Vorträge in der Woche 30.11.2015 bis 06.12.2015

Dienstag, 01.12.2015: On the consistency of a new large cardinal axiom

Rupert McCallum

We shall give an account of large-cardinal axioms in set theory and introduce a new large-cardinal property that I have devised, which generalises large-cardinal properties devised by William Tait. We shall give a proof of the consistency of this large-cardinal axiom relative to the consistency of an \omega-Erd\H{o}s cardinal.

Donnerstag, 03.12.2015: Fasermultiplikatoren auf $L^p$-Faserräumen

R. Heymann (Stellenbosch, Südafrika)

Donnerstag, 03.12.2015: The Dynamics of Random Quantum Walks and Non-Unitary operators.

Dr. Eman Hamza (Univeisité Grenoble Alpes)

Freitag, 04.12.2015: Mori dream spaces and GIT with unstable components in codimension one

Marcel Helmut Maslovaric (Universität Göttingen)

Geometric Invariant Theory (GIT) is a cornerstone of the theory of Mori dream spaces, as introduced by Hu and Keel in their foundational paper on the subject. One of their main theorems asserts that in "good" situations a GIT quotient of an affine variety is a Mori dream space, which includes a description of the interesting data of a Mori dream space (the Picard number, the pseudoeffective cone, the Mori chambers and the rational contractions) in terms of GIT. In particular, the theorem assumes the unstable locus to be small, i.e. of codimension at least two, which seems to complicate its use in practice. In this talk we will discuss a generalization to the case of unstable components in codimension one, again giving a description of the relevant data in terms of GIT. If time permits, and depending on the interests of the audience, we may further discuss the application of this generalized result to quiver moduli, quotients of Mori dream spaces, or to the construction of Mori dream hypersurfaces.

Freitag, 04.12.2015: Derivation of the Vlasov equation

Prof. Peter Pickl (LMU München)

Solving the evolution equation for an interacting N-particle system analytically or numerically is, in many cases, very difficult or even impossible. However, there are situations where the correlations between the particles are negligible. In many such cases it is possible to give an effective one-particle descriptions which explains most of the physics, and to proof the validity of this effective description with mathematical rigor when N goes to infinity ("derive the equation"). One of the most basic systems one can think of is the dynamics of N stars forming a galaxy, interacting via gravitation. The effective one particle description one expects to be valid is the Vlasov equation. Deriving the Vlasov equation for this system is, however, still an open problem: the technical difficulty comes from the singularity of the interaction. In the talk I will present recent results where the interaction is slightly changed by an N-dependent cutoff.