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.
Long-Term Participants (including organizers):
Hirotachi Abo (University of Idaho), Saugata Basu (Purdue University), Alessandra Bernardi (University of Turin), Grigory Blekherman (Georgia Tech), Peter Bürgisser (Technical University of Berlin), Matthias Christandl (ETH Zürich), Jan Draisma (TU Eindhoven), Ioannis Emiris (University of Athens), Jonathan Hauenstein (North Carolina State), Neeraj Kayal (Microsoft Research India), Teresa Krick (University of Buenos Aires), Joseph M. Landsberg (Texas A&M University), Lek-Heng Lim (University of Chicago), Laurent Manivel (University of Grenoble), Ketan Mulmuley (University of Chicago), Giorgio Ottaviani (University of Florence), Frank Sottile (Texas A&M University), Bernd Sturmfels (UC Berkeley), Leslie Valiant (Harvard University), Virginia Vassilevska-Williams (Stanford University), Jerzy Weyman (University of Connecticut)
sympa [at] lists [dot] simons [dot] berkeley [dot] edu (body: subscribe%20ag2014announcements%40lists.simons.berkeley.edu) (Click here to subscribe to our announcements email list for this program.)
Those interested in participating in this program should send email to the organizers alggeometry [at] lists [dot] simons [dot] berkeley [dot] edu (at this address.)
Program image by Jesko Hüttenhain. The image, generated with the help of Mathematica, shows a circuit board superimposed on the algebraic surface with equation x3y + y3z + z3x + 5z = 0.