### Special lectures

#### Current events

Special Lecture "Regularity of solutions to elliptic equations" (3 ECTS)

07.03.2019 - 27.06.2019

Lecturer:

Marcel Braukhoff (TU Wien)Location:

Sem.R. DA grün 03 C (TU Wien)Abstract:

Elliptical equations occur in various applications in physics, chemistry and biology. Examples are equations from electrostatics and gravitation. Furthermore, elliptical equations can be found as stationary problems describing the diffusion of a chemical in a solution. If one wants to calculate the solutions numerically in these cases, it turns out that the numerical methods usually converge faster the more regular the solution of the elliptical equation is. On the one hand, direct methods using the fundamental solution are treated. On the other hand, the $H^m$ regularity and the Hölder regularity of solutions of elliptic equations are also proved.
Course Webpage

#### Past events

Special Lecture "Reaction-diffusion and cross-diffusion systems" (3 ECTS)

01.10.2018 - 28.01.2019

Lecturer:

Esther Daus (TU Wien)Location:

Sem.R. DA grün 03 C (TU Wien)Abstract:

Many applications in physics, chemistry and biology can be modeled by reaction-(cross) diffusion systems, which describe the evolution of the densities or concentrations of a multicomponent system. The focus of the first part of the lecture will be on the mathematical properties of reversible reaction-diffusion systems based on entropy methods. Our goal will be to show how the entropy estimate can be used systematically to get bounds leading to the existence of strong or weak solutions, as well as bounds for the convergence rate to equilibrium.
The second part of this lecture will then be devoted to the study of the existence theory for cross-diffusion systems used in applications, for instance a population dynamics model describing the segregation of species due to competition or the Maxwell-Stefan equations modeling the evolution of a gaseous mixture.

Course Webpage

Special Lecture "The Plateau problem in the Calculus of Variations" (2 ECTS)

03.09.2018 - 12.09.2018

Lecturer:

Luca Lussardi (Politecnico di Torino)
Location:

University of Vienna
Abstract:

The aim of the course is to give an overview of the main techniques for the Plateau problem, that is to find a surface with minimal area that spans a given boundary curve in $\mathbb{R}^3$. This problem dates back to the physical experiments of Joseph Plateau who tried to understand the possible configurations of soap films. From the mathematical point of view the problem is very hard and a lot of possible formulations are available: perhaps still today none of these answers is the answer to the original formulation by Plateau.
In this course first of all I will briefly introduce the problem showing that, at least in the smooth case, if the first variation of the area vanishes then the surface must have zero mean curvature. Then I will describe how the classical solution by Douglas and Rado works, and I will pass to modern formulations of the problem in the context of geometric measure theory: finite perimeter sets approach, currents approach, and minimal sets approach. Possibly, some physical experiments with soap films could be done in order to clarify advantages and drawbacks of the approaches.
For more details about the course, please visit the relative

webpage

.Special Lecture "Introduction to kinetic theory: the Boltzmann equation" (2 ECTS)

30.07.2018 - 03.08.2018

Lecturer:

Francis Filbet (Université Toulouse III & Institut Universitaire de France)Location:

ESI, Vienna (Boltzmanngasse 9, 1090 Vienna)Abstract:

In this lectures we will focus on the Boltzmann equation for rarefied gas dynamics. After a short introduction of the physical background we will review some basic tools in analysis to study the existence of solution for the homogeneous Boltzmann equation. Then, some numerical approximation based on spectral methods will be presented and a rigorous convergence study will be performed.
Course Webpage

Special Lecture "Mathematical modeling of collective motion in biology and life sciences" (3 ECTS)

07.05.2018 - 07.06.2018

Lecturer:

Jan Haskovec (King Abdullah University of Science and Technology, Thuwal, KSA)Location:

TU WienTopics:

- Systems of self-propelled particles, the Cucker-Smale model as a proptotypical example, asymptotic flocking.
- Attraction-repulsion-orientation model. Milling, double-milling and other patterns.
- Models with noise and delay.
- Mesoscopic and hydrodynamic descriptions and their well posedness.

