| FALL 2020 Nonlinear Analysis Seminar Series
*To view the video, click the title of each lecture. |
Thursday 1st October 2020, 10:00–11:00 am JST (UTC+9), online on Zoom Cody Bullett Stockdale, Clemson University Title: Sparse domination results for compact operators Abstract: The boundedness properties of Calderón-Zygmund singular integral operators are of central importance in harmonic analysis, while the corresponding properties on weighted spaces has been of more recent interest. Indeed, within the last decade, optimal bounds for Calderón-Zygmund operators acting on weighted Lebesgue spaces have been obtained using sparse domination techniques. In addition to this theory concerning boundedness of Calderón-Zygmund operators, a theory for compactness of these operators has recently been established. In this talk, we present the extension of compact Calderón-Zygmund theory to weighted spaces using sparse domination methods. This work is joint with Paco Villarroya and Brett Wick. |
Thursday 8th October 2020, 4:00–5:00 pm JST (UTC+9), online on Zoom Augusto Ponce, Catholic University of Louvain Title: A topological toolbox for Sobolev maps Abstract (click to view) |
Thursday 15th October 2020, 10:00–11:00 am JST (UTC+9), online on Zoom Ulrich Menne, National Taiwan Normal University and National Center for Theoretical Sciences Title: A priori geodesic diameter bounds for solutions to a variety of Plateau problems Abstract: Plateau's problem in Euclidean space may be given many distinct formulations with solutions to most of them admitting an associated varifold. This includes Reifenberg's approach based on sets and Čech homology as well as Federer and Fleming's approach using integral currents and their homology. Thus, we employ the setting of varifolds to prove a priori bounds on the geodesic diameter in terms of boundary behaviour. This is ongoing joint work with C. Scharrer. |
Thursday 22nd October 2020, 4:00–5:00 pm JST (UTC+9), online on Zoom Dmitriy Stolyarov, St. Petersburg State University and St. Petersburg Department of Steklov Mathematical Institute Title: Hardy--Littlewood--Sobolev inequality for p=1 Abstract (click to view) |
Thursday 29th October 2020, 10:00–11:00 am JST (UTC+9), online on Zoom Armin Schikorra, University of Pittsburgh Title: Scale-invariant tangent-point energies for knots and fractional harmonic maps Abstract: will report about the theory of minimizing and critical knots under a set of scale invariant knot energies, the so-called tangent-point energy. We obtain lower semicontinuity and weak Sobolev-convergence of minimizing sequences to critical points away from finitely many points in the domain. Extending earlier work on Moebius-, and O'Hara energies we also obtain regularity for such critical points. This is based on joint work with S. Blatt, Ph. Reiter, and N. Vorderobermeier. |
★SPECIAL LECTURE Wednesday 4th November 2020, 4:00–6:00 pm JST (UTC+9), online on Zoom Dmitriy Stolyarov, St. Petersburg State University and St. Petersburg Department of Steklov Mathematical Institute Title: Hardy--Littlewood--Sobolev inequality for p=1: Part 1, Plan. Abstract (click to view) |
Thursday 5th November 2020, 4:00–5:00 pm JST (UTC+9), online on Zoom Takanobu Hara, Hokkaido University Title: Trace inequalities of Sobolev type and nonlinear Dirichlet problems Abstract (click to view) |
★SPECIAL LECTURE Wednesday 11th November 2020, 4:00–6:00 pm JST (UTC+9), online on Zoom Dmitriy Stolyarov, St. Petersburg State University and St. Petersburg Department of Steklov Mathematical Institute Title: Hardy--Littlewood--Sobolev inequality for p=1: Part 2, Proofs (i). Abstract (click to view) |
Thursday 12th November 2020, 10:00–11:00 am JST (UTC+9), online on Zoom Chun-Yen Shen, National Taiwan University Title: Algebraic methods in sum-product estimates and their applications Abstract: In this talk we discuss how algebraic methods play a role in the sum-product problems in additive combinatorics. Moreover, we also discuss how sum-product estimates can be used to make non-trivial progress in geometric measure theory problems. |
★SPECIAL LECTURE Wednesday 18th November 2020, 4:00–5:30 pm JST (UTC+9), online on Zoom Dmitriy Stolyarov, St. Petersburg State University and St. Petersburg Department of Steklov Mathematical Institute Title: Hardy--Littlewood--Sobolev inequality for p=1: Part 2, Proofs (ii). Abstract (click to view) |
Thursday 19th November 2020, 4:00–5:00 pm JST (UTC+9), online on Zoom Franz Gmeineder, University of Bonn Title: A-quasiconvexity and partial regularity Abstract (click to view) |
Thursday 26th November 2020, 10:00–11:00 am JST (UTC+9), online on Zoom Igor Verbitsky, University of Missouri Title: Some classes of solutions of quasilinear elliptic equations with sub-natural growth terms. Abstract (click to view) |
Thursday 3rd December 2020, 4:00–5:00 pm JST (UTC+9), online on Zoom Adolfo Arroyo-Rabasa, University of Warwick Title: Higher-integrability estimates for systems of PDEs with a non-linear pointwise elliptic constraint Abstract: I will discuss (L1,Lp) estimates for systems of PDEs of the form Au = 0, where A is a linear differential operator with constant coefficients and u is a vector-valued map satisfying a pointwise constraint of the form u(x) \in C, where C is a convex cone with sufficiently small aperture. I will collect some applications of this result to discuss higher integrability for Sobolev spaces and other spaces of bounded variation. This is joint work with G. De Philippis, J. Hirsch, F. Rindler and A. Skorobogatova. |
Thursday 10th December 2020, 10:00–11:00 am JST (UTC+9), online on Zoom Brett D. Wick, Washington University Title: Commutators and Bounded Mean Oscillation Abstract: We will discuss some recent results about commutators of certain Calderon-Zygmund operators and BMO spaces and how these generate bounded operators on Lebesgue spaces. Results in other settings and other examples will be explained. This talk is based on joint collaborative work. |
Thursday 17th December 2020, 4:00–5:00 pm JST (UTC+9), online on Zoom Bogdan Raita, Max Planck Institute for Mathematics in the Sciences Title: Old and new in Compensated Compactness theory Abstract: We will review aspects of the theory of Compensated Compactness, starting with the fundamental work of Murat and Tartar and concluding with recent results obtained jointly with A. Guerra, J. Kristensen, and M. Schrecker. Broadly speaking, the object of this study is to gain a better understanding of the interaction between weakly convergent sequences and nonlinear functionals. The general framework will be that of variational integrals defined on spaces of vector fields satisfying linear pde constraints that satisfy Murat's constant rank condition. We will focus on the weak (lower semi-)continuity of these integrals, as well as the Hardy space regularity of the integrands. |
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