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Abstracts for Seminar on Algebra, Geometry and Physics

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Liouville model, Euler factors and constant term identities

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Speaker: 
Vadim Schechtman
Affiliation: 
U Paul Sabatier/MPI
Date: 
Tue, 2012-08-21 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar on Algebra, Geometry and Physics

Some similar integrals appeared independently in two seamingly different areas:
in a study of automorphic L-functions on the one hand and in physicists’ works
on the Liouville model of 2D Conformal field theory and on Chern - Simons
theory on the other.  We will discuss relationships between the two domains, as
well as further connections with Dyson - Macdonald constant term identities.
This is a joint work with Bui Van Binh.

Flexible varieties

Posted in
Speaker: 
Mikhail Zaidenberg
Affiliation: 
Inst. Fourier, Grenoble/MPI
Date: 
Tue, 2012-08-28 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar on Algebra, Geometry and Physics

According to A. Borel and F. Kno,p an algebraic group cannot
act 3-transitively on an irreducible affine algebraic variety.
However the automorphism group of the affine space A^n, n \ge 2,
acts infinitely transitively i.e., m-transitively for any m \ge 1.
An affine algebraic variety X of dimension at least 2 is called
flexible if its special automorphism group
(that is a certain priviledged subgroup
of the full automorphism group Aut(X)) acts infinitely transitively
on the smooth locus of X.

p-adic periods, I

Posted in
Speaker: 
Alexander Beilinson
Affiliation: 
Chicago
Date: 
Tue, 2012-09-18 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar on Algebra, Geometry and Physics 
The talks describe a derived de Rham cohomology
approach to comparison theorems in p-adic Hodge theory.

p-adic periods, II

Posted in
Speaker: 
Akexander Beilinson
Affiliation: 
Chicago
Date: 
Tue, 2012-09-25 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar on Algebra, Geometry and Physics 
The talks describe a derived de Rham cohomology
approach to comparison theorems in p-adic Hodge theory.

Quantum cluster transformations and refined DT theory

Posted in
Speaker: 
Ben Davison
Affiliation: 
HIM
Date: 
Tue, 2012-10-02 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar on Algebra, Geometry and Physics 
In this talk I'll describe what a quantum cluster algebra is, and how quantum cluster coefficients arise in the Donaldson-Thomas theory of a quiver with potential.  In particular, we'll be focusing on the link between purity statements on cohomology of vanishing cycles, and positivity in quantum cluster mutation.  In the case of a graded quiver with nondegenerate graded potential, it turns out that we can prove the general positivity conjecture, and even the stronger "Lefschetz property" considered by A.

Trisymplectic manifolds and the moduli of instantons on $C P^3$

Posted in
Speaker: 
M. Verbitsky
Affiliation: 
Moscow, HSE
Date: 
Tue, 2012-10-09 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar on Algebra, Geometry and Physics

A trisymplectic structure on a complex n-manifold is a triple of holomorphic symplectic forms such that any linear combination of these forms has rank 2n, n or 0. We show that a trisymplectic manifold is equipped with a holomorphic 3-web and the Chern connection of this 3-web is holomorphic, torsion-free, and preserves the three symplectic forms. I will construct a trisymplectic structure on the moduli of regular rational curves in the twistor space of a hyperkaehler manifold.

applications of the tropical vertex group

Posted in
Speaker: 
Jacpo Stoppa
Affiliation: 
HIM
Date: 
Tue, 2012-10-16 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar on Algebra, Geometry and Physics 
The tropical vertex group is generated by certain formal symplectomorphisms of the 2-dimensional algebraic torus. It plays a role in some problems in algebraic geometry and mathematical physics, e.g. wall-crossing. It is known that the group itself can be understood in many ways, for example in terms of "counting" certain rational curves or representations of quivers. This leads to nice correspondences. I will discuss joint work with M. Reineke and T.

Integral operator solution of the Yang-Baxter equation based on the elliptic beta integral

Posted in
Speaker: 
V.P. Spiridonov
Affiliation: 
BLTP, Dubna/MPIM
Date: 
Tue, 2012-10-23 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar on Algebra, Geometry and Physics

A general solution of the Yang-Baxter equation is
constructed as an integral operator with an elliptic hypergeometric
kernel acting in the space of functions of two complex variables.
It intertwines the product of two standard L-operators associated with
the Sklyanin algebra (an elliptic deformation of sl(2)). This R-matrix
is constructed from three operators generating the permutation
group of four parameters entering L-operators. Validity
of the Coxeter relations (including the star-triangle relation) is

Quantum master equation and deformation theory

Posted in
Speaker: 
A. Voronov
Affiliation: 
U of Minnesota/MPI
Date: 
Tue, 2012-10-23 15:00 - 15:50
Location: 
MPIM Lecture Hall
Parent event: 
Seminar on Algebra, Geometry and Physics

Classical deformation theory is based on the Classical Master Equation (CME), a.k.a. the Maurer-Cartan
Equation: dS + 1/2 [S,S] = 0. Physicists have been using a quantized CME, called the Quantum Master Equation
(QME), a.k.a. the Batalin-Vilkovisky (BV) Master Equation: dS + h \DeltaS + 1/2 {S,S} = 0. The CME is defined in a dg
Lie algebra g, whereas the QME is defined in a space V [[h]] of formal power series with values in a differential graded
(dg) BV algebra V. One can anticipate a generalization of classical deformation theory arising from the QME or quantum

Towards a categorification of the boson-fermion correspondence

Posted in
Speaker: 
Vera Serganova
Affiliation: 
Berkeley/MPI
Date: 
Tue, 2012-10-30 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar on Algebra, Geometry and Physics

In this talk I will propose a realization of certain vertex operators acting on the Fock space
in terms of functors acting on the category of tensor sl(infinity) - modules. This realization
gives a non-computational categorical proof for certain identities of vertex operators.
Joint work with Igor Frenkel and Ivan Penkov.

 

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