Course Announcement

Special Lecture "Stochastic Processes and Stochastic Differential Equations"

20.11.2017 - 18.12.2017

Lecturer:

Gaurav Dhariwal (TU Wien)Location:

TU WienTopics:

- Probability and measure
- Lebesgue integration
- Random variables
- Discrete stochastic processes
- Brownian Motion
- Itô Lemma
- SDEs

Course Announcement

Special Lecture "Weak & Strong Compactness and its Applications to Nonlinear Evolution PDEs"

13.11.2017 - 11.12.2017

Lecturer:

Xiuqing Chen (Beijing University of Posts & Telecommunications)Location:

TU WienTopics:

- Basic facts concerning weak convergence and weak compactness for functions and measures.
- Strong compactness in $L_p(0,T;B)$ spaces (i.e. Aubin-Lions-Dubinskii lemmas).
- Application to porous media/fast diffusion equations.
- Application to reaction-diffusion equations.

Course Announcement

Special Lecture "Compressible Navier-Stokes equations"

13.03.2017 - 27.04.2017

Lecturer:

Milan Pokorný (Charles University, Prague)Location:

TU WienUpdate

: On Wednesdays the lecture time has been rescheduled to 16:00-17:30

.
Poster

Special Lecture "Interface and contact problems: From analysis to numerics"

30.05.2016 - 10.06.2016

Lecturer:

Heiko Gimperlein (Heriot-Watt University)Location:

TU WienBrief Syllabus:

- Modelling of interface problems between materials: interface conditions and friction laws
- Obstacle problems, friction and contact: (free) time-independent boundary problems as constrained on nonsmooth variational problems, solution using Uzawa and semismooth Newton methods
- Nonlinear analysis of variational inequalities: functional analytic background, classical theorem on wellposedness and abstract approximation, regularity of solutions
- Approximation by finite and boundary elements - from basics to current research: BEM for dummies, variational inequalities and penalty formulations, error analysis, adaptivity, advanced approximation methods, maybe coupling of FEM and BEM
- Towards time-dependent dynamic contact problems

Course Webpage

Special Lecture "An Introduction to Viscosity Solutions of Fully Nonlinear 2nd Order PDE"

02.05.2016 - 24.05.2016

Lecturer:

Nikos Katzourakis (University of Reading)Location:

TU WienBrief Syllabus:

Part I General Theory

- History, Examples, Motivation and First Definitions
- Second Definitions and Basic Analytic Properties of the Notions
- Stability Properties of the Notions and Existence via Approximation
- Mollification of Viscosity Solutions and Semiconvexity
- Existence of Solution to the Dirichlet Problem via Perron's Method
- Comparison results and Uniqueness of Solution to the Dirichlet Problem

- Minimisers of Convex Functionals and Viscosity Solutions of the Euler-Lagrange PDE
- Existence of Viscosity Solutions to the Dirichlet Problem for the Laplacian

Poster

and TISS page

Special Lecture "Microlocal Analysis and Boundary-Value Problems"

07.04.2016 - 29.04.2016

Lecturer:

Michael Dreher (University of Konstanz)Location:

TU Wien, Sem. R. DB gelb 03- Thursday 10:00-13:00, TU Freihaus, Sem.R. DA grün 03 C
- Friday 14:00-17:00, TU Freihaus, Sem.R. DA grün 03 A

Brief Syllabus:

- Pseudodifferential operators and their mapping properties
- Elliptic operators in the full space and their inverses
- Boundary conditions and BVPs
- Applications to fluiddynamics (QHD)
- Hyperbolic problems and Fourier integral operators

Poster

and
lecture notes

Mini Lecture on "Modeling, analysis and numerical simulation of micro-electro mechanical systems"

