# Geometry Tea

Geometry Tea is the junior geometry seminar series in Cambridge covering all aspects of geometry. Talks are usually given by PhD students or postdocs and take place on Fridays in MR13 at 3pm at the DPMMS, followed by tea and biscuits in the Pavilion E common room. If you would like to give a talk or invite a speaker please get in touch. Expenses can be reimbursed by the department for external speakers, roughly on the level of travel from London.

## Current Year | 2015-16 | 2014-15 | 2013-14

### Lent Term 2017

27/1: Mihajlo Cekić (DPMMS). Calderon problem for Yang-Mills connections We will consider the problem of identifying the connection up to gauge equivalence from the associated Dirichlet-to-Neumann map in the case of Yang-Mills connections. I will sketch the proof in the smooth case for line bundles. The approach is based on picking a special gauge in which the Yang-Mills equations become elliptic and using a unique continuation principle for elliptic systems for identification near the boundary. Along the way, I will try to explain how pseudodifferential operator symbol calculus plays its role in the proof.

3/2: James Gundry (DAMTP). Connections in Twistor Theory Twistor theory solves the self-dual 4D Einstein equations in a single-step procedure by employing complex geometry. In this talk I will review this construction and emphasise the lesser-known role played by affine connections in twistor theory. An understanding of the direct construction of such connections allows us to describe a new version of twistor theory for Newton-Cartan manifolds, in which the connections are not metric.

10/2: Daniel Lütgehetmann (FU Berlin). Configuration Spaces of Graphs The configuration space of a finite number of particles in a topological space is an object of interest in many areas of mathematics, in particular if the ambient space is a manifold. While the geometry of configuration spaces of manifolds is understood quite well, the case of particles in general simplicial complexes remains rather mysterious, even for 1-dimensional complexes. In this talk, I will describe an efficient combinatorial model for configurations of particles in a finite graph, which was first defined by Jacek Światkowski. Afterwards, I will sketch the other techniques we used to prove torsion-freeness and representation stability of those configuration spaces' homology.

24/2: Marco Golla (Uppsala). Heegaard Floer correction terms, semigroups, and plane cuspidal curves What does a low-dimensional topologist think when he sees a curve in the complex projective plane? What do semigroups have to do with Heegaard Floer homology? Come and find out the answer to these and other exciting questions!

3/3: Raúl Sánchez Galán (UCL). Monopoles in $$\mathbb{R}^3$$ We will start defining and giving an overview of monopoles. Then I will explain the calculation of the virtual dimension of the moduli space of SU(2) monopoles on asymptotically conic 3-manifolds done by C. Kottke and its generalisation to SU(n). Finally I will discuss monopoles with singularities.

10/3: Manuel Krannich (University of Copenhagen). Moduli Spaces of Manifolds Initiated by the solution of the Mumford conjecture by Madsen and Weiss shedding light on the cohomology of the moduli space of smooth complex algebraic curves, tremendous progress in our understanding of manifold bundles and moduli spaces of manifolds has recently been made. In this talk, I will make the adventurous attempt to give an overview of this impressive development in geometric topology during the past two decades.

17/3: Paul Wedrich (Imperial). Skein algebra, 3-manifolds and categorification The Jones polynomial and its cousins are invariants of knots and links in the 3-sphere, which are determined by local so-called skein relations. This allows a simple definition of an invariant of oriented 3-manifolds M: the space of all framed links in M modulo the skein relations. Of particular interest are these invariants for thickened surfaces, in which case they carry an algebra structure and act on the invariants of 3-manifolds co-bounding the surface. They are also related to character varieties, quantum Teichmueller spaces and feature in several important conjectures in quantum topology. After surveying this area, I will talk about positive bases for skein algebras that were found by D. Thurston, and how they might be related to Khovanov's categorification of the Jones polynomial and its desired extension to a 4-dimensional TQFT.

### Michaelmas Term 2016

last updated on the 14th March 2017