[Vortraege] Vortragsankündigungen der komm. Woche (KW11)

Fri Mar 6 13:35:52 CET 2009

Sehr geehrte Fakultätsmitglieder,

anbei die Vortragsankündigungen für die nächste Woche, im Anhang finden 
Sie den Text auch als PDF Datei.

Mit freundlichen Grüßen
Margit Honkisz

Mittwoch, 11. März, 16:15 Uhr bis 17:00 Uhr, C 209, UZA 4
(Kaffejause:  15:45 Uhr bis 16:15 Uhr im Common Room)
Mathematisches Kolloquium
Prof. Dr. Alexander Komech (Universität Wien, Fakultät für Mathematik)
„On Global Attraction to Quantum Stationary States “
We consider the Klein-Gordon equation coupled to U(1)-invariant 
nonlinear oscillators. The solitary waves of thecoupled nonlinear system 
form two-dimensional submanifold in the Hilbert phase space of finite 
energy solutions. Our main results read as follows:
Theorem Let all the oscillators are strictly nonlinear.  Then all finite 
energy solutions converge, in the long time limit, to the solitary 
manifold in the local energy seminorms.
The results are obtained
       i) for 1D Klein-Gordon equation coupled to one oscillator [1,2,3];
      ii) for 1D Klein-Gordon equation coupled to finite number of  
oscillators [4];
     iii) for nD Klein-Gordon equation  coupled to one oscillator via 
mean field interaction [5].
The proofs rely on the study of energy radiation to infinity using the 
techniques of the oscillatory integrals, the theory of the 
quasimeasures, and the nonlinear mechanism of the energy transfer from 
low to high  frequencies which is controlled by the Titchmarsh 
Convolution Theorem.
The investigation is inspired by Bohr's postulates on transitions to 
quantum stationary states.
References
[1]  A.I.Komech, On attractor of a singular nonlinear U(1)-invariant 
Klein-Gordon equation,
pp  599-611 in: Proc. of the 3rd ISAAC Congress, Freie Universit\"at 
Berlin, Berlin, 2003.
[2] A.I.Komech, A.A.Komech, On global attraction to solitary waves for 
the Klein-Gordon equation coupled to nonlinear oscillator, C. R., Math., 
Acad. Sci. Paris  343, Issue 2, 15 July 2006, 111-114.
[3]  A.I.Komech, A.A.Komech, Global attractor for a nonlinear oscillator 
coupled to the
Klein-Gordon field, Arch. Rat. Mech. Anal. 185 (2007), 105-142.
[4] A.I.Komech, A.A.Komech, On global attraction to solitary waves for 
the Klein-Gordon field coupled to several nonlinear oscillators, 
submitted to J. Mathematiques Pures et Appl., 2008.
[5] A.I.Komech, A.A.Komech, Global attraction to solitary waves for 
Klein-Gordon equation with mean field interaction, accepted in  Annales 
de l'IHP-ANL, 2008.

(Dekan Univ.-Prof. Dr. Harald Rindler)

Montag, 9. März, 13:00 Uhr bis 15:00 Uhr, D 107, UZA 4
Im Rahmen des Seminars „Transporttheorie“ von o. Univ.-Prof. Dr. Walter 
Schachermayer spricht:
Prof. Dr. Ivar Ekeland (Université de Paris-Dauphine)
„Optimal transport and the pricing of quality“
Optimal transport is the common mathematical structure underlying 
diverse topics in economics. These lectures will cover two of them, 
namely adverse selection and hedonic markets. Both have to do with the 
pricing of quality goods, either by a monopolist or by a competitive 
market. I will also give some idea of numerical problems (including the 
Gale-Shapley algorithm). Notes will be available.

