Programs | Fall 2014Algorithms and Complexity in Algebraic Geometry

21 August to 19 December, 2014

Polynomial equations are ubiquitous in the mathematical sciences. The study of their solutions is the domain of algebraic geometry. Recently, there has been an explosion of activity, as computer scientists, physicists, applied mathematicians, and engineers, have realized the potential utility of modern algebraic geometry. This has brought forth an increased focus on quantitive and algorithmic questions. The semester will emphasize connections to geometric complexity theory. In this novel framework, fundamental lower bound questions can be rephrased and approached via representation theory and algebraic geometry. This applies to an arithmetic version of P versus NP as well as to multilinear algebra problems such as tensor rank and the complexity of matrix multiplication.

Organizers:

Peter Bürgisser (University of Paderborn; chair), Joseph M. Landsberg (Texas A&M University), Ketan Mulmuley (University of Chicago), Bernd Sturmfels (UC Berkeley)

Long-Term Participants (in addition to Organizers):

Saugata Basu (Purdue University), Grigory Blekherman (Georgia Tech), Jonathan Hauenstein (North Carolina State), Neeraj Kayal (Microsoft Research India), Teresa Krick (University of Buenos Aires), Lek-Heng Lim (University of Chicago), Laurent Manivel (University of Grenoble), Leslie Valiant (Harvard), Jerzy Weyman (Northeastern University)

Workshops:

During the semester there will be three workshops spanning the topics of the program. These are planned as follows:

  • Workshop 1 : "Geometric Complexity Theory." Organizers: Peter Bürgisser (University of Paderborn), Laurent Manivel (University of Grenoble), Leslie Valiant (Harvard).
  • Workshop 2 : "Solving Polynomial Equations." Organizers: Jonathan Hauenstein (North Carolina State), Pascal Koiran (ENS Lyon), Frank Sottile (Texas A&M University).
  • Workshop 3 : "Tensors in Computer Science and Geometry." Organizers: Henry Cohn (Microsoft Research), Lek-Heng Lim (University of Chicago), Jason Morton (Penn State), Giorgio Ottaviani (University of Florence).

Participation:

Those interested in participating in this program should send email to the organizers at this address.