Teaching

Type:	Time:	Place:	Start:
PJSE 2 std.	Mo 9:45-11:15	SR08	5.10

In this seminar we would like to discuss some classical inequalities with important applications in analysis like dispersive estimates, global existence and blow-up for nonlinear PDEs etc. For example,

Hanner [LL], Rearrangement [LL], Hausdorff-Young [LL], Hardy-Littlewood-Sobolev [LL], Sobolev inequalites [LL], Rellich [LL], Poincare [LL], Strichartz [LP]

These are just some possibilites and we are open to suggestions from students as well!

Date:	Title:	Speaker:	References:
16.11	Poincaré inequalities	Christopher Rieser	[LL], see also the errata
23.11	Kato's inequality	Alexis Aivaliotis	[LL,Ha]
30.11	Harnack's inequality	Mateusz Piorkowski	[GT,PW]
11.01	Eigenvalue inequalities of Hermitian matrices and Wigner's semicircle law	Peter Mühlbacher	[TT]
18.01	Embedding theorems	Markus Holzleitner	[LL]
25.01	Cwikel-Lieb-Rosenblum type inequalities	Aleksey Kostenko	[S]

References:

1. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, New York, 1998.
2. F. Haslinger, The d-bar Neumann Problem and Schrödinger Operators, De Gryter, Berlin, 2014
3. E. Lieb and M. Loss, Analysis, 2nd ed., GSM 14, AMS, Providence, 2001
4. F. Linares und G. Ponce, Introduction to Nonlinear Dispersive Equations, 2nd ed., Springer, New York, 2015
5. M.H. Potter and H.F. Weinberger, Maximum principles in differential equations, Prentice-Hall, 1967.
6. B. Simon, Trace Ideals and Their Applications, Amer. Math. Soc., Providence, 2005.
7. T. Tao, Topics in random matrix theory, Amer. Math. Soc., Providence, 2013

Preparation and presentation of a chosen topic. Active participation during the course.

Majors in Mathematics (master program, code MANS), Physics, ...