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Workshop

Finsler Geometry June 03, 2002 - June 07, 2002
Registration Deadline: June 07, 2002 over 16 years ago
To apply for Funding you must register by: March 03, 2002 almost 17 years ago
Parent Program: --
Organizers David Bao, Robert Bryant, S.S. Chern, and Zhongmin Shen
Speaker(s)

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Description
Finsler geometry uses families of Minkowski norms, instead of families of inner products, to describe geometry. This situation is entirely analogous to how Banach spaces relate to Hilbert spaces. There has been a steady modernisation of the field during the past decade. Within the last two years, several areas of Finsler geometry have experienced accelerated growth. These include Finsler spaces of constant curvature, as well as applications of Finsler methods to industrial and medical sectors. The purpose of the workshop is to assess the current state of affairs in the field, to provide a forum for technology transfer, and to chart a course for the near future. We would like to bring together a cross section of the researchers working on different aspects of Finsler geometry. There would be expository presentations that are accessible to the differential geometry community at large. There would also be impromptu discussions, among small groups, of more specialised/technical issues. Theoretical topics of the workshop tentatively include: Cartan spaces; classification of Berwald spaces; Finsler spaces of constant flag curvature; Finsler--Einstein metrics; Finslerian volumes and measures; geodesic flows; Kobayashi metrics; Lagrange spaces; metric geometry; projective invariants; rigidity theorems. Topics dealing with applications tentatively include: diffusion on Finsler manifolds; elastiplasticity and non-smooth Finsler metrics; relativistic field theories; seismology and oil exploration; simulations of normal and abnormal cellular growth.      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
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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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Jun 03, 2002
Monday
08:00 AM - 05:00 PM
  A Videotaped Interview with Shiing-Shen Chern
S. S. Chern
09:00 AM - 09:30 AM
  Continental Breakfast (at MSRI)
09:30 AM - 09:55 AM
  Welcome and Introduction (at MSRI)
Loa Nowina-Sapinski
10:30 AM - 11:30 AM
  Volumes in Finsler geometry
Juan Carlos Alvarez-Paiva
11:45 AM - 12:45 PM
  Minimal surfaces of rotation in a special Randers space
Keti Tenenblat
12:45 PM - 02:15 PM
  Lunch
02:15 PM - 03:15 PM
  Rigidity issues in Finsler geometry
Chang-Wan Kim
03:15 PM - 03:45 PM
  Coffee Break
03:45 PM - 04:45 PM
  On Randers metrics of constant positive curvature
Aurel Bejancu
Jun 04, 2002
Tuesday
09:00 AM - 10:00 AM
  Finsler geometry in complex analysis
Giorgio Patrizio (Istituto Nazionale di Alta Matematica "Francesco Severi" (INdAM))
10:00 AM - 10:30 AM
  Morning Tea
10:30 AM - 11:30 AM
  Projective Finsler geometry
Sándor Bácsó
11:45 AM - 12:45 PM
  Kahler fibrations and Finsler manifolds
Tadashi Aikou
12:45 PM - 02:15 PM
  Lunch
02:15 PM - 03:15 PM
  Stochastic analysis on Finsler manifolds
Tomasz Zastawniak
03:45 PM - 04:45 PM
  Finsler structures on holomorphic jet bundles and a Riemann-Roch theorum
Pit-Mann Wong
05:30 PM - 06:30 PM
  Reception (at MSRI)
Jun 05, 2002
Wednesday
09:00 AM - 10:00 AM
  Holonomy groups in Finsler geometry
László Kozma
10:00 AM - 10:30 AM
  Morning Tea
10:45 AM - 11:45 AM
  Remarks on the applications of Finsler geometry to space-time
Panayiotis Stavrinos
11:45 AM - 12:45 PM
  Cartan connections of various geometries
Bradley Lackey
12:45 PM - 02:15 PM
  Lunch
02:15 PM - 03:15 PM
  Cellular growth and Berwald curvatures
Vasile Sabau
03:15 PM - 03:45 PM
  Coffee Break
03:45 PM - 04:45 PM
  The classification of Berwald metrics
Zoltan Szabo (Princeton University)
Jun 06, 2002
Thursday
09:00 AM - 10:00 AM
  Randers metrics and their curvature properties
Xinyue Cheng
10:00 AM - 10:30 AM
  Morning Tea
10:30 AM - 11:30 AM
  A catalog of Schur type results, with examples
Zhongmin Shen (Indiana University--Purdue University)
11:45 AM - 12:45 PM
  Videotaped interview
Shiing-Shen Chern
12:45 PM - 03:00 PM
  Lunch/Break
03:00 PM - 04:00 PM
  Anasov flows and Finsler spaces of non-positive curvature (at MSRI)
Patrick Foulon
04:00 PM - 04:30 PM
  Coffee Break (at MSRI)
04:30 PM - 05:30 PM
  Sphere theorem (at MSRI)
Hans Rademacher
Jun 07, 2002
Friday
09:00 AM - 10:00 AM
  Randers space forms and the Yasuda-Shimada theorum
Hideo Shimada
10:00 AM - 10:30 AM
  Morning Tea
10:30 AM - 11:30 AM
  The generality of Finsler metrics of constant flag curvature and some exotic holonomy groups
Robert Bryant (Duke University)
11:45 AM - 12:45 PM
  Finsler geometry and relativistic field theory
Ralph Beil
12:45 PM - 02:15 PM
  Lunch
02:15 PM - 03:15 PM
  Ricci curvature in Finsler geometry
David Bao (San Francisco State University)
03:15 PM - 03:45 PM
  Coffee Break
03:45 PM - 04:45 PM
  Einstein metrics of Randers type
Colleen Robles