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Autumn Semester 2012

Date / Time Speaker Title Location
21 September 2012
16:00-17:00 		Paolo Stellari
Università di Milano
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Algebraic Geometry and Moduli Seminar

Title Derived categories of cubic hypersurfaces and ACM bundles
Speaker, Affiliation Paolo Stellari, Università di Milano
Date, Time 21 September 2012, 16:00-17:00
Location HG G 43
Abstract In this talk we use Kuznetzov's description of the derived categories of smooth cubic hypersurfaces to answer some questions concerning the geometry of such manifolds. We pay particular attention to moduli problems and we give new constructions of stable ACM bundles on cubic threefolds and fourfolds. Our approach involves moduli spaces of stable sheaves of special algebras on the projective plane and their relation to moduli of Bridgeland stable objects. This is a joint work with M. Lahoz and E. Macri'.
Derived categories of cubic hypersurfaces and ACM bundlesread_more
HG G 43
28 September 2012
16:00-17:00 		Georg Oberdieck
ETH Zürich
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Algebraic Geometry and Moduli Seminar

Title Gromov Witten Invariants for the Hilbert scheme of 2 points of a K3 surface
Speaker, Affiliation Georg Oberdieck, ETH Zürich
Date, Time 28 September 2012, 16:00-17:00
Location HG G 43
Abstract Gromov Witten Invariants for the Hilbert scheme of 2 points of a K3 surface It is explained how to obtain the reduced Gromov Witten Invariants for primitive homology classes on the Hilbert scheme of 2 points of a K3 surface. As a result, we will present the conjectured generating series for these invariants which will be given by a weak Jacobi form.
Gromov Witten Invariants for the Hilbert scheme of 2 points of a K3 surfaceread_more
HG G 43
5 October 2012
16:00-17:00 		Dr. Andrew Morrison
ETH Zurich, Switzerland
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Algebraic Geometry and Moduli Seminar

Title Computing motivic DT invariants
Speaker, Affiliation Dr. Andrew Morrison, ETH Zurich, Switzerland
Date, Time 5 October 2012, 16:00-17:00
Location HG G 43
Abstract In this talk we describe a method to compute motivic Donaldson--Thomas invariants associated to a quiver with potential. The method is valid given that the potential has a linear factor. We obtain product formulas that specialize to those for the numerical invariants previously obtained by torus localization.
Computing motivic DT invariantsread_more
HG G 43
19 October 2012
16:00-17:00 		William Gillam
ETH Zürich
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Algebraic Geometry and Moduli Seminar

Title Logarithmic Flatness
Speaker, Affiliation William Gillam, ETH Zürich
Date, Time 19 October 2012, 16:00-17:00
Location HG G 43
Abstract A morphism of fine log schemes X/Y tautologically induces a map from X to Olsson's algebraic stack Log(Y) of log schemes over Y. A coherent sheaf on X is called "logarithmically flat over Y" if and only if it is flat over Log(Y). The purpose of this talk is to unravel the meaning of logarithmic flatness, starting with an explanation of the terms in the first sentence. It turns out that, for "nodal" X/Y, log flatness boils down to the usual notions of "perfection" or "relativity" along certain loci in X used in the relative Hilbert schemes of relative Donaldson-Thomas theory. Logarithmic flatness should provide a generalization of these notions to a wider class of "degenerations" which should be of use in the study of moduli spaces of sheaves on such degenerations.
Logarithmic Flatnessread_more
HG G 43
26 October 2012
16:00-17:00 		Aaron Pixton
Princeton University
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Algebraic Geometry and Moduli Seminar

Title The tautological ring of the moduli space of stable curves
Speaker, Affiliation Aaron Pixton, Princeton University
Date, Time 26 October 2012, 16:00-17:00
Location HG G 43
The tautological ring of the moduli space of stable curves
HG G 43
2 November 2012
16:00-17:00 		Yaim Cooper
Princeton University
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Algebraic Geometry and Moduli Seminar

Title Stable quotients and stable maps: A comparison.
Speaker, Affiliation Yaim Cooper, Princeton University
Date, Time 2 November 2012, 16:00-17:00
Location HG G 43
Abstract In this talk we will discuss recent results comparing stable quotients and stable maps. We will focus on a comparison of the geometries of the moduli spaces \bar{M}_1(P^r,d) and \bar{Q}_1(P^r,d).
Stable quotients and stable maps: A comparison.read_more
HG G 43
9 November 2012
16:00-17:00 		Qizheng Yin
University of Amsterdam, Netherlands
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Algebraic Geometry and Moduli Seminar

