry, stochastic geometry...), and finish by talking about the heat flow approach to the existence theory of harmonic maps with some open problems related to my research.

Thu, 06 Mar 2014

16:00 - 17:00
C6

Basic examples in deformation quantisation

Emanuele Ghedin
Abstract

Following last week's talk on Beilinson-Bernstein localisation theorem, we give basic notions in deformation quantisation explaining how this theorem can be interpreted as a quantised version of the Springer resolution. Having attended last week's talk will be useful but not necessary.

Fri, 28 Feb 2014

16:00 - 17:00
L4

CALF: A period map for global derived stacks

Carmelo Di Natale
(Cambridge University)
Abstract

In the sixties Griffiths constructed a holomorphic map, known as the local period map, which relates the classification of smooth projective varieties to the associated Hodge structures. Fiorenza and Manetti have recently described it in terms of Schlessinger's deformation functors and, together with Martinengo, have started to look at it in the context of Derived Deformation Theory. In this talk we propose a rigorous way to lift such an extended version of Griffiths period map to a morphism of derived deformation functors and use this to construct a period morphism for global derived stacks.

Fri, 28 Feb 2014

14:30 - 15:30
C5

CALF: Universal D-modules

Emily Cliff
(Oxford University)
Abstract

A universal D-module of dimension n is a rule assigning to every family of smooth $n$-dimensional varieties a family of D-modules, in a compatible way. This seems like a huge amount of data, but it turns out to be entirely determined by its value over a single formal disc. We begin by recalling (or perhaps introducing) the notion of a D-module, and proceed to define the category $M_n$ of universal D-modules. Following Beilinson and Drinfeld we define the Gelfand-Kazhdan structure over a smooth variety (or family of varieties) of dimension $n$, and use it to build examples of universal D-modules and to exhibit a correspondence between $M_n$ and the category of modules over the group-scheme of continuous automorphisms of formal power series in $n$ variables

Thu, 27 Feb 2014

16:00 - 17:00
C6

Beilinson-Bernstein Localization Theorem

Georgia Christodoulou
Abstract

We will talk about the Beilinson-Bernstein localization theorem, which is a major result in geometric representation theory. We will try to explain the main ideas behind the theorem and this will lead us to some geometric constructions that are used in order to produce representations. Finally we will see how the theorem is demonstrated in the specific case of the Lie algebra sl2

Thu, 20 Feb 2014

16:00 - 17:00
C6

Doctor, I look at complex and symplectic structures and I see the same!

Roberto Rubio
Abstract

This talk will give an introduction to generalized complex geometry, where complex and symplectic structures are particular cases of the same structure, namely, a generalized complex structure. We will also talk about a sister theory, generalized complex geometry of type Bn, where generalized complex structures are defined for odd-dimensional manifolds as well as even-dimensional ones.

Thu, 13 Feb 2014

16:00 - 17:00
C6

Cancelled

Cancelled
Thu, 06 Feb 2014

16:00 - 17:00
C6

Derived equivalence between vector bundles and dg-quivers

Lam Yan
Abstract

Quivers are directed graphs which can be thought of as "space" in noncommutative geometry. In this talk, we will try to establish a link between noncommutative geometry and its commutative counterpart. We will show how one can construct (differential graded) quivers which are "equivalent" (in the sense of derived category of representations) to vector bundles on smooth varieties.

Thu, 30 Jan 2014

16:00 - 17:00
C6

Ricci Solitons and Symmetry

Alejandro Betancourt
Abstract

Ricci solitons were introduced by Richard Hamilton in the 80's and they are a generalization of the better know Einstein metrics. During this talk we will define the notion of Ricci soliton and I will try to convince you that these metrics arise "naturally" in a number of different settings. I will also present various examples and talk a bit about some symmetry properties that Ricci solitons have.

Note: This talk is meant to be introductory and no prior knowledge about Einstein metrics will be assumed (or necessary).

Thu, 23 Jan 2014

16:00 - 17:00
C6

On the zeta determinant

Elisabeth Grieger
(King's College London)
Abstract

We give a short exposition on the zeta determinant for a Laplace - type operator on a closed Manifold as first described by Ray and Singer in their attempt to find an analytic counterpart to R-torsion.