07.03.2016 - 10.03.2016

Lecturer:

Alan Lindsay (University of Notre Dame)Location:

TU Wien, Sem. R. DB gelb 03Poster

and detailed abstract

Special Lecture "Kacs Model and the Propagation of Chaos"

25.01.2016 - 28.01.2016

Lecturer:

Amit Einav (University of Cambridge, UK)Location:

TU Wien, Sem. R. DB gelb 03Time:

14:00-16:00Poster

Special Lecture "Entropies - information theory flavored approach to PDEs

19.11.2015 - 26.11.2015

Lecturer:

Mario Bukal (University of Zagreb)Location:

TU Wien, SEM 101BTopics:

- Axiomatic foundation of entropies in information theory (Rényi and Tsallis entropies)
- Entropy power, concavity, and related functional inequalities
- Long-time behavior of nonlinear diffusion equations
- Markov decision processes
- Perception - action cycles and information-to-go

Course Announcement

Special Lecture "Homogenization theory - Multiscale modelling and analysis of physical and biological processes"

08.06.2015 - 02.07.2015

Lecturer:

Mariya Ptashnyk (University of Dundee, UK)Location:

TU WienTopics:

- methods of periodic homogenization
- multiscale modelling and analysis of transport and reaction processes in perforated and partially perforated domains
- duality-porosity
- locally-periodic homogenization
- multiscale analysis of equations of linear elasticity and viscoelasticity
- main ideas of $\Gamma$- and $G$-convergences

Course Announcement

Special Lecture "Optimal Control of Partial Differential Equations"

02.06.2015 - 02.07.2015

Lecturer:

Pina Milišić (University of Zagreb)Location:

TU WienTopics:

- Motivating examples
- Finite-dimensional optimal control problems
- Optimal control of elliptic PDEs
- Optimal control of semilinear elliptic PDEs

Course Announcement

Special Lecture "Numerical methods for time-domain boundary integral equations"

14.04.2015 - 24.04.2015

Lecturer:

Lehel Banjai (Heriot-Watt University)Location:

TU WienTopics:

- Introducing TDBIEs and their discretizations
- Convolution quadrature and a typical analysis of the time-discretization
- Implementation: Use of lower triangular Toeplitz matrices
- Advanced topics (unlikely to cover all): higher-order methods, FEM-BEM coupling, non-linearities

Course Announcement

and
TISS page

Special Lecture "Stochastic Differential Equations in Population Dynamics"

12.01.2015 - 11.02.2015

Lecturer:

Florian Rupp (German University of Technology in Oman)Location:

TU WienKeywords:

- Stochastic modeling of biological processes from first principles
- Ito's and Stratonovich's stochastic integrals
- Existence and uniqueness of solutions of stochastic ordinary differential equations (SODEs) in the strong and weak sense, boundedness of solutions of SODEs in the positive orthant, strong and weak Taylor schemas and the simulation of paths
- Fokker-Planck equation and the evolution of densities
- Random Dynamical Systems, Hopf-bifurcations in SODE-driven systems, crater densities and the approximation of strange attractors during stochastic Hopf-bifurcations.

Course Announcement

and Schedule

Minicourse on "Analytical methods in the theory of Schrödinger operators with quasiperiodic potentials"

25.09.2013 - 27.09.2013

Lecturer:

Wilhelm Schlag (University of Chicago)Location:

Faculty of Mathematics, University of Vienna, Seminar room 15, 3rd floor, OMP1Time:

25.-27.09.2013, Wed, Thu, Fri 10:00 - 12:00Organisers:

Aleksey Kostenko and Gerald TeschlAbstract:

We will present some of the tools developed by Bourgain,
Goldstein, and the speaker to study a class of Schrödinger
operators on both the line Z as well as higher-dimensional lattices.
These methods rely on properties of subharmonic functions, but
also involve ideas from semi-algebraic sets.
Poster