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The Broadhurst-Kreimer conjecture and multiple zeta values

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Speaker: 
Sarah Carr
Affiliation: 
U Paris-Sud, Orsay
Date: 
Wed, 2010-04-21 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Broadhurst and Kreimer proposed a Poincare series for the algebra of multiple zeta values based on large scale numerical computations. In this talk, I will explain how the coefficients in their series are related to period polynomials and to structural properties of the formal multizeta value (double shuffle) Lie algebra.

Galois cohomology

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Speaker: 
G. Scaria
Date: 
Wed, 2010-04-21 16:30 - 17:30
Parent event: 
IMPRS-seminar on modularity

Bounds for arithmetic intersection numbers

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Speaker: 
Ulf Kühn
Affiliation: 
Hamburg
Date: 
Wed, 2010-04-21 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Arakelov geometry associates to an arithmetic surfaces an intrinsic invariant: the arithmetic self-intersection number of the dualizing sheaf. In this talk a result that implies upper bounds for this real number in particular for Fermat curves and modular curves will be presented.

Vector Bundles II

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Speaker: 
M. Hoffmann
Date: 
Wed, 2010-04-21 12:15 - 13:15
Parent event: 
IMPRS-seminar on K-theory

Some constructions of new groups and buildings

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Speaker: 
Kathrin Tent
Affiliation: 
Bielefeld
Date: 
Tue, 2010-04-20 16:30 - 17:30
Location: 
MPIM Lecture Hall

We give model theoretic constructions for a zoo of examples and counterexamples: we build groups and generalized n-gons satisfying strong transitivity properties. An ultraproduct of the latter yields a forest from which we obtain twin trees and homogeneous 1-round CAT(1)-spaces.

On Kac-Moody groups over rings

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Speaker: 
Ralf Gramlich
Affiliation: 
Darmstadt
Date: 
Tue, 2010-04-20 14:00 - 15:00
Location: 
MPIM Lecture Hall

A split Kac-Moody group $G$ over a topological ring $R$ carries a natural topology defined by Kac and Peterson. In case the underlying topological ring $R$ is $k_\omega$, this turns the Kac-Moody group $G$ into a $k_\omega$ group, which allows for a certain amount of control over this topology. Each $\sigma$-compact locally compact ring is a $k_\omega$ ring, hence the above topology allows to study $S$-arithmetic subgroups of topological Kac-Moody groups over local fields.

Fontaine-Lafaille theory II

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Speaker: 
G. Faltings
Date: 
Tue, 2010-04-20 12:00 - 13:00
Location: 
MPIM Lecture Hall

Vector Bundles I

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Speaker: 
M. Hoffmann
Date: 
Tue, 2010-04-20 10:15 - 11:15
Parent event: 
IMPRS-seminar on K-theory

Moduli varieties of real and quaternionic bundles over a curve

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Speaker: 
Florent Schaffhauser
Affiliation: 
IHES/ MPI
Date: 
Mon, 2010-04-19 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Topics in Topology

We examine the moduli problem for real and quaternionic vector bundles over a curve, and we give a gauge-theoretic construction of would-be moduli varieties for such bundles. These moduli varieties are irreducible subsets of real points inside a complex projective variety. We relate our point of view to previous work by Biswas, Huisman and Hurtubise, and we use this to study Gal(C/R)-actions on moduli varieties of semistable holomorphic bundles over a complex curve with a given real structure.

Representations of braid groups and quantum groups

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Speaker: 
Alexandre Kosyak
Affiliation: 
Inst of Math., Kiev/MPI
Date: 
Thu, 2010-04-15 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

We construct some representations of braid groups, arising from the representations of quantum groups.

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