Title On the tautological ring of the universal curve
Speaker, Affiliation Qizheng Yin, University of Amsterdam, Netherlands
Date, Time 9 November 2012, 16:00-17:00
Location HG G 43
Abstract We build connections between the tautological ring of the universal curve and the tautological ring of the universal Jacobian. The rich structures on the Jacobian side provide a new way of producing relations between tautological classes. We shall discuss various theoretical aspects and numerical evidence regarding Faber's conjectures.
On the tautological ring of the universal curveread_more
HG G 43
16 November 2012
16:00-17:00 		Dan Peterson
KTH Stockholm
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Algebraic Geometry and Moduli Seminar

Title The Gorenstein conjecture fails for the tautological ring of stable n-pointed genus two curves
Speaker, Affiliation Dan Peterson, KTH Stockholm
Date, Time 16 November 2012, 16:00-17:00
Location HG G 43
Abstract I discuss recent joint work with Orsola Tommasi, in which we show that the tautological ring of the moduli space of stable n-pointed genus two curves is not Gorenstein in general. In fact, as soon as there are non-tautological cohomology classes in even degree on this space, the Gorenstein conjecture fails. Graber and Pandharipande constructed such classes on \bar M_{2,20}; we give an alternative construction. We expect that both constructions produce the same classes, and that \bar M_{2,20} is actually the first case where there is non-tautological cohomology in even degree.
The Gorenstein conjecture fails for the tautological ring of stable n-pointed genus two curvesread_more
HG G 43
23 November 2012
16:00-17:00 		Ben Davison
Oxford University
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Algebraic Geometry and Moduli Seminar

Title Donaldson-Thomas theory for real 3-manifolds
Speaker, Affiliation Ben Davison, Oxford University
Date, Time 23 November 2012, 16:00-17:00
Location HG G 43
Abstract The category of representations of the fundamental group of a real 3 manifold is the heart of a 3 Calabi-Yau category. As such, there should be a version of motivic Donaldson-Thomas theory for moduli spaces of objects in this category. I will start by explaining how this works for Jacobi algebras, where the theory is most well-developed, and essentially much easier, for reasons that I will also explain. Finally I will present some recent work with Shende on orientation data, which was the missing piece for the foundations of this theory.
Donaldson-Thomas theory for real 3-manifoldsread_more
HG G 43
30 November 2012
16:00-17:00 		Victoria Hoskins
Universität Zürich
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Algebraic Geometry and Moduli Seminar

Title Stratifications of Quot schemes
Speaker, Affiliation Victoria Hoskins, Universität Zürich
Date, Time 30 November 2012, 16:00-17:00
Location HG G 43
Abstract Associated to a reductive group action on a projective scheme, there is a stratification whose open stratum is the GIT semistable set. We study the unstable strata for the action of a special linear group on a Quot scheme parametrising quotient sheaves. For vector bundles on a Riemann surface we recall that the Yang-Mills stratification agrees with the stratification by Harder-Narasimhan types; therefore, one may expect that our stratification should also agree with that by Harder-Narasimhan types. I explain that this is not quite the case and end with some ideas about an algebraic approach to Yang-Mills theory.
Stratifications of Quot schemesread_more
HG G 43
7 December 2012
16:00-17:00 		Prof. Dr. Brent Doran
ETH Zurich, Switzerland
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Algebraic Geometry and Moduli Seminar

Title The moduli space of stable rational curves and non-linearizable actions
Speaker, Affiliation Prof. Dr. Brent Doran, ETH Zurich, Switzerland
Date, Time 7 December 2012, 16:00-17:00
Location HG G 43
The moduli space of stable rational curves and non-linearizable actions
HG G 43
14 December 2012
16:00-17:00 		Prof. Dr. Daniel Huybrechts
Universität Bonn
Details

Algebraic Geometry and Moduli Seminar

Title Cycles on K3 surfaces
Speaker, Affiliation Prof. Dr. Daniel Huybrechts, Universität Bonn
Date, Time 14 December 2012, 16:00-17:00
Location HG G 43
Cycles on K3 surfaces
HG G 43

Organisers: Rahul Pandharipande

Archive: SS 25 AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11

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