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Mathematical Sciences Research Institute

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Workshop

Integral Geometry in Representation Theory October 08, 2001 - October 12, 2001
Registration Deadline: October 12, 2001 over 17 years ago
To apply for Funding you must register by: July 08, 2001 almost 18 years ago
Parent Program:
Organizers Leticia Barchini, Oklahoma State University, Roger Zierau, Oklahoma State University.
Speaker(s)

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Description
This workshop will concentrate on several topics in representation theory and geometric analysis of homogeneous spaces for which techniques in integral geometry play a key role. These topics will include: 1) Spaces of solutions of differential equations on homogeneous spaces and integral transforms representing solutions; Hua equations, Schmid equations, Poisson and Szego transforms, and Radon and Penrose transforms. Also, inversion formulas and various characterizations of the images of these transforms. Included is the geometry of cycle spaces and the holomorphic extensions of a representations to complex domains. 2) Harmonic analysis on homogeneous spaces. A major focus here is the Plancherel theorem for semisimple symmetric spaces. Also included is harmonic analysis on special spaces such as causal spaces and Makarevi\v c spaces. 3) Explicit geometric and analytic realizations of irreducible unitary representations on Hilbert spaces. Many very different techniques are used in this direction: Intertwining operators, degenerate principal series and harmonic analysis, constructions of minimal represenations, restricitions of irreducible representations to subgroups, the geometry of coadjoint orbits and quantization. Group Photo of Participants
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

Additional lodging options (short term housing page - Short Term Housing

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Schedule, Notes/Handouts & Videos
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Oct 08, 2001
Monday
08:00 AM - 05:00 PM
  Applications of the discrete spectrum of semisimple symmetric spaces
Peter Trapa (University of Utah)
10:30 AM - 01:30 PM
  Twisted Radon transforms on Grassmannians
Toshio Oshima
01:30 PM - 02:45 PM
  Symmetry in Integral Geometry
Michael Eastwood (Australian National University)
02:45 PM - 03:45 PM
  The dual horospherical Radon transform for polynomials
Joachim Hilgert
Oct 09, 2001
Tuesday
09:30 AM - 11:00 AM
  Residues in the Plancherel formula for a semisimple symmetric space
Erik van den Ban
11:00 AM - 02:00 PM
  Geometric connection of the Poisson kernel with a Cayley transform for homogeneous Siegel domains
Takaaki Nomura
02:00 PM - 03:30 PM
  The Helgason (KKMOOT) Theorem for non-symmetric Kähler manifolds
Richard Penney
03:30 PM - 04:30 PM
  Totally geodesic Radon transform on symmetric spaces
Sigurdur Helgason
Oct 10, 2001
Wednesday
09:30 AM - 11:00 AM
  D(G/H) and K-finite functions on a reductive symmetric space G/H
Patrick Delorme
11:00 AM - 02:00 PM
  Horospherical transform and Plancherel formula on symmetric spaces
Simon Gindikin (Rutgers University)
02:00 PM - 03:30 PM
  Analysis of Berezin kernels on symmetric spaces
Yurii Neretin
03:30 PM - 04:30 PM
  The Maslor index and bounded cohomology
Bent Ørsted
Oct 11, 2001
Thursday
11:00 AM - 02:00 PM
  Langlands formalism for nonalgebraic groups and applications to character lifting
Peter Trapa (University of Utah)
02:00 PM - 03:30 PM
  Holomorphic aspects of representations: geometry and harmonic analysis
Robert Stanton
03:30 PM - 04:30 PM
  Conformal geometry and analysis on minimal representations of O(p,q)
Toshiyuki Kobayashi
Oct 12, 2001
Friday
11:00 AM - 02:00 PM
  Helgason's conjecture and its generalization to affine symmetric spaces
Jing-Song Huang
02:00 PM - 03:30 PM
  The generalized Cayley map from an algebraic group to its Lie algebra
Bertram Kostant
03:30 PM - 04:30 PM
  Jordan algebras and good models for unipotent representations
Alexander Dvorsky