Algebraic geometry and moduli seminar

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Spring Semester 2014

Note: The highlighted event marks the next occurring event and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Date / Time Speaker Title Location
21 February 2014
Prof. Dr. Nicholas Perrin
Universität Düsseldorf
Quantum K-theory of some homogeneous spaces: finiteness and positivity. HG G 43 
28 February 2014
Prof. Dr. Marc Levine
Universität Essen
An algebraic approach to elliptic genera  HG G 43 
Abstract: This is a report on a joint work with Y. Yang and G. Zhao. We give a purely algebraic approach to a result of Totaro, namely, that the ideal in the Lazard ring (with \Q-coefficients) generated by the difference of classcial flops coincides with the kernel of Krichever's elliptic genus. This result is valid for varieties over a perfect field of arbitrary characteristic. We also prove some general results on the existence of a universal oriented cohomology theory on smooth varieties: over a field of characteristic zero, this is the Levine-Morel-Pandharipande theory of algebraic cobordism, over a perfect field of postivie characteristic, this is shown to exist in the case of \Q-coefficients and is thenthe geometric part of Voevodsky's algebraic cobordism.
* 7 March 2014
Prof. Dr. Luca Migliorini
Università di Bologna
Support theorems for relative Hilbert schemes and compactified Jacobians of planar curves  HG G 43 
Abstract: Given a reduced and irreducible singular curve C with planar singularities, the Betti numbers of its Hilbert schemes and its compactified Jacobian are related by a MacDonald type formula type (Maulik-Yun, Migliorini-Shende, Rennemo). One way to prove this is to imbed the curve in a versal family and prove an analogue of Ngo's support theorem for the relative HIlbert scheme family. If the curve is still reduced, but reducible, though, the relation between the Betti numbers of the HIlbert schemes and of the compactified Jacobian is more subtle: the analogue of Ngo's support theorem fails for the relative Hilbert scheme family, while continuing to hold for the compactified Jacobian family. I will discuss this failure and the correcting terms one has to introduce, involving compactified Jacobian families of connected sub-curves of C. Work in progress with V. Shende and F. Viviani.
14 March 2014
Prof. Dr. Alessio Corti
Imperial College London
Mirror symmetry for orbifold del Pezzo surfaces  HG G 43 
Abstract: I will state some interconnected conjectures on (a) the algebraic geometry and moduli spaces, and (b) mirror symmetry, for orbifolds del Pezzo surfaces. I will present some of the evidence. This is joint work in progress with many people and students of the PRAGMATIC school held last Summer in Catania.
14 March 2014
Francesco Cavazzani
Harvard Unviersity
Complete twisted cubics  HG G 43 
Abstract: Finding characteristic numbers of twisted cubics is a very old problem that can be traced back to Schubert's book "Kalkül der abzählenden Geometrie" in 1879. Even though many solutions have been proposed since then, we still do not have a completely satisfactory moduli space, expecially when it comes to more intricate problems involving tangency or multisecancy conditions. Following the construction of wonderful compactifications by De Concini and Procesi, and taking as model the space of complete conics, we propose a new compactification of the space of twisted cubics; we will show some properties of this space, and discuss why this choice could lead to new characteristic numbers. If time permits, we will describe the geometry in codimension 1 and 2 of the boundary. This is a work in progress (hopefully) towards a PhD thesis.
21 March 2014
Georg Oberdieck
ETH Zürich
Counting rational curves in Hilb(K3,n)  HG G 43 
Abstract: Let X be a smooth projective surface and let Hilb^n(X) be its Hilbert scheme of points parametrizing zero-dimensional subschemes on X. This is a smooth projective variety of dimension 2n and an open set will parametrize n distinct unordered points on X. A particular interesting case is X a K3 surface. Then Hilb^n(X) will inherit from X a holomorphic symplectic form and is projective hyperkaehler. I will explain how to count the number of rational curves in Hilb^n(X) for several good cases (any n). For the K3 surface, this count was classicly given by the Yau-Zaslow formula in terms of the Fourier coefficients of the modular discriminant. In our case, the results will be given by the Fourier coefficients of certain Jacobi Forms of index n-1, the two dimensional analog of modular forms. For n = 1, this will specialize to the YZ expression.
