Algebraic and Symplectic Geometry Seminar
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Tue, 24/04/2012 15:45 |
Algebraic and Symplectic Geometry Seminar  |
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Tue, 01/05/2012 15:45 |
Jonathan Pridham (Cambridge) |
Algebraic and Symplectic Geometry Seminar |
L3 |
| Derived moduli stacks extend moduli stacks to give families over simplicial or dg rings. Lurie's representability theorem gives criteria for a functor to be representable by a derived geometric stack, and I will introduce a variant of it. This establishes representability for problems such as moduli of sheaves and moduli of polarised schemes. | |||
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Tue, 08/05/2012 15:45 |
Algebraic and Symplectic Geometry Seminar |
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Tue, 15/05/2012 15:45 |
Balazs Szendroi (Oxford) |
Algebraic and Symplectic Geometry Seminar |
L3 |
I revisit the identification of Nekrasov's K-theoretic partition function, counting instantons on  , and the (refined) Donaldson-Thomas partition function of the associated local Calabi-Yau threefold. The main example will be the case of the resolved conifold, corresponding to the gauge group  . I will show how recent mathematical results about refined DT theory confirm this identification, and speculate on how one could lift the equality of partition functions to a structural result about vector spaces. |
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Tue, 22/05/2012 15:45 |
Timo Schurg (Bonn) |
Algebraic and Symplectic Geometry Seminar |
L3 |
| A perfect obstruction theory for a commutative ring is a morphism from a perfect complex to the cotangent complex of the ring satisfying some further conditions. In this talk I will present work in progress on how to associate in a functorial manner commutative differential graded algebras to such a perfect obstruction theory. The key property of the differential graded algebra is that its zeroth homology is the ring equipped with the perfect obstruction theory. I will also indicate how the method introduced can be globalized to work on schemes without encountering gluing issues. | |||
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Tue, 29/05/2012 15:45 |
Gavin Brown (Loughborough) |
Algebraic and Symplectic Geometry Seminar |
L3 |
| I show how to construct some Fano 3-folds that have the same Hilbert series but different Betti numbers, and so lie on different components of the Hilbert scheme. I would like to show where these fit in to a speculative (indeed fantastical) geography of Fano 3-folds, and how the projection methods I use may apply to other questions in the geography. | |||
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Tue, 05/06/2012 15:45 |
Frank Gounelas (Oxford) |
Algebraic and Symplectic Geometry Seminar |
L3 |
| This talk will be about various ways in which a variety can be "connected by higher genus curves", mimicking the notion of rational connectedness. At least in characteristic zero, the existence of a curve with a large deformation space of morphisms to a variety implies that the variety is in fact rationally connected. Time permitting I will discuss attempts to show this result in positive characteristic. | |||
