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Abstracts for MPI-Oberseminar

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Cyclic homology of Fukaya categories and the linearized contact homology

Posted in
Speaker: 
Xiaojun Chen
Affiliation: 
MPI
Date: 
Thu, 2012-03-08 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

In this talk I will show that for an exact symplectic manifold M with vanishing first Chern class,
the cyclic cohomology of the Fukaya category of M has an involutive Lie bialgebra structure.
If M has an contact type boundary, then there is a Lie bialgebra homomorphism from the
cyclic cohomology to the linearized contact homology of M. We will also explain our result
from the topological conformal field theory point of view, and if time permits, relate it with
string topology.
 

Knots, 3-manifolds, and SL(2,C) character varieties

Posted in
Speaker: 
H. Boden
Affiliation: 
McMaster/MPI
Date: 
Thu, 2012-03-15 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

In this talk, I will begin with a brief review of character varieties in the
SL(2,C) setting a la Culler and Shalen, including an outline of the main
applications to knots and 3-manifolds. I will then give a report on recent joint
work with C. Curtis on the SL(2,C) Casson invariant for 2-bridge knots, and on a
non-triviality result for the M-degree of the A-polynomial of any non-trivial knot. 

 

The Herman conjecture.

Posted in
Speaker: 
M. Garay
Affiliation: 
Mainz/MPI
Date: 
Thu, 2012-03-22 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

In the nineties, Michel Herman conjectured the existence of invariant  tori at critical points of
Hamiltonian systems under very general  assumptions. I will explain the relations of the
conjecture with  problems in diophantine geometry and group actions on infinite dimensional spaces.



Irregular binomial D-modules

Posted in
Speaker: 
María-Cruz Fernández-Fernández
Affiliation: 
Sevilla/MPI
Date: 
Thu, 2012-03-29 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

D-module theory is an algebraic point of view of systems of linear partial differential equations.
Hypergeometric systems (introduced by Gelfand, Graev, Kapranov and Zelevinsky in the late 80's)
and binomial D-modules (introduced by Dickenstein, Matusevich and Miller, 2010) are special cases.  
These systems generalize classical hypergeometric equations and they have a rich combinatorial
structure. We will talk about the irregularity of such systems.  Part of the talk is based on
joint work with F. Castro."
 

Integrable ODEs with matrix variables. Bi-Hamiltonian approach

Posted in
Speaker: 
Vladimir Sokolov
Affiliation: 
Landau Inst. for Theor. Physics/MPI
Date: 
Thu, 2012-04-05 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Joint work with V.Roubtsov and A.Odesskii.

We consider a special class of linear and quadratic Poisson brackets related to
ODE systems with matrix variables. General properties of such brackets are
investigated. A complete classification of quadratic brackets in the case of two
matrices is presented. Examples of a compatible pairs of quadratic and linear
brackets are found.

 

Non-abelian Poisson brackets: algebraic aspects

Posted in
Speaker: 
V. Roubtsov
Affiliation: 
U d´Angers/MPI
Date: 
Thu, 2012-04-12 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

This is a continuation of the previous Seminar's talk given by prof. V. Sokolov.
I suppose to discuss algebraic questions related to  so-called "non-abelian"
Poisson brackets introduced in the previous talk. I hope to clarify their relations
with brackets of W. Crawley- Boevey and double brackets of M. Van den Bergh.
My talk is based on joint papers (in press and in progress) with A. Odesskii and
V. Sokolov.

 

New guests at the MPIM

Posted in
Speaker: 
Dustin Cartwright, Vincent Emery, Ozgur Ceyhan
Date: 
Thu, 2012-04-19 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Toric varieties and cluster algebras

Posted in
Speaker: 
G. Koshevoy
Affiliation: 
Russian Acad. of Sciences/MPI
Date: 
Thu, 2012-04-26 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

We associate a toric variety to the cluster algebra of the coordinate  ring of GL_n/P
(P is a parabolic subgroup). If such a cluster algebra is finite, then we have a smooth
toric variety.  Our conjecture is that this holds in general.To confirm this conjecture
we construct a smooth toric variety for a  framed acyclic quiver and study relations
between these two constructions of toric varieties.
 

Explicit reciprocity laws and $p$-adic $L$-functions

Posted in
Speaker: 
Denis Benois
Affiliation: 
z.Z. MPI
Date: 
Thu, 2012-05-03 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

In the first part of this talk we review classical  explicit reciprocity laws and its generalizations to p-adic representations from the point of view of Iwasawa theory.
In the second part we explain applications of this theory to the study of special values of
$p$-adic $L$-functions.
 

Automorphisms and subalgebras of free algebras

Posted in
Speaker: 
U. Umirbaev
Affiliation: 
Eurasian National U./Wayne State U./MPI
Date: 
Thu, 2012-05-10 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

P. Cohn proved that free associative algebras are free ideal rings (FI-ring or fir), i.e., 
every submodule of a free module over a free associative algebra is free.  This result easily
implies that subalgebras of free Lie algebras are free and automorphisms of finitely generated free Lie algebras are tame. 

Let $P(x_1,...,x_n)$ be a free Poisson field, i.e., the quotient field of a free Poisson algebra
with extended Poisson bracket. In a joint work with L. Makar-Limanov we proved that

 

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