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.
Mon, 28 May 2012
15:45
L3

Links with splitting number one

Marc Lackenby
(Oxford)
Abstract

 The unknotting number of a knot is an incredibly difficult invariant to compute.
In fact, there are many knots which are conjectured to have unknotting number 2 but for
which no proof of this is currently available. It therefore remains an unsolved problem to find an
algorithm that determines whether a knot has unknotting number one. In my talk, I will
show that an analogous problem for links is soluble. We say that a link has splitting number
one if some crossing change turns it into a split link. I will give an algorithm that
determines whether a link has splitting number one. (In the case where the link has
two components, we must make a hypothesis on their linking number.) The proof
that the algorithm works uses sutured manifolds and normal surfaces.

Mon, 28 May 2012

15:45 - 16:45
L3

Links with splitting number one

Marc Lackenby
(Oxford)
Abstract
The unknotting number of a knot is an incredibly difficult invariant to compute. In fact, there are many knots which are conjectured to have unknotting number 2 but for which no proof of this is currently available. It therefore remains an unsolved problem to find an algorithm that determines whether a knot has unknotting number one. In my talk, I will show that an analogous problem for links is soluble. We say that a link has splitting number one if some crossing change turns it into a split link. I will give an algorithm that determines whether a link has splitting number one. (In the case where the link has two components, we must make a hypothesis on their linking number.) The proof that the algorithm works uses sutured manifolds and normal surfaces.

Subscribe to Oxford