Seminaire de la Tortue
Université de Genève, Section de Mathématiques
Villa Battelle, 7 route de Drize, 1227 Carouge
| 17.12.2012 | from 10:30 at Villa Battelle |
| Monday | Damon's theorem and Schur positivity for Thom polynomials of contact singularities |
| by Natalia Kolokolnikova (UniGe) | |
| Thom polynomials of contact singularities have an important property: they can be expressed in terms of relative Chern classes (this property is known as Damon's theorem) and for this expression the Schur positivity conjecture holds. Damon's theorem is a well-known result, but the references for the proof are hard to come by. I'll give a proof of this theorem and a proof of the Schur positivity conjecture in a way different from Pragacz's. |
| 10.12.2012 | from 10:30 at Villa Battelle |
| Monday | Conormal bundles of Schubert varieties and Yangian weight functions |
| by Richárd Rimányi (University of North Carolina; UniGe) | |
| There are remarkable – more or less canonical – isomorphisms between objects in geometry (e.g. equivariant cohomology of cotangent bundles of flag varieties) and objects in quantum algebra. Using these bridges between geometry and algebra we will present algebraic notions, such as conformal blocks, R-matrices, Yangian weight functions, etc in geometry. I will report on some joint works with Varchenko and Tarasov, as well as results of Maulik and Okounkov. |
| 23.11.2011 | from 10:30 at Villa Battelle |
| Friday | The birthday problem, the chromatic polynomial, and Stanley conjecture |
| by Alexander Paunov (UniGe) | |
| I will present an interesting connection between the generalized birthday problem and Stanley's e-positivity conjecture. The talk will be focused on the properties of claw-free graphs, colorings and extremal points of chromatic functions. |
| 19.11.2012 | from 10:30 at Villa Battelle |
| Monday | Moduli space of Higgs bundles I. |
| by Máté Juhász (UniGe) | |
| In this talk we will review the construction of the Quot scheme and the moduli space of vector bundles, the first step towards the construction of the moduli space of Higgs bundles. As time permits, a few preliminary concepts concerning Higgs bundles shall be introduced as well. The talk presupposes a basic knowledge about GIT. |
| 09.11.2012 | from 10:00 at Villa Battelle |
| Friday | The cohomology ring of Hilbert schemes for K3 surfaces II. |
| by Zsolt Szilágyi (UniGe) | |
| 05.11.2012 | from 10:30 at Villa Battelle |
| Monday | The cohomology ring of Hilbert schemes for K3 surfaces I. |
| by Zsolt Szilágyi (UniGe) | |
| The talk is based on the article "The cup product of Hilbert schemes for K3 surfaces" by M. Lehn and Ch. Sorger and its aim is to present their construction of the cohomology ring of Hilbert schemes. This construction motivated the one by Costello and Grojnowski presented in the previous talks. |
| 26.10.2012 | from 10:00 at Villa Battelle |
| Friday | The cohomology of the Hilbert scheme of points via Cherednik algebras II |
| by Emanuel Stoica (UniGe) | |
| In part I of the talk, we gave a rather schematic outline of the clever construction of the cohomology ring of Hilbert scheme of points on a surface, based on Cherednik algebras, following Costello and Grojnowski. In part II, we will try to clarify the construction with more explanations and details. |
| 22.10.2012 | from 10:30 at Villa Battelle |
| Monday | The cohomology of the Hilbert scheme of points via Cherednik algebras I. |
| by Emanuel Stoica (UniGe) | |
| We will outline the clever construction of the cohomology ring of the Hilbert scheme of points on a smooth surface based on Cherednik algebras, following Costello and Grojnowski. |
| 18.05.2012 | from 10:30 at Villa Battelle |
| Friday | Combinatorial interpretation of e-coefficients of chromatic symmetric functions |
| by Alexander Paunov (UniGe) | |
| 04.05.2012 | from 10:30 at Villa Battelle |
| Friday | Schur-positivity and 3+1 conjecture |
| by Alexander Paunov (UniGe) | |
| 30.04.2012 | from 11:00 at Villa Battelle |
| Monday | Chromatic functions and e-positivity |
| by Alexander Paunov (UniGe) | |
| 13.12.2011 | from 13:30 at Villa Battelle |
| Tueday | Topological recursion relations in enumerative geometry |
| Lecture 4: Some hints towards the proof | |
| by Bertrand Eynard (IPhT, CEA Saclay; UniGe) | |
|
The topology of moduli spaces of Riemann surfaces embedded into a "target space", can be partially understood by computing intersection numbers of various homology classes. Enumerative geometry aims at computing those intersection numbers, or more precisely generating series for families of intersection numbers.
