# 06.12 Infinite mass boundary conditions for Dirac operators and its relation to graphene (Edgardo Stockmeyer)

Title: Infinite mass boundary conditions for Dirac operators and its relation to graphene

Speaker: Edgardo Stockmeyer (Institute of Physics, PUC, Chile)

Abstract: In this talk I will review some recent results on certain Dirac operators defined on a planar domain . In particular, we will present some basic spectral properties of these operators for different boundary conditions and will discuss its relation to graphene flakes. Moreover, for some particular boundary conditions, I will show that the corresponding operator is the limit, as M ! 1, of a Dirac operator defined on the whole plane, with a mass term of size M supported outside.

Time: 6.12.2016, 14:00-15:00

Room: A5 C116

# 01.12 On a class of cross diffusion problems arising in population dynamics (Laurent Desvillettes)

Title: On a class of cross diffusion problems arising in population dynamics

Speaker: Laurent Desvillettes (Paris)

Abstract: We are going to discuss about systems of reaction-cross diffusion equations arising in population dynamics. The mechanism of cross diffusion has been introduced by Shigesada Kawasaki and Terramoto to model the trend of a species to avoid another one and thereby, possibly segregate. The equations model the evolution of individuals belonging to two species in competition, which increase their diffusion rate in order to avoid the individuals of the other (or the same) species. More precisely, we will discuss about new results on the uniqueness, well-posedness, existence and non-existence of weak solutions to such parabolic problems and systems.

Time: 01.12.2016, 14:00-15:00

Room: A5 B139

# 14.11 Transport models of data flows in high performance computing (Richard C. Barnard)

Title: Transport models of data flows in high performance computing

Speaker: Richard C. Barnard (Oak Ridge National Laboratory USA)

Abstract: Scientific computing in high performance computing environments is characterized by distributing over many processors a task which is then performed by iteratively performing subtasks on each processor/node and then performing a communication step. We are interested in developing a predictive model for the performance of computations in large/extreme-scale systems which arises from a discrete description of these processes. This talk will discuss the derivation of a continuum model of these systems, taking the form of a nonlinear multi-dimensional transport equation. We will discuss some theoretical and numerical challenges associated with the model as well as some possible directions for dynamic optimization problems.

Time: 14.11.2016, 10:00-11:00

Room: A5 C116

# Oct. 22 and 23, ANALYSIS WORKSHOP

**Effective one-particle equations for fermionic many-particle Coulomb system: derivation and properties.**

The focus of this meeting is to get people from three working groups (LMU and Uni-Mannheim) together and to concentrate on the derivation and properties of the effective one-particle equations for (fermionic) many particle systems. The emphasis will be on electrons that interact via Coulomb forces among each other and the nucleus. Both, the stationary and the dynamic case will be discussed. In the stationary case the emphasis will be on relativistic Coulomb systems. In the dynamical case, there are few results for Coulomb systems even in the non-relativistic setting. Some of the known results will be presented and further development of mathematical methods which allow the treatment of Coulomb singularities will be discussed. Finally, the effective one-particle equations both in the mesoscopic level (Vlasov type) and hydrodynamic level (Euler-Poisson type) will be introduced and further discussion on the difficulties resulted from external attractive Coulomb case will be carried out.

**Schedule**

**October 22**

**9:00-10:30 Konstantin Merz (LMU)** Die atomare Dichte auf der Skala

**10:30-12:00 Heinz Siedentop (LMU) **Die starke Scottvermutung

**14:00-15:30 Peter Pickl (LMU) **Mean field limits for Fermions

**15:30-16:15 ****Francis Nier (Paris 13)** Mean field quantum problems as semiclassical limits: a review

**16:15-17:00 Sergey Morozov (LMU)** Lower bound on the modulus of Dirac-Coulomb operators by fractional Laplacians

**17:00-17:30 Discussion session **“On possible development of mathematical methods in dealing with additional attractive Coulomb potential”,** **led by** Hongshuo Chen (LMU) **

**October 23**

**9:00-10:30 Qitao Yin (Mannheim) **On the Vlasov-Poisson system

**10:30-12:00 Li Chen (Mannheim) **Solvability of the Euler-Poisson system

**Room: A5,6 C012**

# 27.09 Characterising path-independence of Girsanov transform for stochastic differential equations (Jianglun Wu)

Title: Characterising path-independence of Girsanov transform for stochastic differential equations

Speaker: Jianglun Wu (Swansea, UK)

Abstract: This talk will address a new link from stochastic differential equations (SDEs) to nonlinear parabolic PDEs. Starting from the necessary and sufficient condition of the path-independence of the density of Girsanov transform for SDEs, we derive characterisation by nonlinear parabolic equations of Burgers-KPZ type. Extensions to the case of SDEs on differential manifolds and the case od SDEs with jumps as well as to that of (infinite dimensional) SDEs on separable Hilbert spaces will be discussed. A perspective to stochastically deformed dynamical systems will be briefly considered.

