Mon, 29 Oct 2012

12:00 - 13:00
L3

String compactifications on SU(3) structure manifolds

Magdalena Larfors
(Oxford)
Abstract

In the absence of background fluxes and sources, the compactification of string theories on Calabi-Yau threefolds leads to supersymmetric solutions.Turning on fluxes, e.g. to lift the moduli of the compactification, generically forces the geometry to break the Calabi-Yau conditions, and to satisfy, instead, the weaker condition of reduced structure. In this talk I will discuss manifolds with SU(3) structure, and their relevance for heterotic string compacitications. I will focus on domain wall solutions and how explicit example geometries can be constructed.

Mon, 15 Oct 2012

12:00 - 13:00

The Hodge Plot of Toric Calabi-Yau Threefolds. Webs of K3 Fibrations from Polyhedra with Interchangeable Parts

Andrei Constantin
(Oxford)
Abstract
Even a cursory inspection of the Hodge plot associated with Calabi-Yau threefolds that are hypersurfaces in toric varieties reveals striking structures. These patterns correspond to webs of elliptic-K3 fibrations whose mirror images are also elliptic-K3 fibrations. Such manifolds arise from reflexive polytopes that can be cut into two parts along slices corresponding to the K3 fibers. Any two half-polytopes over a given slice can be combined into a reflexive polytope. This fact, together with a remarkable relation on the additivity of Hodge numbers, explains much of the structure of the observed patterns.
Mon, 08 Oct 2012

12:00 - 13:00
L3

Lines on the Dwork Pencil of Quintic Threefolds

Philip Candelas
(Oxford)
Abstract
I will discuss some of the subtleties involved in counting lines on Calabi-Yau threefolds and then discuss the lines on the Dwork pencil of quintic threefolds. It has been known for some time that the manifolds of the pencil contain continuous families of lines and it is known from the work of Angca Mustata that there are 375 discrete lines and also two families parametrized by isomorphic curves that are 125:1 covers of genus six curves $C_{\pm\varphi}$. The surprise is that an explicit parametrization of these families is not as complicated as might have been anticipated.  We find, in this way, what should have anticipated from the outset, that the curves $C_\varphi$ are the curves of the Wiman pencil.  
Fri, 28 Sep 2012

15:05 - 15:45
L1

Efficient computation of Rankin $p$-adic L-functions

Alan Lauder
(Oxford)
Abstract

I will present an efficient algorithm for computing certain special values of Rankin triple product $p$-adic L-functions and give an application of this to the explicit construction of rational points on elliptic curves.

Tue, 12 Jun 2012
10:30
Gibson 1st Floor SR

The Nekrasov Partition Function

Tim Adamo
(Oxford)
Abstract
Abstract: We'll try to learn something about Nekrasov's conjecture/theorem, which relates an instanton-counting partition function to the Seiberg-Witten prepotential of N=2 SYM theory on R^4. This will entail a review of some salient aspects of N=2 SYM theories, Witten's description of Donaldson invariants in terms of correlation functions in those theories, and the physical and mathematical definition of Nekrasov's partition function. Depending on time, I might talk about computational techniques for the partition function, methods of proof for Nekrasov's conjecture, or the partition function's role in the AGT conjectures.
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