Recently it was realized that many enumerative geometry problems can be solved by a universal topological recursion (recursion on the Euler characteristics).
This mini-course is a basic introduction to those concepts.
Outline: Lecture 1: Introduction to enumerative geometry, Gromov-Witten invariants, Intersection numbers, Kontsevich integral Lecture 2: Recursion relations for Weil-Petersson volumes, for Hurwitz numbers, for the Gromov-Witten theory of C^3. Lecture 3: The remodelling conjecture, introduction to mirror symmetry, statement of the conjecture Lecture 4: some hints towards the proof |
| 06.12.2011 | from 13:30 at Villa Battelle |
| Tuesday | Topological recursion relations in enumerative geometry |
| Lecture 3: The remodelling conjecture, introduction to mirror symmetry, statement of the conjecture | |
| by Bertrand Eynard (IPhT, CEA Saclay; UniGe) | |
|
The topology of moduli spaces of Riemann surfaces embedded into a "target space", can be partially understood by computing intersection numbers of various homology classes. Enumerative geometry aims at computing those intersection numbers, or more precisely generating series for families of intersection numbers. Recently it was realized that many enumerative geometry problems can be solved by a universal topological recursion (recursion on the Euler characteristics).
This minicourse is a basic introduction to those concepts.
Outline: Lecture 1: Introduction to enumerative geometry, Gromov-Witten invariants, Intersection numbers, Kontsevich integral Lecture 2: Recursion relations for Weil-Petersson volumes, for Hurwitz numbers, for the Gromov-Witten theory of C^3. Lecture 3: The remodelling conjecture, introduction to mirror symmetry, statement of the conjecture Lecture 4: some hints towards the proof |
| 02.12.2011 | from 14:00 at Villa Battelle |
| Friday | Mini-course on Jeffrey-Kirwan reduction theorem |
| Lecture 8: Jeffrey-Kirwan reduction theorem, circle case | |
| by Zsolt Szilágyi (UniGe) | |
| Jeffrey-Kirwan formula for symplectic reduction via symplectic cut, circle case. |
| 29.11.2011 | from 13:30 at Villa Battelle |
| Tueday | Topological recursion relations in enumerative geometry |
| Lecture 2: Recursion relations for Weil-Petersson volumes, for Hurwitz numbers, for the Gromov-Witten theory of C^3. | |
| by Bertrand Eynard (IPhT, CEA Saclay; UniGe) | |
|
The topology of moduli spaces of Riemann surfaces embedded into a "target space", can be partially understood by computing intersection numbers of various homology classes. Enumerative geometry aims at computing those intersection numbers, or more precisely generating series for families of intersection numbers.
Recently it was realized that many enumerative geometry problems can be solved by a universal topological recursion (recursion on the Euler characteristics).
This minicourse is a basic introduction to those concepts.
Outline: Lecture 1: Introduction to enumerative geometry, Gromov-Witten invariants, Intersection numbers, Kontsevich integral Lecture 2: Recursion relations for Weil-Petersson volumes, for Hurwitz numbers, for the Gromov-Witten theory of C^3. Lecture 3: The remodelling conjecture, introduction to mirror symmetry, statement of the conjecture Lecture 4: some hints towards the proof |
| 25.11.2011 | from 14:00 at Villa Battelle |
| Friday | Moduli space of Higgs bundles |
| by András Szenes (UniGe) | |
| 22.11.2011 | from 13:30 at Villa Battelle |
| Tuesday | No seminar today. |
| 18.11.2011 | from 14:00 at Villa Battelle |
| Friday | Mini-course on Jeffrey-Kirwan reduction theorem |
| Lecture 7: Symplectic reduction | |
| by Zsolt Szilágyi (Unige) | |
| Finishing the proof AB-BV theorem. Symplectic reduction and symplectic cut. |
| 15.11.2011 | from 13:30 at Villa Battelle |
| Tuesday | Topological recursion relations in enumerative geometry |
| Lecture 1: Introduction to enumerative geometry, Gromov-Witten invariants, Intersection numbers, Kontsevich integral | |
| by Bertrand Eynard (IPhT, CEA Saclay; UniGe) | |
|
The topology of moduli spaces of Riemann surfaces embedded into a "target space", can be partially understood by computing intersection numbers of various homology classes. Enumerative geometry aims at computing those intersection numbers, or more precisely generating series for families of intersection numbers.
