Departement Mathematik

Algebraic geometry and moduli seminar

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Frühjahrssemester 2014

Datum / Zeit Referent:in Titel Ort
21. Februar 2014
16:00-17:00 		Prof. Dr. Nicholas Perrin
Universität Düsseldorf
Details

Algebraic Geometry and Moduli Seminar

Titel Quantum K-theory of some homogeneous spaces: finiteness and positivity.
Referent:in, Affiliation Prof. Dr. Nicholas Perrin, Universität Düsseldorf
Datum, Zeit 21. Februar 2014, 16:00-17:00
Ort HG G 43
Quantum K-theory of some homogeneous spaces: finiteness and positivity.
HG G 43
28. Februar 2014
16:00-17:00 		Prof. Dr. Marc Levine
Universität Essen
Details

Algebraic Geometry and Moduli Seminar

Titel An algebraic approach to elliptic genera
Referent:in, Affiliation Prof. Dr. Marc Levine, Universität Essen
Datum, Zeit 28. Februar 2014, 16:00-17:00
Ort 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.
An algebraic approach to elliptic generaread_more
HG G 43
* 7. März 2014
14:00-15:00 		Prof. Dr. Luca Migliorini
Università di Bologna
Details

Algebraic Geometry and Moduli Seminar

Titel Support theorems for relative Hilbert schemes and compactified Jacobians of planar curves
Referent:in, Affiliation Prof. Dr. Luca Migliorini, Università di Bologna
Datum, Zeit 7. März 2014, 14:00-15:00
Ort 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.
Support theorems for relative Hilbert schemes and compactified Jacobians of planar curvesread_more
HG G 43
14. März 2014
16:00-17:00 		Prof. Dr. Alessio Corti
Imperial College London
Details

Algebraic Geometry and Moduli Seminar

Titel Mirror symmetry for orbifold del Pezzo surfaces
Referent:in, Affiliation Prof. Dr. Alessio Corti, Imperial College London
Datum, Zeit 14. März 2014, 16:00-17:00
Ort 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.
Mirror symmetry for orbifold del Pezzo surfacesread_more
HG G 43
14. März 2014
17:15-18:15 		Francesco Cavazzani
Harvard Unviersity
Details

Algebraic Geometry and Moduli Seminar

Titel Complete twisted cubics
Referent:in, Affiliation Francesco Cavazzani, Harvard Unviersity
Datum, Zeit 14. März 2014, 17:15-18:15
Ort 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.
Complete twisted cubicsread_more
HG G 43
21. März 2014
16:00-17:00 		Georg Oberdieck
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Counting rational curves in Hilb(K3,n)
Referent:in, Affiliation Georg Oberdieck, ETH Zürich
Datum, Zeit 21. März 2014, 16:00-17:00
Ort 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.
Counting rational curves in Hilb(K3,n)read_more
HG G 43
28. März 2014
16:00-17:00 		Prof. Dr. Norbert A'Campo
Universität Basel
Details

Algebraic Geometry and Moduli Seminar

Titel Old and New in plane curve topology
Referent:in, Affiliation Prof. Dr. Norbert A'Campo, Universität Basel
Datum, Zeit 28. März 2014, 16:00-17:00
Ort HG G 43
Old and New in plane curve topology
HG G 43
4. April 2014
16:00-17:00 		Prof. Dr. Timo Schuerg
Universität Augsburg
Details

Algebraic Geometry and Moduli Seminar

Titel Cohomological relations on moduli spaces of curves from Gromov-Witten theory
Referent:in, Affiliation Prof. Dr. Timo Schuerg, Universität Augsburg
Datum, Zeit 4. April 2014, 16:00-17:00
Ort 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.
Cohomological relations on moduli spaces of curves from Gromov-Witten theoryread_more
HG G 43
11. April 2014
16:00-17:00 		Prof. Dr. Martin Möller
Universität Frankfurt
Details

Algebraic Geometry and Moduli Seminar

Titel From Siegel-Veech constants to quasimodular forms
Referent:in, Affiliation Prof. Dr. Martin Möller, Universität Frankfurt
Datum, Zeit 11. April 2014, 16:00-17:00
Ort 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.
From Siegel-Veech constants to quasimodular formsread_more
HG G 43
* 16. April 2014
14:00-15:00 		Prof. Dr. Alexander Kuznetsov
University of Moskow
Details

Algebraic Geometry and Moduli Seminar

Titel Moduli spaces of instanton bundles on Fano varieties
Referent:in, Affiliation Prof. Dr. Alexander Kuznetsov, University of Moskow
Datum, Zeit 16. April 2014, 14:00-15:00
Ort HG G 19.2
Moduli spaces of instanton bundles on Fano varieties
HG G 19.2
* 7. Mai 2014
15:00-16:00 		Ran Tessler
Hebrew Univ.
Details

Algebraic Geometry and Moduli Seminar

Titel An open analog of Witten's KdV conjecture
Referent:in, Affiliation Ran Tessler, Hebrew Univ.
Datum, Zeit 7. Mai 2014, 15:00-16:00
Ort 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.
An open analog of Witten's KdV conjectureread_more
HG G 19.2
16. Mai 2014
16:00-17:00 		Prof. Dr. Jérémy Blanc
Universität Basel
Details

Algebraic Geometry and Moduli Seminar

Titel Blow-up of curves in P3 and in a cubic threefold
Referent:in, Affiliation Prof. Dr. Jérémy Blanc, Universität Basel
Datum, Zeit 16. Mai 2014, 16:00-17:00
Ort 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.
Blow-up of curves in P3 and in a cubic threefoldread_more
HG G 43
23. Mai 2014
16:00-17:00 		Prof. Dr. Tamas Hausel
EPF Lausanne
Details

Algebraic Geometry and Moduli Seminar

Titel p-adic Hamiltonian geometry
Referent:in, Affiliation Prof. Dr. Tamas Hausel, EPF Lausanne
Datum, Zeit 23. Mai 2014, 16:00-17:00
Ort 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.
p-adic Hamiltonian geometryread_more
HG G 43
* 26. Juni 2014
15:00-16:00 		Prof. Dr. Aleksey Zinger
Univ. of Stony Brook
Details

Algebraic Geometry and Moduli Seminar

Titel Enumeration of real rational curves
Referent:in, Affiliation Prof. Dr. Aleksey Zinger, Univ. of Stony Brook
Datum, Zeit 26. Juni 2014, 15:00-16:00
Ort 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.
Enumeration of real rational curvesread_more
HG G 19.1
* 7. Juli 2014
16:30-17:30 		Prof. Dr. Sean Keel
Univ. of Texas, Austin
Details

Algebraic Geometry and Moduli Seminar

Titel A canonical global positioning system for CY manifolds
Referent:in, Affiliation Prof. Dr. Sean Keel, Univ. of Texas, Austin
Datum, Zeit 7. Juli 2014, 16:30-17:30
Ort 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.
A canonical global positioning system for CY manifoldsread_more
HG G 43

Hinweise: mit einem Stern gekennzeichnete Ereignisse (*) zeigen an, dass die Zeit und/oder der Ort von der üblichen Zeit und/oder dem üblichen Ort abweichen.

Organisatoren:innen: Rahul Pandharipande

Archiv: FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 FS 21 HS 20 FS 20 HS 19 FS 19 HS 18 FS 18 HS 17 FS 17 HS 16 FS 16 HS 15 FS 15 HS 14 FS 14 HS 13 FS 13 HS 12 FS 12 HS 11

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