## September – Oktober 2018

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.

Hypertoric variety $Y(A, alpha)$ is a (holomorphic) symplectic variety, which is defined as a Hamiltonian reduction of complex vector space by torus action. This is an analogue of toric variety. Actually, its geometric properties can be studied through the associated hyperplane arrangements (instead of polytopes). By definition, there exists a projective morphism $pi:Y(A, alpha) to Y(A, 0)$, and for generic $alpha$, this gives a crepant resolution of affine hypertoric variety $Y(A, 0)$. In general, for a (conical) symplectic variety and its crepant resolution, Namikawa showed the existence of the universal Poisson deformation space of them. We construct the universal Poisson deformation space of hypertoric varieties $Y(A, alpha)$ and $Y(A, 0)$. We will explain this construction. In application, we can classify affine hypertoric varieties by the associated matroids. If time permits, we will also talk about applications to counting crepant resolutions of affine hypertoric varieties. This talk is based on my master thesis.

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

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

More information you can find on the conference homepage:

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