From Lawvere to Brandenburger-Keisler: Interactive forms of diagonalization and self-reference
Abramsky, S
Zvesper, J
Journal of Computer and System Sciences
volume 81
issue 5
799-812
(01 Aug 2015)
On the universal identity in second order hydrodynamics
Grozdanov, S
Starinets, A
Journal of High Energy Physics
volume 2015
issue 3
7
(02 Mar 2015)
Heterotic QCD axion
Buchbinder, E
Constantin, A
Lukas, A
Physical Review D
volume 91
issue 4
046010
(15 Feb 2015)
Computational techniques for reachability analysis of Max-Plus-Linear systems
Adzkiya, D
De Schutter, B
Abate, A
Automatica
volume 53
293-302
(Mar 2015)
Network science helps us understand many kinds of Big Data. Since the late 20th century it has been increasingly relevant to people's everyday life.
Growth rates of the population in a branching Brownian motion with an inhomogeneous breeding potential
Berestycki, J
Brunet, E
Harris, J
Harris, S
Roberts, M
Stochastic Processes and their Applications
volume 125
issue 5
2096-2145
(29 Dec 2014)
Mon, 27 Apr 2015
17:00 -
18:00
Asymptotic Rigidity of Self-shrinkers of Mean Curvature Flow
Lu Wang
(Imperial College)
Abstract
In this talk, we use Carleman type techniques to address uniqueness of self-shrinkers of mean curvature flow with given asymptotic behaviors.
Mon, 04 May 2015
17:00 -
18:00
L4
On the mathematical theory of Quantum Fluids
Pierangelo Marcati
(University of L' Aquila and Gran Sasso Science Institute GSSI)
Fri, 03 Jun 2016
16:00 -
17:00
L1
Eigenvectors of Tensors
Bernd Sturmfels
(UC Berkeley)
Abstract
Eigenvectors of square matrices are central to linear algebra. Eigenvectors of tensors are a natural generalization. The spectral theory of tensors was pioneered by Lim and Qi around 2005. It has numerous applications, and ties in closely with optimization and dynamical systems. We present an introduction that emphasizes algebraic and geometric aspects
Fri, 20 Nov 2015
16:00 -
17:00
L1
Effective behaviour of random media: From an error analysis to elliptic regularity theory
Felix Otto
(Max-Plank-Institute)
Abstract
Heterogeneous media, like a sediment, are often naturally described in statistical terms. How to extract their effective behaviour on large scales, like the permeability in Darcy's law, from the statistical specifications? A practioners numerical approach is to sample the medium according to these specifications and to determine the permeability in the Cartesian directions by imposing simple boundary conditions. What is the error made in terms of the size of this "representative volume element''? Our interest in what is called "stochastic homogenization'' grew out of this error analysis.
In the course of developing such an error analysis, connections with the classical regularity theory for elliptic operators have emerged. It turns out that the randomness, in conjunction with statistical homogeneity, of the coefficient field (which can be seen as a Riemannian metric) generates large-scale regularity of harmonic functions (w.r.t. the corresponding Laplace-Beltrami operator). This is embodied by a hierarchy of Liouville properties:
Almost surely, the space of harmonic functions of given but arbitrary growth rate has the same dimension as in the flat (i. e. Euclidean) case.
Classical examples show that from a deterministic point of view, the Liouville property fails already for a small growth rate:
There are (smooth) coefficient fields, which correspond to the geometry of a cone at infinity, that allow for sublinearly growing but non-constant harmonic functions.