Past

We discuss a model of finite strain gradient plasticity including phenomenological Prager type linear kinematical hardening and nonlocal kinematical hardening due to dislocation interaction. Based on the multiplicative decomposition a thermodynamically admissible flow rule for F_p is described involving as plastic gradient Curl F_p. The formulation is covariant w.r.t. superposed rigid rotations of the reference, intermediate and spatial configuration but the model is not spin-free due to the nonlocal dislocation interaction and cannot be reduced to a dependenceon the plastic metric C_p=F_p^T F_p.
The linearization leads to a thermodynamically admissible model of infinitesimal plasticity involving only the Curl of the non-symmetric plastic distortion p. Linearized spatial and material covariance under constant infinitesimal rotations is satisfied.
Uniqueness of strong solutions of the infinitesimal model is obtained if two non-classical boundary conditions on the plastic distortion p are introduced: d_tp.τ=0 on the microscopically hard boundary Γ_D⊂∂Ω and [Curlp].τ=0 on the microscopically free boundary ∂Ω\Γ_D, where τ are the tangential vectors at the boundary ∂Ω. Moreover, I show that a weak reformulation of the infinitesimal model allows for a global in-time solution of the corresponding rate-independent initial boundary value problem. The method of choice are a formulation as a quasivariational inequality with symmetric and coercive bilinear form, following the abstract framework proposed by Reddy. Use is made of new Hilbert-space suitable for dislocation density dependent plasticity.

Now that the "classical" philosophies that have danced attendance upon intuitionistic mathematics (Brouwer's subjectivism, Heyting's eclecticism, and contemporary anti-realism) are recognized as failures, it is encumbent upon intuitionists to develop new foundations for their mathematics. In this talk, we assay such efforts, in particular, investigations into the various mathematical grounds on the basis of which the law of the excluded third might be proven invalid. It will also be necessary, along the way, to explode certain mistaken ideas about intuitionism, among them the notion that the logical signs of the intuitionists bear meanings different from those attached to the corresponding signs in conventional mathematics.

Please let Bruno Whittle (@email) know if you would like to go out to dinner with the speaker after the seminar.

We consider a linearly edge-reinforced random walk

on a class of two-dimensional graphs with constant

initial weights. The graphs are obtained

from Z^2 by replacing every edge by a sufficiently large, but fixed

number of edges in series.

We prove that a linearly edge-reinforced random walk on these graphs

is recurrent. Furthermore, we derive bounds for the probability that

the edge-reinforced random walk hits the boundary of a large box

before returning to its starting point.

Part I will also include an overview on the history of the model.

In part II, some more details about the proofs will be explained.

The Borel conjecture asserts that aspherical manifolds are topologically rigid, i.e., every homotopy equivalence between such manifolds is homotopic to a homeomorphism. This conjecture is strongly related to the Farrell-Jones conjectures in algebraic K- and L-theory. We will give an introduction to these conjectures and discuss the proof of the Borel conjecture for high-dimensional aspherical manifolds with word-hyperbolic fundamental groups.

We consider a linearly edge-reinforced random walk

on a class of two-dimensional graphs with constant

initial weights. The graphs are obtained

from Z^2 by replacing every edge by a sufficiently large, but fixed

number of edges in series.

We prove that a linearly edge-reinforced random walk on these graphs

is recurrent. Furthermore, we derive bounds for the probability that

the edge-reinforced random walk hits the boundary of a large box

before returning to its starting point.

Part I will also include an overview on the history of the model.

In part II, some more details about the proofs will be explained.

Abstract: We discuss the string-inspired approach to gauge theory amplitudes prompted by the work of Alday and Maldacena, in particular its application to weak coupling.

We shall present work in progress in collaboration with E. Hrushovski on the geometry of spaces of stably dominated types in connection with non archimedean geometry \`a la Berkovich

When liquidating large portfolios of securities one faces a trade off between adverse market impact of sell orders and the impatience to generate proceeds. We present a Black-Scholes model with an impact factor describing the market's distress arising from previous transactions and show how to solve the ensuing optimization problem via classical calculus of variations. (Joint work with Dirk Becherer, Humboldt Universität zu

Berlin)

Meshfree methods become more and more important for the numerical simulation of complex real-world processes. Compared to classical, mesh-based methods they have the advantage of being more flexible, in particular for higher dimensional problems and for problems, where the underlying geometry is changing. However, often, they are also combined with classical methods to form hybrid methods.

In this talk, I will discuss meshfree, kernel based methods. After a short introduction along the lines of optimal recovery, I will concentrate on results concerning convergence orders and stability. After that I will address efficient numerical algorithms. Finally, I will present some examples, including one from fluid-structure-interaction, which will demonstrate why these methods are currently becoming Airbus's preferred solution in Aeroelasticity.

The partition function of the random cluster model on a graph $G$ is also known as its Potts model partition function. (Only the points at which it is evaluated differ in the two models.) This is a multivariate generalization of the Tutte polynomial of $G$, and encodes a wealth of enumerative information about spanning trees and forests, connected spanning subgraphs, electrical properties, and so on.

An elementary property of electrical networks translates into the statement that any two distinct edges are negatively correlated if one picks a spanning tree uniformly at random. Grimmett and Winkler have conjectured the analogous correlation inequalities for random forests or random connected spanning subgraphs. I'll survey some recent related work, partial results, and more specific conjectures, without going into all the gory details.

We outline a method to solve the stationary Einstein equations with source a body in rigid rotation consisting of elastic matter.

This is work in progress by R.B., B.G.Schmidt, and L.Andersson