Montag, 9. März, ab 10:00 Uhr bis Freitag, 13. März, ESI Boltzmann 
Lecture Hall, Boltzmanngasse 9, 1090 Wien
ESI instructional workshop
„Number Theory and Physics“
Organized by A. Carey, H. Grosse, D. Kreimer, S. Paycha, S. Rosenberg, 
N. Yui
Monday, March 9th, 2009
10:00 K. Yeats “Dyson-Schwinger equations” III
11:30 D. Manchon “Connected Hopf algebras and renormalization” IV
14:30 S. Paycha “Renormalised multiple sums and integrals with constraints:
application to multiple zeta values and Feynman type integrals” I
Tuesday, March 10th, 2009
10:00 S. Paycha “Renormalised multiple sums and integrals with constraints:
application to multiple zeta values and Feynman type integrals”III
11:30 K. Yeats “Dyson-Schwinger equations” IV
14:30 M. Laca “Equilibrium and Symmetries from Number Theory” I
Wednesday, March 11th, 2009
10:00 A. Carey tba
11:30 S. Paycha “Renormalised multiple sums and integrals with constraints:
application to multiple zeta values and Feynman type integrals”IV
14:30 M. Laca “Equilibrium and Symmetries from Number Theory” II
Thursday, March 12th, 2009
10:00 A. Carey tba
11:30 M. Laca “Equilibrium and Symmetries from Number Theory” III
14:30 S. Rosenberg “Index Theorems in Riemannian and Noncommutative 
Geometry” I
Friday, March 13th, 2009
10:00 S. Rosenberg “Index Theorems in Riemannian and Noncommutative 
Geometry” II
11:30 M. Laca “Equilibrium and Symmetries from Number Theory” I

Dienstag, 10. März, 12:15 Uhr bis 13:45 Uhr, Seminarraum S1, 
Althanstraße 12-14, 1090 Wien
Complex Analysis Seminar
Dr. Erlend Fornaess Wold (University of Oslo)
„Holomorphic convexity and totally real manifolds“
We will discuss generic properties of totally real manifolds (not 
necessarily compact) in Cn. The results are the following: if M is a 
totally real manifold which is holomorphically convex with bounded 
exhaustion hulls (an empty condition in the compact case) in Cn, then a 
sufficiently small C1-perturbation (in the sense of Carleman) of M 
enjoys the same two properties. In the other direction, if M is any 
totally real manifold with (real) co-dimension 1, then given any 
continuous function f(x) on M, there exists a C1 f-perturbation M' of M 
such that M' is polynomially convex and has bounded exhaustion hulls in Cn.

Mittwoch, 11. März, 17:30 Uhr, ESI Boltzmann Lecture Hall, 
Boltzmanngasse 9, 1090 Wien
ESI
Leo Kadanoff (University of Chicago)
„Making a Splash, Breaking a Neck: The Development of Complexity in 
Physical Systems“

Freitag, 13. März, 14:00 Uhr, D 101, UZA 4
Öffentliche Defensio
Mag. Marcus Wunsch (Universität Wien, Fakultät für Mathematik)
„Asymptotics of Nonlinear Diffusion and Fluid Dynamics Equations“
This thesis consists of three parts.
The first part commences with a historical introduction to the theory of 
optimal transport starting with the original formulation of the Monge 
problem, and displays the first result of the author on the large-time 
asymptotics of solutions to the drift-diffusion-Poisson system. 
Moreover, it is proven that a constrained minimization problem in the 
quadraticWasserstein space is uniquely solvable, yielding a 
time-discrete scheme approximating the solution to a nonlocal 
Fokker-Planck equation.
The second part is concerned with two equations in one space dimension 
related to the Euler equations. For special cases, we describe the 
propagation of regularity of solutions to the generalized 
Proudman-Johnson - equation. Moreover, this part presents a continuation 
result for solutions to the generalized Constantin-Lax-Majda - equation 
reminiscent of the three-dimensional case.
In the last part, we introduce a construction of monotonously increasing 
singular functions (singularity meaning that the derivative vanishes 
almost everywhere).

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