Wed, 04 Jun 2008
12:00 -
13:00
L3
Techniques for one-loop amplitudes in QCD
Giulia Zanderighi
(Oxford)
Abstract
Abstract: We discuss recent techniques to compute one-loop amplitudes in QCD and show that all N-gluon one-loop helicity amplitudes can be computed numerically for arbitrary N with an algorithm which has a polynomial growth in N.
Mon, 28 Apr 2008
12:00 -
13:00
L3
$G_2$ manifolds with isolated conical singularities
Spiro Karigiannis
(Oxford)
Abstract
Abstract: Compact $G_2$ manifolds with isolated conical singularities arise naturally in M-theory. I will discuss such manifolds, and explain a method to ``desingularize'' them by glueing in pieces of asymptotically conical $G_2$ manifolds. There are topological obstructions to such desingularizations that depend on the rate of convergence to the cone at the singularities, and on the geometry of the links of the cones. If time permits, I will also briefly discuss a new related project with Dominic Joyce which could provide the first examples of such manifolds, as well as a possible new construction of smooth compact $G_2$ manifolds.
Wed, 30 Apr 2008
16:00
16:00
L3
Mon, 12 May 2008
14:15
14:15
L3
Tue, 03 Jun 2008
15:45 -
16:45
L3
Generalized Donaldson-Thomas invariants. II. Invariants and transformation laws.
Dominic Joyce
(Oxford)
Abstract
This is the second of two seminars this afternoon describing a generalization of Donaldson-Thomas invariants, joint work of Yinan Song and Dominic Joyce. (Still work in progress.)
Behrend showed that conventional Donaldson-Thomas invariants can be written as the Euler characteristic of the moduli space of semistable sheaves weighted by a "microlocal obstruction function" \mu.
In previous work, the speaker defined Donaldson-Thomas type invariants "counting" coherent sheaves on a Calabi-Yau 3-fold using
Euler characteristics of sheaf moduli spaces, and more generally, of moduli spaces of "configurations" of sheaves. However, these invariants are not deformation-invariant.
We now combine these ideas, and insert Behrend's microlocal obstruction \mu into the speaker's previous definition to get new generalized Donaldson-Thomas invariants. Microlocal functions \mu have a multiplicative property implying that the new invariants transform according to the same multiplicative transformation law as the previous invariants under change of stability condition.
Then we show that the invariants counting pairs in the previous seminar are sums of products of the new generalized Donaldson-Thomas invariants. Since the pair invariants are deformation invariant, we can deduce by induction on rank that the new generalized Donaldson-Thomas invariants are unchanged under deformations of the underlying Calabi-Yau 3-fold.
Tue, 03 Jun 2008
14:15 -
15:15
L1
Generalized Donaldson-Thomas invariants. I. An invariant counting pairs.
Yinan Song
(Oxford)
Abstract
This is the first of two seminars this afternoon describing a generalization of Donaldson-Thomas invariants, joint work of Yinan Song and Dominic Joyce. We shall define invariants "counting" semistable coherent sheaves on a Calabi-Yau 3-fold. Our invariants are invariant under deformations of the complex structure of the underlying Calabi-Yau 3-fold, and have known transformation law under change of stability condition.
This first seminar constructs an auxiliary invariant "counting" stable pairs (s,E), where E is a Gieseker semistable coherent sheaf with fixed Hilbert polynomial and s : O(-n) --> E for n >> 0 is a morphism of sheaves, and (s,E) satisfies a stability condition. Using Behrend-Fantechi's approach to obstruction theories and virtual classes we prove this auxiliary invariant is unchanged under deformation of the underlying Calabi-Yau 3-fold.