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Wissenschaftskolleg (PhD program) Differential Equations
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Time Table

TimeEvent
27/06-03/07, 2010 WK Summer Camp 2010
12/04-16/04, 2010 Short course: Shear Layer Instabilities
05/07-11/07, 2009 WK Summer Camp 2009
06/07-13/07, 2008 WK Summer Camp 2008
21/01-23/01, 2008 Short course: Inverse Problems in Biophysical Models
01/07-08/07, 2007 WK Summer Camp 2007
23/04-29/04, 2007 Short course: Finite Volume and Finite Element Methods in CFD
06/11-08/11, 2006 Workshop: Mathematical Modelling of Actin-Based Motility
02/09-23/09, 2006 Summer school: Mathematics in molecular cell biology
02/07-09/07, 2006 WK Summer Camp 2006
12/06-14/06, 2006 Workshop: The Gross-Pitaevskii and related equations with nonzero boundary conditions at infinity
26/04-12/05, 2006 Short course: Wavelets and PDEs
10/04-14/04, 2006 Workshop: Navier-Stokes and turbulence
22/03-24/03, 2006 Workshop: Feynman-Kac formulas and their applications
21/03-22/03, 2006 Workshop: Free boundaries and PDEs in biology
13/03-17/03, 2006 Workshop: Euler equations: theory and numerical simulations
27/02-02/03, 2006 Short course: The young persons guide to Euler and Navier-Stokes equations:
how not to earn one million dollars with mathematics
23/01-27/01, 2006 Workshop: Symmetries of solutions of nonlinear elliptic PDEs
16/01-27/01, 2006 Short course: Numerical methods for conservation laws
10/11-12/11, 2005 Workshop: Cell motility and cytoskeletal dynamics
24/10-25/10, 2005 Conference: Nonlinear PDEs (in honor of L. Caffarelli)
19/07-27/07, 2005 Summer school: Nonlinear PDEs
10/07-17/07, 2005 WK Summer Camp 2005
25/01-03/02, 2005 Short course: An introduction to homogenization theory
24/11-27/11, 2004 Workshop: Analysis and numerics of (semi/non-)relativistic approximations of the Vlasov-Maxwell system
08/11-12/11, 2004 Workshop: Modelling of cell motility and angiogenesis
14/10-28/10, 2004 Short course: Viscosity solutions for nonlinear elliptic partial differential equations
07/07-14/07, 2004 Summer school: Nonlinear wave equations
04/07-11/07, 2004 WK Summer Camp 2004, (Pictures)
05/07-11/07, 2003 WK Summer Camp 2003, (Pictures)
12/06-17/06, 2003 Short Course: Numerical methods for collisional kinetic equations
17/03-21/03, 2003 Short Course: Coherent structures, mixing and flow control using dynamical system methods
03/03-14/03, 2003 Short Course: Asymptotic theory of flow separation
22/07-26/07, 2002 WK Summer Camp 2002
20/05-24/05, 2002 Workshop: Nonlinear models and analysis
12/03-21/03, 2002 Short Course: Scaling limits of interacting particles systems
22/11-25/11, 2001 Workshop: Semiclassical limits: WKB methods vs Wigner transform methods
22/10-24/10, 2001 Workshop: Hydrodynamic Limits: Results and Perspectives
02/10-11/10, 2001 Short Course: Introduction to Hydrodynamic Limits and Fluctuations
25/07-10/08, 2001 Summer School: NLS
21/06-25/06, 2001 Short Course: Applied Fluid Mechanics
13/06-22/06, 2001 Workshop: Poisson Geometry
06/06-07/06, 2001 Short Course: Invariant Manifolds in Singular Perturbation Theory
30/05-31/05, 2001 Short Course: 3D Navier-Stokes and Euler Equations with Initial Data Characterized by Uniformly Large Vorticity
29/05-01/06, 2001 Short Course: Inverse Problems in Differential Equations




WK Summer Camp 2010


Time: June 27 - July 3, 2010

Location: Hotel Regitnig, Weißensee, Kärnten

Program: Short courses taught by Christian Schmeiser and Klemens Fellner, student presentations, research work in small groups, swimming, hiking and other outdoor activities



Short Course: Shear Layer Instabilities


Speaker: Prof. Jonathan J. Healy (Keele University, UK)

Location: TU Vienna, seminar room 322, Resselgasse 2, Stiege 2

Time: Monday, April 12, 4pm to 6pm
Tuesday, April 13, 4pm to 6pm
Thursday, April 15, 4pm to 6pm

