29/04/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Filippo Viviani, University Rome 3
On the birational geometry of the universal Picard variety
We compute the Kodaira dimension and the Iitaka fibration of the universal Picard variety parameterizing line bundles of degree on curves of genus under the (technical) assumption that . We also give partial results for arbitrary degrees and we investigate for which degrees the universal Picard varieties are birational. This is a joint work with G. Bini and C. Fontanari.
29/04/2011, 13:30 — 14:30 — Room P3.10, Mathematics Building
Yongbin Ruan, Michigan University
Gromov-Witten theory of elliptic orbifold and quasi-modular form
Gromov-Witten invariants count the number of pseudo-holomorphic curves. One often writes them in terms of generating functions. Occasionally, it posses some very beautiful properties such as being a quasi-modular form. In the talk, we will explain this phenomenon for elliptic orbifold . This is a joint work with Milanov, Krawitz and Shen.
21/03/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Michael Viscardi, Harvard University
Alternate compactifications of the moduli space of genus one maps
14/03/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Arnaud Beauville, Nice University
Involutions of holomorphic symplectic manifolds
The involutions of K3 surfaces have been completely classified by Nikulin. Can we extend his results to holomorphic symplectic manifolds, the natural generalization of K3 surfaces in higher dimension? I will describe some (very partial) results obtained recently in this direction.
07/03/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Vivek Shende, Princeton University
Hilbert schemes of singular curves and the HOMFLY polynomial of their links
28/02/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Richard Thomas, Imperial College
Nodal curves old and new
I will describe a classical problem going back to 1848 (Steiner, Cayley, Salmon,...) and a solution using simple techniques, but techniques that one would never really have thought of without ideas coming from string theory (Gromov-Witten invariants, BPS states) and modern geometry (the Maulik-Nekrasov-Okounkov-Pandharipande conjecture). In generic families of curves on a complex surface , nodal curves - those with the simplest possible singularities - appear in codimension 1. More generally those with nodes occur in codimension . In particular a d-dimensional linear family of curves should contain a finite number of such nodal curves. The classical problem - at least in the case of being the projective plane - is to determine this number. The Göttsche conjecture states that the answer should be topological, given by a universal degree polynomial in the four numbers and . There are now proofs in various settings; a completely algebraic proof was found recently by Tzeng. I will explain a simpler approach which is joint work with Martijn Kool and Vivek Shende.
21/02/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Vivek Shende, Princeton University
Hilbert schemes of plane curve singularities and the singularities of Severi varieties
14/02/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Indranil Biswas, TIFR (Bombay)
Brauer group of some moduli of bundles on a curve
07/02/2011, 15:00 — 16:00 — Room P3, Mathematics Building, IST
Pietro Tortella, SISSA
Moduli spaces for Lie-algebroid connections
In a paper of '94 C. Simpson constructed moduli spaces for a large class of objects, namely semistable -modules. Main examples of this include flat connections, Higgs bundles, connection along foliations and logaritmic connections. We shall show that Simpson's axioms for the algebra canonically associate to it a Lie algebroid and an element of the second cohomology of the algebroid, so that the objects that one get through Simpson's formalism are Lie algebroid connections whose curvature is controlled by the second cohomology class.
17/12/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building
Alina Marian, University of Illinois at Chicago
Verlinde Relations in the Tautological Ring of
06/12/2010, 15:00 — 16:00 — Room P3, Mathematics Building, IST
Paul Johnson, Imperial College
Polynomiality and Hurwitz Numbers
19/11/2010, 15:00 — 16:00 — Room P3.31, Mathematics Building
Rahul Pandharipande, Princeton University
Hilbert schemes II
08/11/2010, 15:00 — 16:00 — Room P3, Mathematics Building, IST
Andrea Bruno, Università di Roma III
On the automorphism group of
25/10/2010, 15:00 — 16:00 — Room P3, Mathematics Building, IST
Yaim Cooper, Princeton University
The geometry of stable quotients in genus 1
18/10/2010, 15:00 — 16:00 — Room P3, Mathematics Building, IST
Aaron Pixton, Princeton University
Rationality of the stable pairs vertex
04/10/2010, 15:00 — 16:00 — Room P3, Mathematics Building, IST
Rahul Pandharipande, Princeton University
Hilbert schemes I
15/09/2010, 15:00 — 16:00 — Room P3, Mathematics Building, IST
Carel Faber, KTH Stockholm
Cohomology of the the moduli space of curves via point counting
27/08/2010, 15:00 — 16:00 — Room P3, Mathematics Building, IST
Ivan Smith, University of Cambridge
Quadrics, 3-manifolds and Floer cohomology