Mon, 12 Jan 2009
14:00
L3

Zermelo set theory, Mac Lane set theory and set forcing

Adrian Mathias
(Reunion)
Abstract

Over certain transitive models of Z, the usual treatment of forcing goes awry. But the provident closure of any such set is a provident model of Z, over which, as shown in "Provident sets and rudimentary set forcing", forcing works well. In "The Strength of Mac Lane Set Theory" a process is described of passing from a transitive model of Z + Tco to what is here called its lune, which is a larger model of Z + KP.

Theorem: Over a provident model of Z, the two operations of forming lunes and generic extensions commute.

Corresponding results hold for transitive models of Mac Lane set theory + Tco.

Tue, 17 Feb 2009

15:45 - 16:45
L3

Flag varieties and the HOMFLY polynomial II

Jacob Rasmussen
(Cambridge)
Abstract

Khovanov homology is an invariant of knots in $S^3$. In its original form,

it is a "homological version of the Jones polynomial"; Khovanov and

Rozansky have generalized it to other knot polynomials, including the

HOMFLY polynomial.

In the second talk, I'll discuss how Khovanov homology and its generalizations lead to a relation between the HOMFLY polynomial and the topology of flag varieties.

Tue, 10 Feb 2009

15:45 - 16:45
L3

Moduli theoretic compactifications of the space of smooth rational curves

Young-Houn Kiem
(Seoul National University)
Abstract

The space of smooth rational curves of degree d in projective space admits various moduli theoretic compactifications via GIT, stable maps, stable sheaves, Hilbert scheme and so on. I will discuss how these compactifications are related by explicit blow-ups and -downs for d

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