Recently it was realized that many enumerative geometry problems can be solved by a universal topological recursion (recursion on the Euler characteristics).
This minicourse is a basic introduction to those concepts.
Outline: Lecture 1: Introduction to enumerative geometry, Gromov-Witten invariants, Intersection numbers, Kontsevich integral Lecture 2: Recursion relations for Weil-Petersson volumes, for Hurwitz numbers, for the Gromov-Witten theory of C^3. Lecture 3: The remodelling conjecture, introduction to mirror symmetry, statement of the conjecture Lecture 4: some hints towards the proof |
| 11.11.2011 | from 14:00 at Villa Battelle |
| Fridaz | Mini-course on Jeffrey-Kirwan reduction theorem |
| Lecture 6: Atiyah-Bott-Berline-Vergne localization theorem | |
| by Zsolt Szilágyi (UniGe) | |
| Equivariant integration and AB-BV localization theorem |
| 08.11.2011 | "Lie group and moduli space" seminar from 13h30. |
| Tuesday |
For more information visit: http://www.unige.ch/math/seminaires/lie-sem/#201111081330 |
| 04.11.2011 | No seminar today. |
| Friday | |
| 01.11.2011 | from 15:00 at Villa Battelle |
| Tuesday | Mini-course on Thom polynomials |
| Lecture 5: Groebner basis | |
| by András Szenes (UniGe) | |
| Groebner basis |
| 28.10.2011 | from 14:00 at Villa Battelle |
| Friday | Mini-course on Jeffrey-Kirwan reduction theorem |
| Lecture 5: (Equivariant) characteristic classes, part 2. | |
| by Zsolt Szilágyi (UniGe) | |
| Continuation from last time: characteristic classes via Chern-Weil theory, equivariant characteristic classes |
| 25.10.2011 | No seminar today. |
| Tuesday | |
| 21.10.2011 | from 14:00 at Villa Battelle |
| Friday | Mini-course on Jeffrey-Kirwan reduction theorem |
| Lecture 4: (Equivariant) characteristic classes | |
| by Zsolt Szilágyi (UniGe) | |
| Cartan map (continued from last time), characteristic classes of vector bundles, equivariant characteristic classes |
| 18.10.2011 | from 13:30 at Villa Battelle |
| Tuesday | Mini-course on Thom polynomials |
| Lecture 4: Thom polynomials and commutative algebra | |
| by András Szenes (UniGe) | |
| Resolutions, Groebner bases and Thom polynomials |
| 14.10.2011 | from 14:00 at Villa Battelle |
| Friday | Mini-course on Jeffrey-Kirwan reduction theorem |
| Lecture 3: Cartan model | |
| by Zsolt Szilágyi (UniGe) | |
| From Borel model to Cartan model using Kalkman's trick, characteristic map, Chern-Weil transgression, Cartan isomorphism. |
| 11.10.2011 | from 13:30 at Villa Battelle |
| Tuesday | Mini-course on Thom polynomials |
| Lecture 3: The Thom polynomials and syzygies | |
| by András Szenes (UniGe) | |
| Hilbert syzygy theorem, Hilbert functions and Hilbert polynomials, first construction of Thom polynomials. |
| 07.10.2011 | from 14:00 at Villa Battelle |
| Friday | Jeffrey-Kirwan reduction formula II. |
| by Zsolt Szilágyi (UniGe) | |
|
Second talk on equivariant cohomology.
This talk is part of a series of talks, aiming to explain the Jeffrey-Kirwan reduction formula. |
| 04.10.2011 | from 13:30 at Villa Battelle |
| Tuesday | Mini-course on Thom polynomials |
| Lecture 2: How to ask a question in eumerative geometry? | |
| by András Szenes (UniGe) | |
| Principal and associated bundles, introduction to Thom polynomials. |
| 30.09.2011 | from 14:00 at Villa Battelle |
| Friday | Jeffrey-Kirwan reduction formula I. |
| by Zsolt Szilágyi (UniGe) | |
| Introduction to equivariant cohomology, following the book of Guillemin-Sternberg: Supersymmetry and equivariant de Rham theory. This talk is part of a series of talks, aiming to explain the Jeffrey-Kirwan reduction formula. |
| 27.09.2011 | from 13:30 at Villa Battelle |
| Tuesday | Mini-course on Thom polynomials |
| Lecture 1: Enumerative Geometry and Cohomology | |
| by András Szenes (UniGe) | |
| Vector bundles, Chern classes, Bott localization formula. |