Werkgroep 'Algebra en Meetkunde'
Tijd en Plaats, / Time Table
During the academic year 2011-2012 there will be regular
meetings starting on Monday September 19th 2011.
Program
- September 19, 2011, Tijd/time :16.00
Jochen Heinloth:
On motives of moduli spaces of Higgs bundles
We want to explain a recent approach to the computation of the
cohomology of the moduli spaces of Higgs bundles on curves. We begin the
computation by a computation for the moduli stacks of chains, avoiding
the variation of stability parameters.
This is joint work with O. Garcia-Prada and A. Schmitt.
- Zaal/Room: Science Park A1.04
- October 3, 2011, Tijd/time :16.00
Chris van Dorp:
Constructing generators for a module of vector-valued Siegel modular forms
By generalising the Rankin-Cohen bracket, we will construct vector-valued
modular forms of genus $2$ weight $\Sym^6\otimes\det^k$ with $k$ odd. We
then show that the constructed forms generate all modular forms of weight
$\Sym^6\otimes\det^k$ as a module over the ring of classical modular forms
of even weight.
- Thursday (!) October 27, 2011, Tijd/time :16.00
Miles Reid (Warwick) : Gorenstein in dimension 4.
- Zaal/Room: Science Park D1.110
- Monday November 28, 2011,
Tijd/time :15.00 ; Room D1.114
Motohico Mulase (UC Davis): The mirror dual of Catalan numbers and the Eynard-Orantin formalism
Abstract: Homological mirror symmetry is a categorial equivalence
between a derived Fukaya category on the A-model side and a derived
category of coherent sheaves on the B-model side. If we place Catalan
numbers on the A-model side, then what is the B-model mirror counterpart?
By answering this question, I will introduce the Eynard-Orantin
formalism, which is a conjectural universal B-model for all integrable
Gromov-Witten theory. Still a general mathematical theory is under
construction, so this talk is focused on presenting a concrete example
for which all details are mathematically proved.
The talk is elementary, and no prerequisite is assumed.
Time: 16:00; Room D 1.114
George Shabat( Moscow):
On the critical stratification of moduli spaces of curves
Click here
for the abstract.
- December 5, 2011, Tijd/time :15.00; Room A1.08
Alexandr Buryak: Cohomology groups of quasihomogeneous Hilbert schemes
Abstract:
We consider Nakajima's quiver varieties associated to cyclic graphs. We
prove that for the particular action of the torus the Betti numbers of the
fixed point set are equal (with a shift) to the Betti numbers of the quiver
variety. As an application we find the generating series of Betti numbers
of quasihomogeneous Hilbert schemes and get new combinatorial identities.
The talk is based on joint work with B. L. Feigin.
- December 12, 2011, Tijd/time :16.00; Room A1.04
Karl Roekaeus: The class of a torus in the Grothendieck ring of varieties
Abstract: We compute the images of certain tori inside the Grothendieck ring of varieties, expressing them in terms of the class of the affine line and of zero-dimensional varieties.
- January 23, 2012; Tijd/time :16.00; Room B0.209
Petr Dunin-Barkovskiy:
Lattice theta constants vs Riemann theta constants and NSR superstring
measures
Abstract:
We discuss relations between two different representations of hypothetical
holomorphic NSR superstring measures, based on two different ways of)--(all)---
constructing Siegel semi-modular forms of weight 8. One of these ways is to
build forms from the ordinary Riemann theta constants and another one -- from
the lattice theta constants. We discuss unexpectedly elegant relations between
lattice theta constants, corresponding to 16-dimensional self-dual lattices,
and Riemann theta constants and present explicit formulae expressing the former
ones through the latter. This allows us to explicitly prove that two available
ans\"atze for NSR measures coincide with each other up to genus 4. Starting
from genus 5 the modular-form approach to construction of NSR measures runs
into problems and there is a risk that it fails completely already at genus 6.
------------------
Based on P. Dunin-Barkowski, A. Morozov, A. Sleptsov, "Lattice theta constants
vs Riemann theta constants and NSR superstring measures", Journal of High
Energy Physics 10 (2009) 072, arXiv:0908.2113.
- January 30, 2012; Tijd/time :16.00; Room A1.04
Gavril Farkas:
Green's conjecture for curves on arbitrary K3 surfaces
Abstract:
Mark Green's Conjecture on syzygies of canonical curves, has been one of
the most studied questions in the theory of Riemann surfaces in the last
few decades. Formulated in 1984 and still open in its full generality, it
is a deceptively simple statement which predicts that the intrinsic
geometry of the curve (in the form of linear series) can be recovered in a
precise way from the extrinsic geometry of the canonical embedding (in the
form of syzygies). I will discuss how one can use Voisin's solution to
Green's Conjecture for GENERAL curves together with the geometry of the
moduli space of curves, in order to prove Green's Conjecture for ALL
curves lying on K3 surfaces. This is joint work with M. Aprodu.
- March 5, 2012; Tijd/time :16.00; Room B0.209
Mehdi Tavakol:
Tautological classes on the space of stable n-pointed curves of compact type of genus one.
- Tuesday March 13, 2012; Time: 16:00, Room D1.113
Lenny Taelman: Arithmetic of the Carlitz module
Abstract: The Carlitz module is a fundamental object of function field
arithmetic, discovered independently by Carlitz in the 1930s and by
Drinfeld in the 1970s. In this talk I will explain what this object
is, describe its role in function field arithmetic, and present some
recent progress on its more subtle arithmetic properties.
- Monday March 19, 2012; Time: 16:00, Room B0.209
Nicolai Reshetikhin : On moduli spaces of flat superconnections
Abstract:
Locally, a superconnection is a mixed form in
a $\Z$ graded vector bundle which satisfies the flatness condition
$dA+\frac{1}{2}[A\wedge A]=0$. This talk is a survey of
classical field theories where moduli spaces of such superconnections,
and other similar moduli spaces, appear as gauge classes of solutions
to Euler-Lagrange equations for certain classical gauge field theories.
- Tuesday March 27, 2012; Time: 16:00, Room B0.209
Guenter Harder: t.b.a. This talk is cancelled.
- Monday May 7, 2012; Time: 16:00, Room A1.06
Oleg Karpenkov (TU Graz): Geometry of continued fractions
Abstract: In this talk we show a generalization geometry of numbers
encoded in the corresponding continued fractions. We introduce the
basics of lattice trigonometry which is behind this geometric
interpretation and discuss its applications to toric geometry. Finally
we show the link between infinitesimal continued fractions and
trajectories of points that moves according to the second Kepler law.
- Monday June 4, 2012; Time: 16:00, Room ?
Karl Roekaeus: New curves with many points over small finite fields
Abstract:
We use class field theory to search for curves with many rational
points, finding a number of improvements of the old records. In particular, we
settle the question of how many points a curve over F2 of genus 17 can have, by
finding one with 18 points.
Voor verdere inlichtingen kan men terecht bij
Gerard van der Geer. Belangstellenden zijn van harte welkom.