Mon, 09 Dec 2013

16:00 - 17:00
C5

A lattice construction of 2d Spin Topological Field Theories

Sebastian Novak
(University of Hamburg)
Abstract

TQFTs have received widespread attention in recent years. In mathematics

for example due to Lurie's proof of the cobordism hypothesis. In physics

they are used as toy models to understand structure, especially

boundaries and defects.

I will present a lattice construction of 2d Spin TFT. This mostly

motivated as both a toy model and stepping stone for a mathematical

construction of rational conformal field theories with fermions.

I will first describe a combinatorial model for spin surfaces that

consists of a triangulation and a finte set of extra data. This model is

then used to construct TFT correlators as morphisms in a symmetric

monoidal category, given a Frobenius algebra as input. The result is

shown to be independent of the triangulation used, and one obtains thus

a 2dTFT.

All results and constructions can be generalised to framed surfaces in a

relatively straightforward way.

Thu, 05 Dec 2013

16:00 - 17:30
C6

Groups acting on trees and beyond

Montse Casals
Abstract

In this talk, we will review the classical Bass-Serre theory of groups acting on trees and introduce its real version, Rips' theory. If time permits, I will briefly discuss some higher dimensional spaces that are currently being investigated, namely cubings and real cubings.

Thu, 28 Nov 2013

16:00 - 17:30
C6

Star products and formal connections

Paolo Masulli
(Aarhus University)
Abstract

I will introduce star products and formal connections and describe approaches to the problem of finding a trivialization of the formal Hitchin connection, using graph-theoretical computations.

Thu, 21 Nov 2013

16:00 - 17:30
C6

On the Beilinson Theorem

Alberto Cazzaniga
Abstract

We motivate and dicuss the Beilinson Theorem for sheaves on projective spaces. Hopefully we see some examples along the way.

Thu, 14 Nov 2013

16:00 - 17:30
C5

The Andersen--Kashaev TQFT

Jens-Jakob Kratmann Nissen
(Aarhus University)
Abstract

By using the Weil-Gel'fand-Zak transform of Faddeev's quantum dilogarithm,

Andersen and Kasheav have proposed a new state-integral model for the

Andersen--Kashaev TQFT, where the circle valued state variables live on

the edges of oriented levelled shaped triangulations. I will look at a

couple of examples which give an idea of how the theories are coupled.

Thu, 07 Nov 2013

16:00 - 17:30
C6

Quantum ergodicity and arithmetic heat kernels

Jan Vonk
Abstract

In this talk, I will describe how the eigenvalues of the Atkin operator on overconvergent modular forms might be related to the classical study of the Laplacian on certain manifolds. The goal is to phrase everything geometrically, so as to maximally engage the audience in discussion on possible approaches to study the spectral flow of this operator.

Thu, 31 Oct 2013

16:00 - 17:30
C6

D-modules: PDEs, flat connections, and crystals

Emily Cliff
Abstract

Motivated by the study of PDEs, we introduce the notion of a D-module on a variety X and give the basics of three perspectives on the theory: modules over the sheaf of differential operators on X; quasi-coherent modules with flat connection; and crystals on X. This talk will assume basic knowledge of algebraic geometry (such as rudimentary sheaf theory).

Thu, 24 Oct 2013

16:00 - 17:30
C6

GIT, Symplectic Reduction and the Kempf-Ness Theorem

Tom Hawes
Abstract

Consider a smooth, complex projective variety X inside P^n and an action of a reductive linear algebraic group G inside GL(n+1,C). On the one hand, we can view this as an algebra-geometric set-up and use geometric invariant theory (GIT) to construct a quotient variety X // G, which parameterises `most' of the closed orbits of X. On the other hand, X is naturally a symplectic manifold, and since G is reductive we can take a maximal real compact Lie subgroup K of G and consider the symplectic reduction of X by K with respect to an appropriate moment map. The Kempf-Ness theorem then says that the results of these two constructions are homeomorphic. In this talk I will define GIT and symplectic reduction and try to sketch the proof of the Kempf-Ness theorem.

Thu, 17 Oct 2013

16:00 - 17:30
C6

Quillen's determinant line bundle

Jakob Blaavand
Abstract

In the talk we will discuss Quillen's construction of a determinant line bundle associated to a family of Cauchy-Riemann operators. I will first of all try to convince you why this is a cool thing and mention some of the many different applications. The bulk of the talk will be focused on constructing the line bundle, its hermitian metric and calculating the curvature. Hopefully a talk accessible to many.