## September – Oktober 2018

More information you can find on the conference homepage:

https://www-user.tu-chemnitz.de/~sevc/WorkshopMPI-2018.html

Attention: this talk has to be cancelled

I will discuss the existence of an open set of n1× n2× n3 tensors of rank r on which a popular and eﬃcient class of algorithms for computing tensor rank decompositions based on a reduction to a linear matrix pencil, typically followed by a generalized eigendecomposition, is arbitrarily numerically forward unstable. The analysis shows that this problem is caused by the fact that the condition number of the tensor rank decomposition can be much larger for n1× n2× 2 tensors than for the n1× n2× n3 input tensor. Moreover, I present a lower bound for the limiting distribution of the condition number of random tensor rank decompositions of third-order tensors. The numerical experiments illustrate that for random tensor rank decompositions one should anticipate a loss of precision of a few digits. Joint work with Carlos Beltran and Nick Vannieuwenhoven.

More information you can find on the conference homepage:

https://www-user.tu-chemnitz.de/~sevc/WorkshopMPI-2018.html

Vortrag in der Reihe: Arbeitsgemeinschaft ANGEWANDTE ANALYSIS

In a population where individuals reproduce at different rates (i.e. have different “fitness”), the fraction of high-fitness types naturally increases over time—this is what Darwin coined “natural selection”. This process can be represented abstractly as a non-linear yet exactly soluble integro-differential equation. I will show that this equation possesses self-similar solutions and describe their basins of attractions. The presentation will be guided by analogies with extreme value statistics on the one hand and and mean-field coarsening dynamics on the other.

In my talk I will propose and discuss a set of combinatorial invariants of simplicial complexes. The invariants are very elementary and defined by counting connected components and/or homological features of induced subcomplexes, but admit a commutative algebra interpretation as weighted sums of graded Betti numbers of the underlying complex.

I will first define these invariants, state an Alexander-Dehn-Sommerville type identity they satisfy, and connect them to natural operations on triangulated manifolds and spheres. Then I will present a (non-optimal) upper bound for arbitrary pure and strongly connected simplicial complexes and discuss the very natural conjecture that, for triangulated spheres of a given f-vector, the invariants are maximised for the Billera-Lee-spheres.

This is joint work with Giulia Codenotti and Francisco Santos, see https://arxiv.org/abs/1808.04220.

This is a topical survey talk about certain canonical dynamical systems on the space of proabability measures when considered as an infinite dimensional manifold equipped with Otto’s Riemannian structure for optimal transportation. Apart from classical gradient flows we will discuss Hamiltonian systems and connections to Quantum mechanics as well as candidate processes for what can be considered Brownian motion associated to the corresponding infinite dimensional Laplace-Beltrami operator.

More information you can find on the conference homepage:

https://www.mis.mpg.de/calendar/conferences/2018/QFT2018/index.html

More information you can find on the conference homepage:

https://www.mis.mpg.de/calendar/conferences/2018/QFT2018/index.html