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Workshop

Introductory Workshop in Topological Aspects of Real Algebraic Geometry January 12, 2004 - January 16, 2004
To apply for Funding you must register by: September 22, 2003 over 9 years ago
Parent Program: Topological Aspects of Real Algebraic Geometry
Organizers Selman Akbulut, Grisha Mikhalkin, Victoria Powers, Boris Shapiro, Frank Sottile, and Oleg Viro
Speaker(s) Severine Fiedler, Laureano Gonzalez-Vega, Johannes Huisman, Richard Kenyon, Henry King, Sanjay Lall, Clinton McCrory, Grigory Mikhalkin, Jim Renegar, Bernd Sturmfels (UC Berkeley Math Faculty), Oleg Viro
Description The topological study of real algebraic varieties originated in the 19th century -- it was featured in Hilbert's 16th problem on the classification of real algebraic plane curves. This subject has recently grown in many directions, including higher dimensional real varieties, amoebas and tropical algebraic geometry, J-holomorphic curves from symplectic geometry, and enumerative real algebraic geometry. Some of these developments have led to advances important to applications and to the problem of real solutions to polynomial equations, including algorithms. This introductory workshop will feature survey lectures intended to introduce these topics and convey their interdependence to the mathematical public. This program will include the following talks.
  • Oleg Viro: Topology of real algebraic curves
  • Grisha Mikhalkin and Bernd Sturmfels: Tropical algebraic geometry and amoebas.
  • Frank Sottile: Enumerative problems and real solutions to equations.
  • Lalo Gonzalez-Vega: Real algebraic geometry in industry

Schedule
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Jan 12, 2004
09:00 AM - 10:00 AM
  Topology of Real Algebraic Varieties I
Oleg Viro
10:30 AM - 11:30 AM
  "Nash and beyond: putting real algebraic structures on topological objects"
Henry King
02:00 PM - 03:00 PM
  "Uniruled real algebraic 3-folds" I
Johannes Huisman
03:30 PM - 04:30 PM
  "Real solutions to polynominal equations and enumerative real algebraic geometry"
Frank Sottile (Texas A & M University)
Jan 13, 2004
09:00 AM - 10:00 AM
  Topology of Real Algebraic Varieties II
Oleg Viro
10:30 AM - 11:30 AM
  "Upper bounds in enumerative real algebraic geometry"
Frank Sottile (Texas A & M University)
02:00 PM - 03:00 PM
  "Uniruled real algebraic 3-folds" II
Johannes Huisman
03:30 PM - 04:30 PM
  "Introduction to tropical geometry"
Grigory Mikhalkin
Jan 14, 2004
09:00 AM - 10:00 AM
  Topology of Real Algebraic Varieties III
Oleg Viro
10:30 AM - 11:30 AM
  "The positive part of a tropical variety"
Bernd Sturmfels (UC Berkeley Math Faculty)
Jan 15, 2004
09:00 AM - 10:00 AM
  Topology of Real Algebraic Varieties IV
Oleg Viro
10:30 AM - 11:30 AM
  "Topology of real flexible and real algebraic curves"
Severine Fiedler
02:00 PM - 03:00 PM
  "Lower bounds in enumerative real algebraic geometry"
Frank Sottile (Texas A & M University)
Jan 16, 2004
02:00 AM - 03:00 AM
  TBA
Sanjay Lall
09:00 AM - 10:00 AM
  "Real agebraic geometry in industry"
Laureano Gonzalez-Vega
10:30 AM - 11:30 AM
  "Dimers and Harnack curves"
Richard Kenyon
03:30 PM - 04:30 PM
  "Topology of real algebraic sets in dimension four"
Clinton McCrory