29.03.2017

from 14:00 in Villa Battelle

Wednesday

Quantum groups and the cohomology of quiver varieties, III

by Eric Vasserot (Université Pierre et Marie Curie / Université Paris Diderot)

We'll first give an introduction to Nakajima's quiver varieties and their cohomology and/or K-theory.Next, when the quiver is of finite type, we'll construct the action of yangians/quantum affine algebras on these cohomology groups. Finally, when the quiver is of Jordan type, we'll construct the action of the elliptic Hall algebra.

13.03.2017

from 14:00 in Villa Battelle

Monday

Quantum groups and the cohomology of quiver varieties, II

by Eric Vasserot (Université Pierre et Marie Curie / Université Paris Diderot)

We'll first give an introduction to Nakajima's quiver varieties and their cohomology and/or K-theory.Next, when the quiver is of finite type, we'll construct the action of yangians/quantum affine algebras on these cohomology groups. Finally, when the quiver is of Jordan type, we'll construct the action of the elliptic Hall algebra.

10.03.2017

from 14:00 in Villa Battelle

Friday

Quantum groups and the cohomology of quiver varieties, I

by Eric Vasserot (Université Pierre et Marie Curie / Université Paris Diderot)

We'll first give an introduction to Nakajima's quiver varieties and their cohomology and/or K-theory.Next, when the quiver is of finite type, we'll construct the action of yangians/quantum affine algebras on these cohomology groups. Finally, when the quiver is of Jordan type, we'll construct the action of the elliptic Hall algebra.

08.03.2017

from 13:30 in Villa Battelle

Wednesday

Introduction to the derived category of sheaves.

by Anton Fonarev (HSE Moscow)

23.02.2017

from 14:30 in Villa Battelle

Wednesday

The logarithmic deRham complex

by Simone Chiarello (UniGe)

I will prove that the deRham cohomology of a smooth complex algebraic variety can be computed as the hypercohomology of a suitable complex of sheaves, defined over a compactification of the variety; this allows to put a mixed Hodge structure on its cohomology. The exposition will be enhanced by some down-to-earth examples.

08.03.2016

from 10:30 in Villa Battelle

Tuesday

Introduction to Higgs Bundles

by Simone Chiarello (UniGe)

We will give an introduction to the construction of the moduli spaces of Higgs bundles on a Riemann surface based on the work of Hitchin.

03.03.2014

from 10:30 in Villa Battelle

Monday

Inversion of adjunction for rational and Du Bois singularities

by Sandor Kovacs (University of Washington)

We prove that Du Bois singularities are invariant under small deformation and that the relationship of the notions of rational and Du Bois singularities resembles that of canonical and log canonical varieties. In particular, if a member of a family has Du Bois singularities, then the total space of the family has rational singularities near the given fiber.

This is joint work with Karl Schwede.

28.02.2014

from 10:30 in Villa Battelle

Friday

Moduli spaces of parabolic lambda-connections on a curve and Hilbert
schemes of points on surfaces

by Szilard Szabo (EPFL and Budapest University of Technology)

We outline the construction of a birational map from the moduli
space of parabolic logarithmic connections (or Higgs bundles) on a complex
projective curve to a Hilbert scheme of points on a birational modification
of the total space of its twisted cotangent bundle. The construction relies
on representing connections by opers. Time permitting, we discuss known results
about the image of this map,  and its connection to other similar maps which have
appeared in the literature.

Joint work in progress with Masa-Hiko Saito.

06.12.2013

from 11:30 in Villa Battelle

Friday

Schur polynomials, tableau and the Littlewood–Richardson rule 2

by Alexander Paunov (UniGe)

05.12.2013

from 16:15 in Villa Battelle

Thursday

Holomorphic maps between projective spaces are maximally singular

by Laszlo Feher (ELTE Budapest)

We conjecture that a nonlineal homorphic map between projective spaces is maximally singular: Suppose that  a contact singularity  x can be represented with polynomials of degree at most k. Suppose moreover that the expected dimension of the locus of x-type singularities is non-negative. Then  for any holomorphic map  of degree at least k there is an x-type  (or more complicated) singularity.
We can prove the conjecture for "almost all" cases, and for important special cases.

29.11.2013

from 10:30 in Villa Battelle

Friday

Localization of Hirzebruch chi_y-genus

by Andrzej Weber (University of Warsaw)

We study genera of complex algebraic varieties. If a genus g satisfies g(E)=g(F)g(B) for a fibration F->E->B with F being a projective space then it is called rigid. It turns out that the universal such genus is the Hirzebruch chi_y-genus. The rigidity property has two important consequences:
1) there exists an additive extension of Hirzebruch chi_y-genus to singular and noncomplete varieties, that is g(X)=g(X-Y)+g(Y) for a closed subvariety of X,

2) the Hirzebruch genus can be localized for varieties with torus action: g(X) is equal to the sum of local contributions coming from the fixed points.

The situation when the action has discrete fixed points set is of particular interest. We will give samples of computations and investigate positivity property in particular cases. Also, we will discuss the underlying construction on the level of K-theory.

15.11.2013

from 10:30 in Villa Battelle

Friday

Schur polynomials, tableau and the Littlewood–Richardson rule 1

by Alexander Paunov (UniGe)

11.11.2013

from 10:30 in Villa Battelle

Monday

Rimanyi's method of restriction equations: computing Thom and "residual" polynomials for multisingularities

by Natalia Kolokolnikova (UniGe)

08.11.2013

from 10:30 in Villa Battelle

Friday

Espace des arc des variétés sphériques et intégration motivique

by Anne Moreau (Université de Poitiers)

Résumé: Cet exposé porte sur des travaux (passés et en cours) en commun avec Victor Batyrev. Nous nous intéressons à l'intégrale motivique sur l'espace des arcs d'une G-variété sphérique Q-Gorenstein X où G est un groupe réductif connexe. Nous donnons une formule pour la fonction de cordes de X en terme de son éventail colorié associé. Grâce à cette formule, nous établissons un nouveau critère de lissité pour les variétés horosphériques localement factorielles. Nous conjecturons que ce critère reste valable pour les variétés sphériques.

27.09.2013

from 10:30 in Villa Battelle

Friday

On a problem in real enumerative geometry

by László Fehér (ELTE, Budapest)

12.06.2013

from 14:30 in Villa Battelle

Wednesday

Universal polynomials for counting singular subvarieties

by Yu-jong Tzeng (Harvard)

How many nodal degree d plane curves are tangent to a given line? The celebrated Caporaso-Harris recursion formula gives a complete answer for any number of nodes, degrees, and all possible tangency conditions. In this talk, I will report my recent work on the numbers of singular curves with given tangency conditions on general surfaces, and singular subvarieties of higher dimensional subvarieties. These numbers are given by universal polynomials, which generalizes Gottsche's conjecture. Unlike the nodal curve case, these polynomials are not determined yet but it is possible to discuss their asymptotic behavior and some properties of the generating function.

15.03.2013

from 14:30 in Villa Battelle

Friday

Nekrasov's partition function and refined Donaldson-Thomas theory

by Balázs Szendrői (Oxford)

01.03.2013

from 11:15 in Villa Battelle

Friday

Mock theta functions and representations of affine Lie superalgebras

by Victor Kac (MIT)

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.