Alternierend an der Universität Wien (mit Prof's Schachermayer, Schmeiser, Beiglböck) und TU Wien.
Vortragsplan:
6.10., 17:00 (st), Jan Maas: "Entropy gradient flows in discrete systems", Uni Wien, 2nd floor, room SR12
13.10. no meeting
20.10., 17:00 (st), Esther Daus: "Convergence to equilibrium for a linearized multi-species Boltzmann system", TU Wien, green math-tower, 3rd floor, Besprechungsraum E101
27.10., 17:00 (st), Anton Arnold: "Entropy method for degenerate Fokker-Planck equations 1", Uni Wien, 2nd floor, room SR12
3.11., 17:00 (st), Anton Arnold: "Entropy method for degenerate Fokker-Planck equations 2", TU Wien, green math-tower, 3rd floor, Besprechungsraum E101
+ Jan Haskovec: "On Uniform Decay of the Entropy for Reaction–Diffusion Systems"
10.11., 17:00 (st), Walter Schachermayer: "Exponentially concave functions and multiplicative cyclical monotonicity", Uni Wien, 2nd floor, room SR12
Abstract: I shall give motivation and background for the talk of S. Pal on Nov 17 in this seminar: Soumik Pal will then talk on his work with T. Wong on the connections of arbitrage to optimal transport. I present on Nov 10 a multiplicative version of the notion of cyclical monotonicity which plays a crucial role in optimal transport.
17.11., 17:00 (st), Soumik Pal: "On an optimal transport problem in information geometry and mathematical finance", TU Wien, green math-tower, 3rd floor, Besprechungsraum E101
Abstract: We consider a transport problem on the multidimensional unit simplex with a cost function that can be loosely described as the log of the partition function. The solutions characterize functions from the unit simplex to itself with an interesting financial interpretation. These are the only portfolios such that if one trades according to them, no matter how future stock prices behave, the trader will ultimately perform better than the stock market index. We describe solutions to this problem in terms of concave functions on the unit simplex.
We also show that it is closely related to another transport problem with a cost function given by the relative entropy. The key property driving all the proofs is an interesting multiplicative version of the usual cyclical monotonicity property for the Euclidean squared distance. Based on joint work with Leonard Wong.
1.12., 17:00 (st), Pedro Sanchez: "A journey from kinetic transport models to fractional-diffusion-advection equations", Uni Wien, 2nd floor, room SR12
26.1.2015, 17:00 (st), Wen Yue: “Understanding Entropy Decay Estimates via the Bochner-Bakry-Emery Approach from a Probabilistic View Point and a PDE View Point", TU Wien, green math-tower, 3rd floor, Besprechungsraum E101
References:
1. Convex Entropy Decay via the Bochner-Bakry-Emery Approach. Pietro Caputo, Paolo Dai Pra, and Gustavo Posta. http://arxiv.org/abs/0712.2578
2. Geodesic convexity of the relative entropy in reversible Markov Chains. Alexander Mielke. http://link.springer.com/article/10.1007%2Fs00526-012-0538-8
3.Gradient structures and geodesic convexity for reaction-diffusion systems. Matthias Liero and Alexander Mielke.
http://rsta.royalsocietypublishing.org/content/roypta/371/2005/20120346.full.pdf
Beachten Sie beim Verfassen der Ausarbeitung bitte die Richtlinie der TU Wien zum Umgang mit Plagiaten:
Leitfaden zum Umgang mit Plagiaten (PDF)Beachten Sie beim Verfassen der Ausarbeitung bitte die Richtlinie der TU Wien zum Umgang mit Plagiaten:
Leitfaden zum Umgang mit Plagiaten (PDF)