28 March 2014
Prof. Dr. Norbert A'Campo
Universität Basel
Old and New in plane curve topology HG G 43 
4 April 2014
Prof. Dr. Timo Schuerg
Universität Augsburg
Cohomological relations on moduli spaces of curves from Gromov-Witten theory  HG G 43 
Abstract: I will review how Jun Li’s degeneration formula leads to natural relations between cohomology classes on moduli spaces of curves. I will then discuss possible applications to the question if virtual fundamental classes of moduli spaces of stable maps are tautological classes.
11 April 2014
Prof. Dr. Martin Möller
Universität Frankfurt
From Siegel-Veech constants to quasimodular forms  HG G 43 
Abstract: Siegel-Veech constants arise characteristic quantities of billard tables, counting the asymptotic growth rate of closed trajectories. We interpret Siegel-Veech constants as intersection numbers of cohomology classes on Hurwitz spaces and show that their generating functions are quasimodular forms. This can be used to determine the large genus asymptotics of Siegel-Veech constants.
* 16 April 2014
Prof. Dr. Alexander Kuznetsov
University of Moskow
Moduli spaces of instanton bundles on Fano varieties HG G 19.2 
* 7 May 2014
Ran Tessler
Hebrew Univ.
An open analog of Witten's KdV conjecture  HG G 19.2 
Abstract: We define the moduli space of stable marked discs and its tautological line bundles. We continue to define intersection numbers for these bundles. It turns out that, the generating series of these numbers obeys an integrable system of PDEs very similar to the KdV equations in the closed case. If time permits we will prove a topological recursion (in genus 0). Based on a joint work with R. Pandharipande and J. Solomon.
16 May 2014
Prof. Dr. Jérémy Blanc
Universität Basel
Blow-up of curves in P3 and in a cubic threefold  HG G 43 
Abstract: In 2012, Stéphane Lamy and myself characterised smooth curves in P3 whose blow-up produces a threefold with anticanonical divisor big and nef. These are curves C of degree d and genus g lying on a smooth quartic, such that (i) 4d−30 ≤ g ≤ 14 or (g,d) = (19,12), (ii) there is no 5-secant line, 9- secant conic, nor 13-secant twisted cubic to C. This generalises the classical similar situation for the blow-up of points in P2. In this talk, I will describe the situation for curves in a smooth cubic threefold, and also show that the geometry of this threefold seems to be as rich as the one of P3.
23 May 2014
Prof. Dr. Tamas Hausel
EPF Lausanne
p-adic Hamiltonian geometry  HG G 43 
Abstract: We discuss a p-adic analytic approach to the Liouville volume of symplectic quotients, by finding arithmetic analogues of the Duistermaat-Heckman theorem. In good cases it will specialize to the point count of symplectic quotients over finite fields. This gives an analytic approach to the arithmetic volume of symplectic varieties; and in particular justifies the use of the term "volume" for point count over finite fields.
* 26 June 2014
Prof. Dr. Aleksey Zinger
Univ. of Stony Brook
Enumeration of real rational curves  HG G 19.1 
Abstract: The classical problem of enumerating rational curves in projective spaces is solved using a recursion formula for Gromov-Witten invariants. In this talk, I will describe a similar relation for real Gromov-Witten invariants with conjugate pairs of constraints. An application of this relation provides a complete recursion for counts of real rational curves with such constraints in odd-dimensional projective spaces. I will outline the proof and discuss some vanishing and non-vanishing results. This is joint work with P. Georgieva.
* 7 July 2014
Prof. Dr. Sean Keel
Univ. of Texas, Austin
A canonical global positioning system for CY manifolds  HG G 43 
Abstract: I'll explain, in language aimed at a second year graduate student in geometry, my conjecuture, joint with Gross and Hacking, that an affine variety with (the right sort of) volume form comes with "theta functions", a canonical basis of regular functions, summarize our results -- the proof in dim 2, and, together with Kontsevich, for cluster varieties of all dimensions, and then spend most of the talk explaining some of the many applications to representation theory, birational geometry, Teichmuller theory, and mirror symmetry.

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 14:23:05 CEST 2017
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