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Interactions Between Analysis and Geometry

Workshop IV: Quasiconformal Geometry and Elliptic PDEs

May 20 - 24, 2013

Organizing Committee | Scientific Overview | Speaker List

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Organizing Committee

John Garnett (University of California, Los Angeles (UCLA), Mathematics)
Tadeusz Iwaniec (Syracuse University)
Steffen Rohde (University of Washington, Mathematics)
Eero Saksman (University of Helsinki)
Tatiana Toro (University of Washington, Mathematics)

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Scientific Overview

The theories of quasiconformal mappings and elliptic partial differential equations have classical connections dating back the work of Vekua, Bers, Bojarski, and others. During the last ten years these connections have been revitalized through new methods and breakthroughs and surprising applications that merge geometric and analytic methods. These include the solution of Calderón’s problem of impedance tomography in the plane by Astala and Paivarinta. Current research suggests that the methods of geometric analysis will also be applicable to problems in materials sciences, such as in elasticity and stochastic homogenization. Another development is the extension of the theory to degenerate elliptic equations, through the work of David, Iwaniec, Koskela, Martin and many others. Here the geometric counterpart is the theory of mappings of finite distortion, which played a vital role in recent work on random geometry. The workshop will also study the conformal geometry related open problems in SLE and quantum gravity.

With support from the Finnish government, part of the workshop will commemorate the 60th birthday of Professor Kari Astala and his many important contributions to its topics.

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Confirmed Speakers

Marianna Csörnyei (University of Chicago)
Daniel Faraco (Autonomous University of Madrid)
James Gill (Saint Louis University)
Maria Gonzalez (University of Cádiz)
Stanislav Hencl (Charles University)
Jarmo Jaaskelainen (Autonomous University of Madrid)
Pekka Koskela (University of Jyväskylä)
Izabella Laba (University of British Columbia)
Michael Lacey (Georgia Institute of Technology)
Joan Lind (University of Tennessee)
Gaven Martin (Massey University)
Gregory Miermont (École Normale Supérieure de Lyon)
Jason Miller (Massachusetts Institute of Technology)
Jani Onninen (Syracuse University)
Istvan Prause (University of Helsinki)
Xavier Tolsa (Universitat Autònoma de Barcelona)
Brent Werness (University of Washington)
Jang-Mei Wu (University of Illinois at Urbana-Champaign)
Dapeng Zhan (Michigan State University)
Michel Zinsmeister (Université d'Orléans)

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Contact Us:

Institute for Pure and Applied Mathematics (IPAM)
Attn: IAGWS4
460 Portola Plaza
Los Angeles CA 90095-7121
Phone: 310 825-4755
Fax: 310 825-4756
Email: ipam@ucla.edu
Website: http://www.ipam.ucla.edu/programs/iagws4/

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