Zurich Colloquium in Mathematics
A Panorama
Universität Zürich, Karl Schmid Strasse 4, 8006 Zürich, Kollegiengebäude 2, Hörsaal K02-F-150
Dienstag: 17.15 bis 18.15 Uhr
Spring Semester 2012
| Date |
Speaker |
Title |
Location |
| 21-feb-2012 (tue) |
Richard Thomas
|
The Göttsche conjecture
|
KO2 F 150 |
| Abstract: |
I will describe a classical problem going back to 1848 (Steiner, Cayley, Salmon,...) and a solution using simple techniques that one would never 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 C on a complex surface S, nodal curves - those with the simplest possible singularities - appear in codimension 1. More generally those with d nodes occur in codimension d. In particular a d-dimensional linear family of curves should contain a finite number of such d-nodal curves. The classical problem - at least in the case of S being the projective plane - is to determine this number. The Göttsche conjecture states that the answer should be topological, given by a universal degree d polynomial in the four numbers C.C, c_1(S).C, c_1(S)^2 and c_2(S). There are now proofs in various settings; a completely algebraic proof was found recently by Tzeng. I will explain a simpler proof which was joint work with Martijn Kool and Vivek Shende. |
| Speakers: |
Prof. Dr. Richard Thomas
(Imperial College, London, UK)
|
|
| 6-mar-2012 (tue) |
Burkhard Wilking
|
Structure of fundamental groups of manifolds with lower Ricci curvature bounds
|
KO2 F 150 |
| Speakers: |
Prof. Dr. Burkhard Wilking
(Universität Münster, Deutschland)
|
|
| 3-apr-2012 (tue) |
Emmanuel Hebey
|
Blow-up theory and elliptic stability
|
KO2 F 150 |
| Speakers: |
Prof. Dr. Emmanuel Hebey
(Université de Cergy-Pontoise, Paris)
|
|
| 24-apr-2012 (tue) |
Endre Süli
|
Navier-Stokes-Fokker-Planck systems: analysis and approximation
|
KO2 F 150 |
| Abstract: |
The talk will survey recent developments concerning the existence and the approximation of global weak solutions to a general class of coupled microscopic-macroscopic bead-spring chain models that arise in the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side of the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck type parabolic equation. Models of this kind were proposed in work of Hans Kramers in the early 1940's, and the existence of global weak solutions to the model has been a long-standing question in the mathematical analysis of kinetic models of dilute polymers.
We also discuss computational challenges associated with the numerical approximation of the high-dimensional Fokker-Planck equation featuring in the model. |
| Speakers: |
Prof. Dr. Endre Süli
(University of Oxford, UK)
|
|
| 22-may-2012 (tue) |
Brendan Hassett
|
Fibrations in rational surfaces and their sections
|
KO2 F 150 |
| Abstract: |
A fibration is a surjective morphism from a smooth projective variety to a smooth curve, all defined over a field k. Assume the fibers are rational surfaces. Then every fibration admits a section, when k is algebraically closed. There is a conjectural framework for deciding whether there is a section when k is finite, expressed in terms of the Brauer group and the existence of local sections.
Our approach to these questions hinges on understanding the geometry of the scheme parametrizing all sections of our fibration, especially in contexts where the rational surfaces are relatively simple, e.g., quadric surfaces and intersections of two quadric hypersurfaces. The main application is the existence of sections provided the fibration is sufficiently general, in a sense that can be made precise.
(Joint with Yuri Tschinkel) |
| Speakers: |
Brendan Hassett
(Rice University, Houston, TX, USA)
|
|
Alle Interessentinnen - insbesondere
auch die Studierenden beider Hochschulen - sind herzlich eingeladen. Im
Anschluss an das Kolloquium findet ein Apéro statt.