Contents:
Derivation of disturbance equations (Rayleigh and Orr-Sommerfeld)

Inviscid Flows:
Inviscid stability theorems (inflexion points, Howard's semi-circle), Piecewise linear inviscid profiles (Kelvin-Helmholtz, a boundary layer),
Critical layer (Tollmien's solutions), Long wave inviscid solutions giving a layered structure,
Matched asymptotic expansions to derive dispersion relations

Viscous Flows:
Weakly nonparallel flow, Upper branch scalings, Destabilizing effect of viscosity, Lower branch scalings

Weakly nonlinear theory:
Solvability conditions, Multiple-scales theory, Amplitude equations, Wave interaction

Absolute and convective instabilities

Case studies:
Rotating disc boundary layer, Swirling jets and vortex breakdown, Mixing layers



WK Summer Camp 2009


Time: July 5-11, 2009

Location: Hotel Regitnig, Weißensee, Kärnten

Program: 3 short courses taught by Heinrich Freistühler (Univ. Konstanz), Jürgen Jost (MPIM Leipzig), Slides: part 1, part 2, part 3 and Vuc Milisic (IMAG Grenoble), slides ; student presentations, slides: Sofi Esterhazy, Ilona Gucwa, Jan Sprenger, research work in small groups, swimming, hiking and other outdoor activities



WK Summer Camp 2008


Time: July 6-13, 2008

Location: Hotel Regitnig, Weißensee, Kärnten

Program: 3 short courses, research work in small groups, swimming, hiking and other outdoor activities

Topics in Traffic Flow: Short course taught by Michel Rascle (WPI and Univ. de Nice),
Slides: part 1, part 2, part 3

Compactness Methods in PDE Theory: Short course taught by Jan Haskovec (TU Wien)

TBA: Short course taught by Christian Schmeiser (Univ. Wien)



WK Summer Camp 2007


Time: July 1-8, 2007

Location: Hotel Regitnig, Weißensee, Kärnten

Program: 3 short courses, research work in small groups, swimming, hiking and other outdoor activities

Topics in Mass Transportation: Short course taught by Marco di Francesco (Univ. l'Aquila)

Functions of Self-Adjoint Operators: Short course taught by Jens Bierwirth (TU Wien)
  1. semi-groups of linear operators (and Stone's theorem),
  2. functions of self-adjoint operators,
  3. application, a formal solution of the one-way-wave equation

Diagonal defect measures and the 2D Keller-Segel model: Short course taught by Christian Schmeiser



Short course: Finite Volume and Finite Element Methods in CFD


Time: April 23-29, 2007

Location: WPI seminar room

Lecturer: Miloslav Feistauer (Praha)

Contents: Fundamental laws and equations of fluid dynamics,
Finite volume methods for the Euler equations,
combined finite volume - finite element methods for the Navier-Stokes equations,
Discontinuous Galerkin finite element method



WK Summer Camp 2006


Time: July 2-9, 2006

Location: Hotel Regitnig, Weißensee, Kärnten

Program: 3 short courses, research work in small groups, swimming, hiking and other outdoor activities

Introduction to Elasticity Theory: Short course taught by Yasmin Dolak-Struss (Univ. Wien)

TBA: Short course taught by Klemens Fellner (Univ. Wien)

Brownian Motion and Ito Calculus: Short course taught by Christian Bayer (TU Wien)



Short Course: Numerical methods for conservation laws


Time: Jan. 16 - Jan. 25 (2006)

Speaker: Prof. Christian Ringhofer (Arizona State University)

Location: WK seminar room, Nordbergstrasse 15

Timetable: Jan. 16, 11:00-12:30
Jan. 17, 14:00-15:30
Jan. 18, 11:00-12:30
Jan. 23, 11:00-12:30
Jan. 24, 12:30-14:00
Jan. 25, 14:00-15:30



WK Summer Camp 2005


Time: July 10-17, 2005

Location: Hotel Regitnig, Weißensee, Kärnten

Program: 2 or 3 short courses, research work in small groups, swimming, hiking and other outdoor activities



Short Course: An introduction to homogenization theory


Time: Jan. 25, Jan. 27, Feb. 1, Feb. 3 (2005), 16:00

Speaker: Prof. Thierry Goudon (Univ. de Lille 1)

Location: WK seminar room, Nordbergstrasse 15

Tentative table of contents:
Homogenization of elliptic problems
Compensated compactness
Double scale convergence and applications
Time dependent problems



