RG Analysis and Partial Differential Equations
S5B1  Graduate Seminar on Advanced Topics in PDE
Winter term 2013/14
Instructors
Prof. Dr. Herbert Koch, Prof. Dr. Christoph ThieleLectures
Friday, 14 (c.t.)  16, Seminar room 0.011Talks
 October 18, 2013: Regularity of the free boundaries for the elliptic thin obstacle problem [Wenhui Shi] (postponed to Oberseminar on October, 24)

Abstract: I will describe an ongoing project on the higher regularity of the free boundaries in the elliptic thin obstacle problem.
The main method we use is the appropriate generalization of the partial hodographLegendre transformation, which was used by
Kinderlehrer and Nirenberg in the classical obstacle problem.
 October 25, 2013: postponed
 November 8, 2013 at 14:45 pm: Global maximizers for the sphere adjoint Fourier restriction inequality [Diogo Oliveira e Silva]

Abstract: M. Christ and S. Shao were the first ones to study extremizers for the endpoint restriction problem on a
compact manifold. Their work generated a lot of interest in the area, but basic questions remained unanswered.
In particular, how do global maximizers for the TomasStein inequality on the 2sphere look like?
Just this past week, D. Foschi uploaded a paper to the arXiv with a beautiful solution of this problem.
I plan to cover his proof in detail and discuss some possible further applications of his methods.
 November 15, 2013: Multiparameter singular integrals on homogeneous nilpotent groups [Genadi Uraltsev]
 November 22, 2013: Weak type (1, 1) inequalities for discrete rough maximal functions [Mariusz Mirek]
 November 27, 2013  Extra Seminar in Room 1.007, 12:1514:00: Pointwise estimates outside exceptional sets for
the Carleson operator and the directional Hilbert transform [Francesco DiPlinio]

Abstract: One of the possible approaches to L^p bounds for the Carleson operator, somewhat reminiscent of the original proof by Carleson, and originating in the work of DemeterLaceyTaoThiele on improved range in Bourgain's return times theorem, relies on pointwise estimates outside exceptional sets. In the same spirit, but in the combinatorially more challenging twoparameter phase plane setting, we will prove sharp L^p bounds for a finitary model of the related Hilbert transform along vector fields in the plane. We also describe an adaptation of the argument proving bounds near L^1 for the lacunary Carleson operator.
 November 29, 2013: L^p estimates for entangled multilinear forms [Polona Durcik]
 December 6, 2013: Partial Regularity with Angular Integrability for the NavierStokes Equation [Renato Luca]

Abstract: We focus on suitable weak solutions of the NavierStokes equation with
small initial data in weighted Lebesgue spaces with angular integrability.
We show how the regularity of the solutions improves under higher angular
integrabilty assumption.
 December 20, 2013: We will have two seminar talks:
 14:15: Polynomial Carleson operators on the paraboloid [Po Lam Yung]
 15:25: Innerouter factorization of analytic matrixvalued functions [Joris Roos]
 January 10, 2014: Hilbert transform along measurable vector fields constant on Lipschitz curves [Shaoming Guo]
 January 24, 2014: Linear inviscid damping in low Sobolev regularity [Christian Zillinger]
News
Bonner Mathematik beim CHERanking wieder in Spitzengruppe
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Berufspraktisches Kolloquium im SS 2018
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Prof. Peter Scholze erhält einen der zehn EMSPreise
HumboldtForschungspreis für Daniel Tataru
Prof. Peter Scholze erhält den Gottfried Wilhelm LeibnizPreis 2016