司靈得 (Daniel Spector)

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FALL 2022 Nonlinear Analysis Seminar Series

*To view the video, click the title of each lecture.

Tuesday 20th September 2022, 9:00–10:00 TST (GMT+8), online on Zoom

Prof. Alexander Volberg, Michigan State University  

Title: Dyadic rectangles

Abstract: Weighted Carleson embedding (weighted paraproduct estimates in another language) lies in the core of various harmonic analysis and PDE results. Not much is known about it in multi-parameter situation, while one parameter is completely understood. I will formulate several new results on weighted multi-parameter Carleson embedding on multi-trees and their corollaries as embeddings of Hilbert spaces of analytic functions on poly-discs. I will also formulate corresponding Poincar\'e inequalities on multi-trees and poly-discs. Some of those results are final, but even embedding of Hardy space on bi-disc is not completely described. My presentation is based on joint works with N. Arcozzi, I. Holmes, P. Mozolyako, P. Zorin-Kranich.


Tuesday 27th September 2022, 15:00–16:00 TST (GMT+8), online on Zoom

Assistant Professor Lenka Slavikova, Charles University   

Title: Classical multiplier theorems and their sharp variants

Abstract: The question of finding good sufficient conditions on a bounded function $m$ guaranteeing the $L^p$-boundedness of the associated Fourier multiplier operator is a long-standing open problem in harmonic analysis. In this talk, I will recall the classical multiplier theorems of H\"ormander and Marcinkiewicz and present their sharp variants in which the multiplier belongs to a certain fractional Sobolev space. The talk is based in part on a joint work with L. Grafakos and M. Masty\l o.



Tuesday 30th September 2022, 9:00–10:00 TST (GMT+8), online on Zoom

Professor Jie Xiao, Memorial University of Newfoundland 

Title: Mean Hoelder-Lipschitz Potentials in Curved Campanato-Radon Spaces

Abstract:
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Tuesday 4th October 2022, 9:00–10:00 TST (GMT+8), online on Zoom

Professor Francesco Maggi, University of Texas at Austin    

Title: A Mesoscale Flatness Criterion & Its Application to Exterior Isopermetry

Abstract: TBA



Tuesday 18th October 2022, 15:00–16:00 TST (GMT+8), online on Zoom

Professor Jin-Cheng Jiang, National Tsing Hua University

Title: On the Cauchy problem for the cutoff Boltzmann equation with small initial data

Abstract: We prove the global existence of the non-negative unique mild solution for the Cauchy problem of the cutoff Boltzmann equation for soft potential model −1<=γ<0 with the small initial data in three dimensional space. Thus our result fixes the gap for the case γ=−1 in three dimensional space in the authors' previous work where the estimate for the loss term was improperly used. The other gap there for the case γ=0 in two dimensional space is recently fixed by Chen, Denlinger and Pavlović. The initial data f0 is non-negative, small in weighted L3_{x,v} and finite in weighted L15/8_{x,v}. We also show that the solution scatters with respect to the kinetic transport operator. The novel contribution of this work lies in the exploration of the symmetric property of the gain term in terms of weighted estimate. It is the key ingredient for solving the model −1<γ<0 when applying the Strichartz estimates.


Tuesday 25th October 2022, 9:00–10:00 TST (GMT+8), online on Zoom

Assistant Professor Theresa Anderson, Carnege Mellon University
 
Title: Two Meetings of Analysis and Number Theory

Abstract: TBA


Tuesday 1st November 2022, 15:00–16:00 TST (GMT+8), online on Zoom

Professor Carolin Kreisbeck, Katholischen Universität Eichstätt - Ingolstadt

Title: Dealing with Nonlocalities in Variational Functionals: Convexity notions, lower semicontinuity, and relaxation

Abstract: TBA



Tuesday 8th November 2022, 15:00–16:00 TST (GMT+8), online on Zoom

Professor Lubos Pick, Charles Univeresity

Title: Optimality problems in Orlicz spaces

Abstract: TBA



Tuesday 22nd November 2022, 15:00–16:00 TST (GMT+8), online on Zoom

Luz Roncal, Basque Center for Applied Mathematics

Title: Unique continuation for fractional discrete elliptic equations

Abstract: TBA



Tuesday 29th November 2022, 9:00–10:00 TST (GMT+8), online on Zoom

Professor Neal Bez, Saitama University   

Title: An introduction to Strichartz estimates I

Abstract: The aim of these lectures is to give a gentle introduction to Strichartz estimates, with an emphasis on particular cases such as the linear Schr\"odinger and wave equations. The associated dispersive estimates play a highly important role in the theory of Strichartz estimates so I will begin in Lecture 1 by proving the required dispersive estimates.

Next, in Lecture 2, I will prove the homogeneous Strichartz estimates in all admissible cases, including the so-called Keel--Tao endpoint case. Building on the content of the first two lectures, in Lecture 3, I will discuss the situation regarding inhomogeneous Strichartz estimates.

You can find the note of this lecture here!



Tuesday 6th December 2022, 9:00–10:00 TST (GMT+8), online on Zoom

Professor Neal Bez, Saitama University   

Title: An introduction to Strichartz estimates II

Abstract: The aim of these lectures is to give a gentle introduction to Strichartz estimates, with an emphasis on particular cases such as the linear Schr\"odinger and wave equations. The associated dispersive estimates play a highly important role in the theory of Strichartz estimates so I will begin in Lecture 1 by proving the required dispersive estimates.

Next, in Lecture 2, I will prove the homogeneous Strichartz estimates in all admissible cases, including the so-called Keel--Tao endpoint case. Building on the content of the first two lectures, in Lecture 3, I will discuss the situation regarding inhomogeneous Strichartz estimates.

You can find the note of this lecture here!


Tuesday 13th December 2022, 9:00–10:00 TST (GMT+8), online on Zoom

Professor Neal Bez, Saitama University   

Title: An introduction to Strichartz estimates III

Abstract: The aim of these lectures is to give a gentle introduction to Strichartz estimates, with an emphasis on particular cases such as the linear Schr\"odinger and wave equations. The associated dispersive estimates play a highly important role in the theory of Strichartz estimates so I will begin in Lecture 1 by proving the required dispersive estimates.

Next, in Lecture 2, I will prove the homogeneous Strichartz estimates in all admissible cases, including the so-called Keel--Tao endpoint case. Building on the content of the first two lectures, in Lecture 3, I will discuss the situation regarding inhomogeneous Strichartz estimates.

You can find the note of this lecture here!

 
 
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