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Abstracts for MPI-Oberseminar

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Tropical curves and Gromov-Witten invariants

Posted in
Speaker: 
Brett Parker
Affiliation: 
MPI
Date: 
Thu, 2011-07-28 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

I will explain how tropical curves arise when studying holomorphic curves
under certain degenerations, and what role tropical curves play in calculating
Gromov-Witten invariants.

The geometry of the Double Gyroid wire network: Quantum and Classical

Posted in
Speaker: 
Birgit Kaufmann
Date: 
Thu, 2011-08-04 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

We discuss a novel nano material structure of a Double Gyroid (DG)
wire network. We start by introducing the geometrical structure of the DG
and its
fabrication as background. We then use methods of commutative and
 non-commutative geometry
to describe this quantum wire network. Its non--commutative geometry
is closely related to non-commutative 3-tori as we discuss in detail.
This is joint work with R. Kaufmann and S. Khlebnikov.

Relative Hofer Geometry and the Asymptotic Hofer-Lipschitz Constant

Posted in
Speaker: 
Fabian Ziltener
Date: 
Thu, 2011-08-11 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Let $(M,omega)$ be a symplectic manifold and $U$ an open subset of  $M$. I
study the natural inclusion of the group of Hamiltonian  diffeomorphisms of
$U$ into the group of Hamiltonian diffeomorphisms  of $M$. The main result
is an upper bound for this map in terms of the  Hofer norms for $U$ and
$M$. Applications are upper bounds on the  relative Hofer diameter of $U$
and the asymptotic Hofer-Lipschitz  constant, which are often sharp up to
constant factors. As another  consequence, the relative Hofer diameter of

Non-abelian homological algebra and universal higher K-theory

Posted in
Speaker: 
Alexander Rosenberg
Affiliation: 
Kansas State University/MPIM
Date: 
Thu, 2011-08-18 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

We start with a sketch a fragment of non-abelian homological algebra adopting an intermediate level of generality, which
allows to begin along the lines of Grothendieck's Tohoku lectures replacing abelian categories by right (or left)
exact categories with initial (resp. final) objects. Further analysis leads to the notion of the stable
category of a left exact category and to the notions of quasi-suspended and quasi-triangulated categories.

We define K_0 of a right exact category, introduce a structure of right exact category on the category

UC hierarchy, monodromy preserving deformation and hypergeometric function

Posted in
Speaker: 
T. Tsuda
Affiliation: 
Kyushu University
Date: 
Thu, 2011-08-25 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

The UC hierarchy is an extension of the KP hierarchy, which possesses
not only an infinite set of positive time evolutions but also that of
negative ones.
Through a similarity reduction, the UC hierarchy yields a broad class of
Schlesinger systems including (higher order) Painleve VI and Garnier
systems, which describe monodromy preserving deformations of Fuchsian
linear differential equations with certain spectral types.
The above class of Schlesinger systems has interesting features as
polynomial Hamiltonian structure, Weyl group symmetry, algebraic

Functional determinants and representation theory

Posted in
Speaker: 
Bent Orsted
Date: 
Thu, 2011-09-01 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Functional determinants provide a way, using zeta
functions, of defining the determinants of certain elliptic
differential operators on compact manifolds. In this lecture
we shall study how such determinants depend on the geometric
data and explain how this is connected to representation theory
of semisimple Lie groups. Functional determinants play a role
in string theory and other physical theories, and the
representation theory involves inequalities satisfied by
Knapp-Stein intertwining operators.
 

On a tropical dual Nullstellensatz

Posted in
Speaker: 
D. Grigoriev
Date: 
Thu, 2011-09-08 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Since a tropical Nullstellensatz fails even for univariate polynomials we study
a conjecture on a tropical {\it dual} Nullstellensatz in terms of the tropical
Cayley matrix. The conjecture is proved for tropical univariate polynomials.
Also we produce an algorithm (being a tropical version of the Gram-Schmidt
process) for solving tropical linear systems and a criterion of their solvability
via the tropical and Kapranov ranks

Fixed point formula of Lefschetz type in Arakelov geometry

Posted in
Speaker: 
Shun Tang
Date: 
Thu, 2011-09-15 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

R. Thomason has proved a concentration theorem for algebraic
equivariant K-theory on the schemes which are endowed with the action
of a diagonalisable group scheme. As usual, such a concentration
theorem induces a fixed point formula of Lefschetz type which can be
used to calculate the equivariant Euler-Poincare characteristics of
equivariant vector bundles. In this talk, I will try to explain how to
generalize Thomason's results to Arakelov geometry.

The "law of conservation of manifolds" and the surgery analysis or bordisms

Posted in
Speaker: 
Diarmuid Crowley
Date: 
Thu, 2011-09-22 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

in this talk I will recall how the s-cobordism theorem is used in
the classification of high dimensional compact manifolds via surgery
theory.  I will review aspects of both classicial surgery theory due to
Browder, Novikov, Sullivan and Wall and its modification by Kreck.  I will
also discuss some new results and open problems in these areas.

Lifting homotopy algebra maps to algebra maps

Posted in
Speaker: 
Justin Noel
Date: 
Thu, 2011-09-29 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

I will discuss an obstruction theory for lifting homotopy algebra maps
to algebra maps developed with Niles Johnson. Although our primary
interest is in a topological setting, I will mostly restrict myself to
the algebraic setting during this talk. I will examine the analogue of
this question in the setting of rational chain complexes and show how
examples arising from the study of manifolds rationally give
interesting examples in this situation.  Finally, I will explain why
these examples can be moved into stable homotopy theory to answer

 

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