Workshop: Modelling of Cell Motility and Angiogenesis


Organizers: Y. Dolak, H. Othmer, B. Perthame, C. Schmeiser, A. Stevens

Time: November 8-12, 2004

More information



Short Course: Viscosity solutions for nonlinear elliptic partial differential equations


Time: October 14-28, 2004

Speaker: Prof. Jorge Salazar (CMAF Lisboa and Univ. de Evora)

Location: WK seminar room, Nordbergstrasse 15

Schedule:
Lecture 1: Oct. 14, 15:00
Lecture 2: Oct. 21, 15:00
Lecture 3: Oct. 28, 15:00

Abstract: The theory of viscosity solutions was originally developed to understand 1st. order equations. Later, it was successfully extended to cover fully nonlinear 2nd. order elliptic and parabolic equations. This notion of solutions is surprisingly weak. Since candidates for solutions are just continuous functions. In fact, we only require that "test" polynomials (those who are tangent to the graph of u) satisfy the correct differential inequality (at the point of tangency). Very general existence results are combined with regularity theory to obtain a well developed and powerful tool to study a large class of PDE's. In these three talks, we'll focus on fully nonlinear elliptic equations, maximum principle, Harnack inequality and uniqueness (if time permits).



WK Summer Camp 2004


Time: July 4-11, 2004

Location: Hotel Regitnig, Weißensee, Kärnten

Program: Lectures, research work in small groups, swimming, hiking and other outdoor activities



WK Summer Camp 2003


Time: July 5-11, 2003

Location: Hotel Regitnig, Weißensee, Kärnten

Program: Research work in small groups, a small number of lectures, swimming, hiking and other outdoor activities



Short Course: Numerical methods for collisional kinetic equations


Time: June 12-17, 2003

Speaker: Prof. Lorenzo Pareschi (Ferrara)

Program:

Lecture 1: Boltzmann equations
Time: Thursday, June 12, 2:00 p.m.
Location: seminar room, Boltzmanngasse 9

Lecture 2: Spectral methods
Time: Friday, June 13, 10:00 a.m.
Location: seminar room, Wiedner Hauptstr. 8-10, 4th floor

Lecture 3: Monte Carlo methods
Time: Monday, June 16, 4:00 p.m.
Location: seminar room, Wiedner Hauptstr. 8-10, 4th floor

Lecture 4: Other methods
Time: Tuesday, June 17, 3:30 p.m.
Location: seminar room, Wiedner Hauptstr. 8-10, 4th floor


Short Course: Coherent structures, mixing and flow control using dynamical system methods


Time: First lecture: Tuesday, March 18, 2003, 10:30

Location: Seminar room of the Institute for Mechanics, Wiedner Hauptstraße 8-10, yellow area, 3rd floor

Speaker: Prof. George Haller (MIT)


Short Course: Asymptotic theory of flow separation


Time: Mondays, Wednesdays, and Fridays between March 3 and March 14, 2003, at 14:15 - 15:45

Location: Seminar room of the Institut für Strömungslehre und Wärmeuebertragung, TU, Resselgasse 3

Speaker: Prof. A. Ruban (Manchester)


WK Summer Camp 2002


Time: July 22-26, 2002

Location: Embergeralm (1800m altitude), Kärnten

Program: Research work in small groups, a small number of lectures, hiking and other outdoor activities



Workshop: Nonlinear models and analysis


Organizers: L. Caffarelli, R. Manasevich, P.A. Markowich, H. Shahgholian

Time: May 20-24, 2002

Location: ESI lecture room, Boltzmanngasse 9

Topics: Free boundaries, fully nonlinear equations, variational methods, quasilinear elliptic and parabolic equations, nonlinear transport equations

Introductory talks:
Y. Brenier: Optimal Current Transportation: from Monge to Maxwell (abstract)
L. Caffarelli: Navier-Stokes Equations - A Millenium Problem
P. Souganidis: Fully Nonlinear Stochastic PDEs
J.L. Vazquez: Nonlinear Diffusion Equations
C. Villani: Qualitative Properties of Kinetic Models

Some other talks:
M.Crandall: An Efficient Derivation of the Aronsson Equation
M.Elgueta: Blow up for solutions
J.Busca: Moment Methods and Qualitative Properties of Entire
A.Farina: Symmetry for nonlinear PDE`s: a geometrical approach
J.Dolbeault: Bubble-tower radial solutions in the slightly supercritical Brezis-Nirenberg problem
C.Gutierrez: Second derivatives estimates for the linearized Monge-Ampere equation
M.J.Esteban: On the nonrelativistic limit of the Dirac-Fock equations and its relation with quantum field theory


Short Course: Scaling limits of interacting particles systems


Lecturer: Claudio Landim

Times: March 12, 14, 19, and 21; 2-4 p.m.

