Tue, 02 Nov 2021
14:15
L5

Solving semidecidable problems in group theory

Giles Gardam
(Münster)
Abstract

Group theory is littered with undecidable problems. A classic example is the word problem: there are groups for which there exists no algorithm that can decide if a product of generators represents the trivial element or not. Many problems (the word problem included) are at least semidecidable, meaning that there is a correct algorithm guaranteed to terminate if the answer is "yes", but with no guarantee on how long one has to wait. I will discuss strategies to try and tackle various semidecidable problems computationally using modern solvers for Boolean satisfiability, with the key example being the discovery of a counterexample to the Kaplansky unit conjecture.

Mon, 03 Feb 2020

14:15 - 15:15
L4

Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds

Christoph Bohm
(Münster)
Abstract

We  show that homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, using that they admit periodic, integrally minimal foliations by homogeneous hypersurfaces. For the geometric flow induced by the orbit-Einstein condition, we construct a Lyapunov function based on curvature estimates which come from real GIT.

Thu, 01 Mar 2018
16:00
L6

Character varieties and (\varphi_L,\Gamma_L)-modules

Peter Schneider
(Münster)
Abstract

After reviewing old work with Teitelbaum, in which we constructed the character variety X of the additive group o_L in a finite extension L/Q_p and established the Fourier isomorphism for the distribution algebra of o_L, I will briefly report on more recent work with Berger and Xie, in which we establish the theory of (\varphi_L,\Gamma_L)-modules over X and relate it to Galois representations. Then I will discuss an ongoing project with Venjakob. Our goal is to use this theory over X for Iwasawa theory.

Thu, 16 Feb 2017

16:00 - 17:00
L6

P-adic representations attached to vector bundles on smooth complete p-adic varieties

Christopher Deninger
(Münster)
Abstract

We discuss vector bundles with numerically stable reduction on smooth complete varieties over a p-adic number field and sketch the construction of associated p-adic representations of the geometric fundamental group. On projective varieties, such bundles are semistable with respect to every polarization and have vanishing Chern classes. One of the main problems in the construction consisted in getting rid of infinitely many obstruction classes. This is achieved by adapting a theory of Bhatt based on de Jongs's alteration method. One also needs control over numerically flat bundles on arbitrary singular varieties over finite fields. The singular Riemann Roch Theorem of Baum Fulton Macpherson is a key ingredient for this step. This is joint work with Annette Werner.
 

Thu, 11 May 2017
17:30
L6

Ample geometries of finite Morley rank

Katrin Tent
(Münster)
Abstract

I will explain the model theoretic notion of ampleness
and present the geometric context of recent constructions.

Thu, 03 Dec 2015
17:30
L6

Near-henselian fields - valuation theory in the language of rings

Franziska Jahnke
(Münster)
Abstract

Abstract: (Joint work with Sylvy Anscombe) We consider four properties 
of a field K related to the existence of (definable) henselian 
valuations on K and on elementarily equivalent fields and study the 
implications between them. Surprisingly, the full pictures look very 
different in equicharacteristic and mixed characteristic.

Mon, 26 Jan 2015
14:15
L5

Ends of the moduli space of Higgs bundles

Frederik Witt
(Münster)
Abstract

Hitchin's existence theorem asserts that a stable Higgs bundle of rank two carries a unitary connection satisfying Hitchin's self-duality equation. In this talk we discuss a new proof, via gluing methods, for
elements in the ends of the Higgs bundle moduli space and identify a dense open subset of the boundary of the compactification of this moduli space.
 

Fri, 10 Jun 2005
12:00
L3

On the Farrell-Jones Conjecture for higher algebraic K-Theory

Holger Reich
(Münster)
Abstract
The Farrell-Jones Conjecture predicts that the algebraic K-Theory of a group ring RG can be expressed in terms of the algebraic K-Theory of the coefficient ring R and homological information about the group. After an introduction to this circle of ideas the talk will report on recent joint work with A. Bartels which builds up on earlier joint work with A. Bartels, T. Farrell and L. Jones. We prove that the Farrell-Jones Conjecture holds in the case where the group is the fundamental group of a closed Riemannian manifold with strictly negative sectional curvature. The result holds for all of K-Theory, in particular for higher K-Theory, and for arbitrary coefficient rings R.
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