Time: 27.09.2016, 14:00-15:00

Room: A5 C116

# 20.07 Pseudo-parabolic equation with small perturbation (Y. Cao)

Title: Pseudo-parabolic equation with small perturbation

Speaker: Yang Cao (Dalian University of Technology)

Time: 20.07.2016, 9:30-10:30

Room: A5 B143

# 03.05 Acceleration in reaction-diffusion equations (Christopher Henderson)

Title: Acceleration in reaction-diffusion equations

Speaker: Christopher Henderson (ENS de Lyon)

Abstract: Widely used in mathematical biology, reaction-diffusion equations, and in particular the Fisher-KPP equation, are used to model the spreading of a population through a new environment. The earliest results showed that populations moved at a constant speed (i.e. linear in time). However, about five years ago, Hamel and Roques discovered acceleration, or super-linear in time propagation of the population, when the initial population is very spread out. Over the last few years, acceleration has been discovered in a number of other settings. In this talk, I will discuss several of these settings, with the aim of developing an intuition for what causes and what blocks acceleration. The work in this talk is joint with Emeric Bouin and Lenya Ryzhik.

Time: 03.05.2016, 14:00-15:00

Room: A5 C116

# 19.04 On existence results for finite energy weak solutions to a class of Quantum Hydrodynamic systems (Paolo Antonelli)

Title: On existence results for finite energy weak solutions to a class of Quantum Hydrodynamic systems

Speaker: Paolo Antonelli (L'Aquila)

Abstract: Quantum Hydrodynamic models arise in the description of superfluid, Bose-Einstein condensates, or in the modeling of semiconductor devices. I will discuss some existence results for finite energy weak solutions, globally in time. By using the underlying wave function dynamics and a polar factorisation technique, which circumvents the use of the WKB ansatz, we are able to set up a consistent theory in terms of mass and current densities, without the need to define the velocity field in the vacuum region. I will then present some recent progresses about models for quantum fluids with self-generated electromagnetic fields and I will try to discuss the open problems in this direction.

Time: 19.04.2016, 14:00-15:00

Room: A5 C116

# 05.04 Derivation and analysis of a system modeling the chemotactic movement of hematopoietic stem cells (Maria Neuss-Radu)

Title: Derivation and analysis of a system modeling the chemotactic movement of hematopoietic stem cells

Speaker: Maria Neuss-Radu (Erlangen)

Abstract: It has been shown that hematopoietic stem cells migrate in vitro and in vivo towards a gradient of a chemotactic factor produced by stroma cells. In this paper, a mathematical model for this process is presented. The model consists of chemotaxis equations coupled with an ordinary differential equation on the boundary of the domain and subjected to nonlinear boundary conditions. The existence and uniqueness of a local solution is proved and the model is simulated numerically. It turns out that for adequate parameter ranges, the qualitative behavior of the stem cells observed in the experiment is in good agreement with the numerical results.

Time: 05.04.2016, 14:00-15:00

Room: A5 C116

# 02.03 Three seminar talks on fluid dynamic systems

Title: Global Well-Posedness for a Model of Incompressible Navier-Stokes in Three Dimensions

Speaker: Shuguang Shao (Beijing)

Time: 02.03.2016, 12:30-13:15

Room: A5 B139

Title: Axially Symmetric Incompressible Flow of Three-dimensional Magnetohydrodynamics

Speaker: Jihui Wu (Beijing)

Time: 02.03.2016, 13:15-14:00

Room: A5 B139

Title: The Solution of a Quasilinear Differential Equation with Closed Non-convex Initial Discontinuity

Speaker: Haiping Niu (Beijing)

Time: 02.03.2016, 14:15-15:00

Room: A5 B139

# 23.02 Sign-Changing Two-Peak Solutions For An Elliptic Free Boundary Problem Related To Confined Plasmas (Giovanni Pisante)

Title: Sign-Changing Two-Peak Solutions For An Elliptic Free Boundary Problem Related To Confined Plasmas

Speaker: Giovanni Pisante (Napoli)

Abstract: Motivated by the description of equilibrium states for plasmas in a tokamak, we consider a singular problem defined on a planar domain that generalizes the classical model for plasma confinement. This problem shares some structural similarities with the equation describing the desingularized solutions for the Euler equation of two point vortices with opposite signs and it is well known that in these type of problems there is a strong connection between the existence of roughly saying ``bubbling solutions'' and the critical points of the associated Kirchoff-Routh type functional. The aim of the talk is to show how to exploit this relation to prove, via a perturbative method, the existence of solutions with two opposite-signed sharp peaks and to establish some physically relevant qualitative properties for such solutions. These are results from a recent project in collaboration with Tonia Ricciardi (Univ. "Federico II" in Naples).

Time: 23.02.2016, 14:00-15:00

Room: A5 C116

# 17.02 Effective one particle equations II (H. Siedentop)

Title: Effective one particle equations II

Speaker: Heinz Siedentop (LMU)

Time: 17.02.2016, 14:00-15:00

Room: A5 C116