Location: Seminar room, Boltzmanngasse 9

Program:
1) Central Limit Theorem for Martingales and Markov Chains.
2) Central Limit Theorem for Markov Processes. Reversibility and sector conditions.
3) Simple exclusion processes and tagged particles.
4) Central Limit Theorem for a tagged particle in the exclusion process.

Literature:
1) Liggett, Interacting particle systems, Springer 1985.
2) Kipnis and Landim. Scaling limits of interacting particles systems, Springer 1999.
3) Landim, Olla, Central Limit Theorems for Markov Processes, Notes, 2001.



Workshop: Semiclassical limits: WKB methods vs Wigner transform methods


Organizers: P. Gerard, Shi Jin, P.A. Markowich, N.J. Mauser

Time: November 22-25, 2001

Location: ESI lecture room, Boltzmanngasse 9

Program



Workshop: Hydrodynamic Limits: Results and Perspectives


Organizers: P.A. Markowich, N.J. Mauser

Time: October 22-24, 2001

Location: ESI lecture room, Boltzmanngasse 9

Program



Short Course: Introduction to Hydrodynamic Limits and Fluctuations


Lecturer: Davide Gabrielli (Univ. l'Aquila)

Abstract

Times: October 2, 3, 4, 9, 10, and 11; 10-12 a.m.

Location: Seminar room, Boltzmanngasse 9



Summer School: NLS


Time: July 25 - August 10, 2001

Location: Erwin Schrödinger Institute, Boltzmanngasse 9

Courses:
July 25 - Aug 3: Wilhelm Schlag (Caltech), Harmonic Analysis and PDEs (Lecture Notes)
July 25 - July 31: Alexander Komech (Moscow), On attractors of nonlinear Hamiltonian wave equations. Relations to mathematical problems of quantum physics
Aug 1 - 7: Norbert J. Mauser (Wien), Wigner transform techniques for NLS
Aug 6 - 10: Frank Merle (Cergy-Pontoise), Blow-up for NLS and critical GKdV equation: existence and description
Aug 8 - 10: Philippe Bechouche (Wien), NLS in a crystal: Wigner-Bloch series

Program



Short Course: Applied Fluid Mechanics


Lecturers: Yuriko Renardy (Virginia Tech), Michael Renardy (Virginia Tech)

Times: June 21, 22, and 25, 11 a.m. - 12 a.m.

Location: Seminar room, Boltzmanngasse 9

Lecture titles:
1) Numerical simulations of bamboo waves (abstract)
2) Numerical simulations of drop deformation and breakup (abstract)
3) Breakup and non-breakup of viscoelastic fluid jets (abstract)
4) Shape control in linear elasticity (abstract)



Workshop: Poisson Geometry


Organizer: P. Michor

Time: June 13 - June 22, 2001

Location: Erwin Schrödinger Institute, Boltzmanngasse 9

Program



Short Course: Invariant Manifolds in Singular Perturbation Theory


Lecturer: Stefan Siegmund (Univ. Augsburg), stefan.siegmund@math.uni-augsburg.de

Times:
June 6, 10 a.m. - 11 a.m. and 11:30 a.m. - 12:30 p.m.
June 7, 10 a.m. - 11 a.m.

Location: Seminar room, Wiedner Hauptstraße 8-10, green area, 4th floor



Short Course: 3D Navier-Stokes and Euler Equations with Initial Data Characterized by Uniformly Large Vorticity


Lecturer: Alex Mahalov (Arizona State University), alex@taylor.la.asu.edu

Times and Locations:
May 30, 2 p.m. - 3 p.m., seminar room, Boltzmanngasse 9
May 31, 4 p.m. - 5 p.m., seminar room, Boltzmanngasse 9



Short Course: Inverse Problems in Differential Equations


Lecturer: Jorge Zubelli (IMPA), zubelli@impa.br

Times and Locations:
May 29, 11 a.m. - 12 a.m., seminar room, Boltzmanngasse 9
May 30, 11 a.m. - 12 a.m., seminar room, Boltzmanngasse 9
May 31, 11 a.m. - 12 a.m., seminar room, Boltzmanngasse 9
June 1, 11 a.m. - 12 a.m., seminar room, Boltzmanngasse 9

Transparencies 1, Transparencies 2, Transparencies 3 (ps.gz-files)