## Geometry and Physics Seminars

### Programme

All seminars are held at 11:00am in room M/2.06, Senghennydd Road, Cardiff unless stated otherwise. All are welcome.

Programme Organiser and Contact: Professor Stefan Hollands

##### 7 October 2011

**Speaker:** Jan Holland (Cardiff)

**Title:** Algebraic structures in quantum field theory.

**Abstract:** TBC

##### 14 October 2011

**Speaker: **Andrew Bruce.

**Title:** L_{\infty}-algebroids and higher Schouten structures.

**Abstract:** L_{\infty}-algebras are the "homotopy-relative" of Lie
algebras. That is we have a series of n-array brackets (n \geq 0) on a
vector space that satisfies a series of higher order Jacobi
identities. In this talk I describe how to pass from a vector space
to a vector bundle and define the notion of an L_{\infty}-algebroid. I
will also show that such algebroids can be encoded in an
L_{\infty}-algebra version of a Schouten bracket.

##### 18 November 2011

**Speaker:** Florian Robl (Cardiff)

**Title:** Nuclearity and split property in Algebraic Quantum Field Theory

**Abstract:** TBC

##### 25 November 2011

**Speaker:** Roger Behrend (Cardiff)

**Title:** Proof of the alternating sign matrix and descending plane partition conjecture.

**Abstract:** Alternating sign matrices (ASMs) and descending plane partitions (DPPs) are combinatorial objects, each of which arose about 30 years ago, but in somewhat different contexts. However, it was conjectured by Mills, Robbins and Rumsey in 1983 that these objects are closely connected. Specifically, they conjectured that certain finite sets of ASMs have the same sizes as certain finite sets of DPPs, where these sets are comprised of all ASMs or DPPs with fixed values of particular statistics. In this talk, some background on ASMs and DPPs will be discussed, and some details of the first known proof of the conjecture will be presented. The proof will use various intermediate combinatorial objects and results, but no prior knowledge of these will be assumed. This is joint work with Philippe Di Francesco and Paul Zinn-Justin.

##### 9 December 2011

**Speaker:** Stephen Fairhurst (Cardiff).

**Title:** TBC

**Abstract:** TBC

##### 17 February 2012

**Speaker:** Thomas Prellberg (Queen Mary, University of London)

**Title:** Exact solution of a model of a vesicle attached to a wall subject

to mechanical deformation.

**Abstract:**Area-weighted Dyck-paths are a two-dimensional model for vesicles attached

to a wall. We model the mechanical response of a vesicle to a pulling

force by extending this model, and find a resulting non-trivial phase

transition.

We obtain an exact solution using two different approaches, leading to a

q-deformation of an algebraic functional equation, and a q-deformation of

a linear functional equation with a catalytic variable, respectively.

While the non-deformed linear functional equation is solved by

substitution of special values of the catalytic variable (the so-called

"kernel method"), the q-deformed case is solved by iterative substitution

of the catalytic variable.

This talk will be a gentle introduction to the modern techniques available

for studying this and a large class of related problems.

##### 27 April 2012

**Speaker:** Mark Hannam (Cardiff).

**Title:** Worse than dummies: black holes for computers.

**Abstract:** Numerical solutions of Einstein's equations for configurations of colliding black holes are an essential part of efforts to detect gravitational waves. They are also a rich source of problems in mathematical relativity, numerical analysis, and numerical methods. In this talk I will focus on the novel representations of black-hole geometries that have appeared in numerical simulations, some of the issues we have in disentangling physical effects from "mere" coordinate (gauge) artifacts, and some of the remaining open questions in the field.