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SUMMARY:Augusto Ponce (Catholic University of Louvain)
DTSTART:20201008T070000Z
DTEND:20201008T080000Z
DTSTAMP:20260422T212108Z
UID:OIST_Nonlinear_Analysis_Unit/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OIST_Nonline
 ar_Analysis_Unit/1/">A topological toolbox for Sobolev maps</a>\nby August
 o Ponce (Catholic University of Louvain) as part of FALL 2020 Nonlinear An
 alysis Seminar Series\n\n\nAbstract\nClassical works by F. Bethuel and by 
 F. Hang and F-H. Lin have identified the local and global topological obst
 ructions that prevent smooth maps from being dense in the Sobolev space \\
 (W^{1\, p}(M^{m}\; N^{n})\\) between two Riemannian manifolds when \\(p < 
 m\\). They are related to the extension of continuous maps from subsets of
  \\(M^{m}\\) to \\(N^{n}\\). In this talk I will present some work in prog
 ress with P. Bousquet (Toulouse) and J. Van Schaftingen (UCLouvain)\, insp
 ired from the notions of modulus introduced by B. Fuglede and degree for V
 MO maps by H. Brezis and L. Nirenberg. I shall explain how one can decide 
 whether a specific Sobolev map \\(u : M^{m} \\to N^{n}\\) can be approxima
 ted or not by smooth ones\, even in the presence of topological obstructio
 ns from \\(M^{m}\\) or \\(N^{n}\\).\n
LOCATION:https://researchseminars.org/talk/OIST_Nonlinear_Analysis_Unit/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Menne (National Taiwan Normal University and National Cente
 r for Theoretical Sciences)
DTSTART:20201015T010000Z
DTEND:20201015T020000Z
DTSTAMP:20260422T212108Z
UID:OIST_Nonlinear_Analysis_Unit/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OIST_Nonline
 ar_Analysis_Unit/2/">A priori geodesic diameter bounds for solutions to a 
 variety of Plateau problems</a>\nby Ulrich Menne (National Taiwan Normal U
 niversity and National Center for Theoretical Sciences) as part of FALL 20
 20 Nonlinear Analysis Seminar Series\n\n\nAbstract\nPlateau's problem in E
 uclidean space may be given many distinct formulations with solutions to m
 ost of them admitting an associated varifold. This includes Reifenberg's a
 pproach 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.\
 n
LOCATION:https://researchseminars.org/talk/OIST_Nonlinear_Analysis_Unit/2/
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BEGIN:VEVENT
SUMMARY:Yutaka Terasawa (Nagoya University)
DTSTART:20201022T070000Z
DTEND:20201022T080000Z
DTSTAMP:20260422T212108Z
UID:OIST_Nonlinear_Analysis_Unit/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OIST_Nonline
 ar_Analysis_Unit/3/">Weak Solutions for a Diffuse Interface Model for Two-
 Phase Flows of Incompressible Fluids with Different Densities and Nonlocal
  Free Energies</a>\nby Yutaka Terasawa (Nagoya University) as part of FALL
  2020 Nonlinear Analysis Seminar Series\n\n\nAbstract\nWe prove existence 
 of weak solutions for a diffuse interface model for the flow of two viscou
 s incompressible Newtonian fluids with different densities in a bounded do
 main in two and three space dimensions. In contrast to previous works\, we
  study a model with a singular non-local free energy\, which controls the 
 fractional Sobolev norm of the volume fraction. We show existence of weak 
 solutions for large times with the aid of an implicit time discretization.
  This talk is based on joint work with Professor Helmut Abels (Regensburg)
 .\n
LOCATION:https://researchseminars.org/talk/OIST_Nonlinear_Analysis_Unit/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armin Schikorra (University of Pittsburgh)
DTSTART:20201029T010000Z
DTEND:20201029T020000Z
DTSTAMP:20260422T212108Z
UID:OIST_Nonlinear_Analysis_Unit/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OIST_Nonline
 ar_Analysis_Unit/4/">Scale-invariant tangent-point energies for knots and 
 fractional harmonic maps</a>\nby Armin Schikorra (University of Pittsburgh
 ) as part of FALL 2020 Nonlinear Analysis Seminar Series\n\n\nAbstract\nI 
 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 seq
 uences to critical points away from finitely many points in the domain. Ex
 tending earlier work on Moebius-\, and O'Hara energies we also obtain regu
 larity for such critical points. This is based on joint work with S. Blatt
 \, Ph. Reiter\, and N. Vorderobermeier.\n
LOCATION:https://researchseminars.org/talk/OIST_Nonlinear_Analysis_Unit/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cody Stockdale (Clemson University)
DTSTART:20201001T010000Z
DTEND:20201001T020000Z
DTSTAMP:20260422T212108Z
UID:OIST_Nonlinear_Analysis_Unit/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OIST_Nonline
 ar_Analysis_Unit/5/">Sparse domination results for compact operators</a>\n
 by Cody Stockdale (Clemson University) as part of FALL 2020 Nonlinear Anal
 ysis Seminar Series\n\n\nAbstract\nThe 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 b
 een obtained using sparse domination techniques. In addition to this theor
 y concerning boundedness of Calderón-Zygmund operators\, a theory for com
 pactness of these operators has recently been established. In this talk\, 
 we present the extension of compact Calderón-Zygmund theory to weighted s
 paces using sparse domination methods. This work is joint with Paco Villar
 roya and Brett Wick.\n
LOCATION:https://researchseminars.org/talk/OIST_Nonlinear_Analysis_Unit/5/
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