Algebraic geometry and moduli seminar

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Autumn Semester 2012

Note: The highlighted event marks the next occurring event.

Date / Time Speaker Title Location
21 September 2012
Paolo Stellari
Università di Milano
Derived categories of cubic hypersurfaces and ACM bundles  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'.
28 September 2012
Georg Oberdieck
ETH Zürich
Gromov Witten Invariants for the Hilbert scheme of 2 points of a K3 surface  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.
5 October 2012
Dr. Andrew Morrison
ETH Zurich, Switzerland
Computing motivic DT invariants  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.
19 October 2012
William Gillam
ETH Zürich
Logarithmic Flatness  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.
26 October 2012
Aaron Pixton
Princeton University
The tautological ring of the moduli space of stable curves HG G 43 
2 November 2012
Yaim Cooper
Princeton University
Stable quotients and stable maps: A comparison.  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).
9 November 2012
Qizheng Yin
University of Amsterdam, Netherlands
On the tautological ring of the universal curve  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.
16 November 2012
Dan Peterson
KTH Stockholm
The Gorenstein conjecture fails for the tautological ring of stable n-pointed genus two curves  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.
23 November 2012
Ben Davison
Oxford University
Donaldson-Thomas theory for real 3-manifolds  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.
30 November 2012
Victoria Hoskins
Universität Zürich
Stratifications of Quot schemes  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.
7 December 2012
Prof. Dr. Brent Doran
ETH Zurich, Switzerland
The moduli space of stable rational curves and non-linearizable actions HG G 43 
14 December 2012
Prof. Dr. Daniel Huybrechts
Universität Bonn
Cycles on K3 surfaces HG G 43 

Organizers: Rahul Pandharipande 

Archive: 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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Sat Jun 24 14:22:59 CEST 2017
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