# 23.07 Rate of convergence towards Hartree dynamics

Title: Rate of convergence towards Hartree dynamics

Speaker: Lee Jinyeop (KAIST)

Abstract: We consider interacting $N$-bosons in three dimensions. It is known that the difference between the many-body Schrödinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$. We investigate

(1) the rate of convergence for more singular interaction potential,

(2) the time dependence of the difference, and

(3) the rate of convergence for mixture condensation with $p$-components.

To the investigation, we will review quantum mechanics briefly from very basic ideas to the concept of Bose-Einstein condensation. Moreover, to introduce the main technique of the proof, we will also cover the basics of Fock space representation. Strichartz estimate and time decay estimate are main new analytic tools for the proof.

Date: 23 July 2019 (Tues)

Time: 10:00 - 11:30

Location: TBA

# 11.07 The Global dynamics on 1D compressible MHD

Title: The Global Dynamics on 1D compressible MHD

Speaker: Ronghua Pan (Geogia Institie of Technology)

Abstract: Global dynamics of classical Solutions of 1D Compressible MHD with large initial data has an interesting history and is challenging. We will report a recent Progress made by my Joint work with X. Qin.

Time: 16:00-17:30, 11.07.2019

Place: B6 A303

# 11.07 Multi-species cross-diffusion population models: existence of solutions and derivation from underlying particle models (Esther Daus)

Title : Title: Multi-species cross-diffusion population models: existence of

solutions and derivation from underlying particle models

Speaker: Esther Daus (TU Wien )

Abstract : In the first part of this talk, we focus on the proof of the existence of global-in-time weak solutions to reaction-cross-diffusion Systems for an arbitrary number of competing population species. In the case of linear transition rates, the model extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a detailed balance or weak cross-diffusion condition, where the detailed balance condition is related to the symmetry of the mobility matrix, which mirrors Onsager's principle in thermodynamics. The second part of the talk links at the formal level the entropy structure of the cross-diffusion system satisfying the detailed balance condition with the entropy structure of a reversible microscopic many-particle Markov process on a discretised space. Moreover, we present a very recent proof of a rigorous mean-field limit from a stochastic particle model to a cross diffusion model. These results are based on a joint work with Xiuqing Chen and Ansgar Juengel, a Joint work with Helge Dietert and Laurent Desvillettes, and a joint work with Li Chen and Ansgar Juengel.

Time: 14:30-16:00, 11.07. 2019

Place: B6 A303

# 11.07 Random horizon principal-agent problem (Junjian Yang)

Title : Random horizon principal-agent problem

Speaker: Junjian Yang (TU Wien )

Abstract :We consider a general formulation of the principal-agent problem with a continuous payment and a lump-sum payment on a random horizon. We ﬁrst ﬁnd the contract that is optimal among those for which the agents value process allows a dynamic programming representation, in which case the agents optimal eﬀort is straightforward to ﬁnd. We then show that the optimization over this restricted family of contracts represents no loss of generality. Using this approach, we reduced a non-zero-sum stochastic diﬀerential game to a stochastic control problem which may be solved by standard methods of stochastic control theory. At the beginning of the talk, I will also give an overview about the interplay between PDE and

stochastics.

Time: 13:00-14:30, 11.07. 2019

Place: B6 A303