[Mathkoll] ESI Senior Research Fellow Program; WS 03/04
Institut für Mathematik
sekr.mathematik@univie.ac.at
Tue, 15 Jul 2003 10:43:31 +0200
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Liebe KollegInnen,
liebe StudentInnen,
beiliegend als Attachement und Text nun die vollstaendige Ankuendigung mi=
t
Beginnzeiten der Lehrveranstaltungen im Rahmen des ESI Senior Research
Fellow Programms im Wintersemester 2003/04.
Ich bitte Sie, dies allen DissertantInnen und Interessierten bekanntzugeb=
en.
Mit herzlichen Gruessen
Joachim Schwermer
als Koordinator des ESI Senior Research Fellow Programms
____________________________________________________________________
ESI SENIOR RESEARCH FELLOW PROGRAM WINTERSEMESTER 2003/0=
4
Im Rahmen des von der Universit=E4t Wien und der Technischen Universit=E4=
t Wien
unterst=FCtzten ESI - Senior Research Fellow Programms werden im
Wintersemester 2003/04 die folgenden Vorlesungen f=FCr DissertantInnen un=
d
alle Interessenten in Mathematik und Physik angeboten:
=B7 Sobolev spaces with applications to partial differential equations
by Prof. Vladimir Maz'ya (Link=F6ping University, Sweden)
Sobolev spaces play an outstanding role in modern analysis, in particular=
,
in the theory of partial differential equations and its applications in
mathematical physics. They form an indispensable tool in approximation
theory, spectral theory, differential geometry etc.. Needless to say the
theory of these spaces is of interest in itself being a beautiful domain =
of
analysis. I include the basics on Sobolev spaces, approximation and
extension theorems, imbeddings and compactness theorems, their connection
with isoperimetric inequalities, capacities with applications to Sobolev
spaces, Besov spaces, boundary traces of Sobolev functions, pointwise
inequalities for derivatives, Gagliardo-Nirenberg inequalities, pointwise
multipliers, variational approach to elliptic equations, inequalities for
general differential operators. Some open problems will be formulated as
well. At the beginning of each lecture, I provide the students with copie=
s
of its content. I distribute problems for my students which illustrate my
course and we discuss their solutions during 30 minutes each week.
I do not follow any textbook but a part of the material is borrowed from =
the
monographs
V. Maz'ya "Sobolev Spaces", Springer, 1985
V. Maz'ya, S. Poborchi "Differentiable Functions on Bad Domains", World
Scientific 1997
Beginn: Montag, 29.09.2003, 14 - 16 Uhr bzw. Dienstag, 30.09., 12 - 12.45
Uhr, ESI
=B7 Quantenfeldtheorie auf nichtkommutativen R=E4umen
by Prof. Julius Wess (Universit=E4t M=FCnchen, Deutschland)
Quantum Field Theories will be constructed on non-commutative space-time
structures. Suit-able non-commutative coordinate spaces will be introduce=
d
such that they can be mapped with the help of the star-product formalism =
to
the concepts of deformation quantization. In the deformation quantization
formalism functions of commuting variables are the basic objects. These
functions will be identified with physical fields and their dynamics will=
be
studied. It will be strongly influenced by symmetry properties in the
algebra which appear as Hopf algebras in non-commutative spaces (quantum
groups).
Lekt=FCre:
1. q-Deformed Heisenberg Algebras, Proceedings, Schladming 1999, Springer=
,
LNP 543, p. 311
2. Deformation Quantization: Genesis, Developments and Metamorphoses,
Giuseppe Dito, Daniel Stern-heimer, http://arxiv.org/abs/math.QA/0201168
3. Quantum Field Theory on Noncommutative Spaces, Richard J. Szabo
http://arxiv.org/hepth/0109162
Beginn: Mittwoch, 15.10.2003, 17.15 - 19 Uhr, ESI
=B7 Algebraic Groups over number fields and related geometric questions
by Prof. J=FCrgen Rohlfs (Kath. Universit=E4t Eichst=E4tt, Deutschland)
In der Vorlesung werden folgende Begriffe eingef=FChrt: Adele, Idele,
Normrestsymbol, Klassen-k=F6rpertheorie, L-Funktionen, Gruppenkohomologie=
,
Tate-Nakayama-Isomorphismus, starker Approximationssatz, Tamagawazahlen u=
nd
Covolumina, Galoiskohomologie und Hasse-Prinzip. Ausgehend von der Theori=
e
f=FCr Tori werden die relevanten Begriffsbildungen auf lineare algebraisc=
he
Gruppen ausgedehnt, und es werden geometrisch-arithmetische Anwendungen
gegeben. =97 Einf=FChrende Literatur:
J=FCrgen Neukirch: Algebraic Number Theory, Grundlehren der math. Wiss. 3=
22,
Springer Verlag (1992).
T.A. Springer: Linear algebraic groups, Progress in Mathematics, Vol. 9,
Birkh=E4user-Verlag (1981).
Beginn: Mittwoch, 15.10.2003, 11 - 13 Uhr bzw. 14 - 15 Uhr, ESI
Die Veranstaltungen finden im Erwin-Schr=F6dinger-Institut, Boltzmanngass=
e 9,
A-1090 Wien statt.
Angaben zum Beginn und zum Inhalt der Vorlesungen werden rechtzeitig auf =
der
Homepage des ESI unter http://www.esi.ac.at/activities/courses eingestell=
t.
-------------------------------------------------------------------------=
---
---------------------------------------------------
ESI SENIOR RESEARCH FELLOW PROGRAM coordinated by Prof. Joachim Schwermer=
,
Institut f=FCr Mathematik, Universit=E4t Wien, Strudlhofgasse 4, A-1090 W=
ien
(Joachim.Schwermer@univie.ac.at).
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------=_NextPart_000_002C_01C34ABD.EFDE6630--