Fall 2014

Algorithms and Complexity in Algebraic Geometry

Aug. 21Dec. 19, 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.

sympa [at] lists [dot] simons [dot] berkeley [dot] edu (body: (Click here to subscribe to our announcements email list for this program.)

Peter Bürgisser (Technical University of Berlin; chair), Joseph M. Landsberg (Texas A&M University), Ketan Mulmuley (University of Chicago), Bernd Sturmfels (UC Berkeley).
Long-Term Participants (including Organizers): 
Hirotachi Abo (University of Idaho), Saugata Basu (Purdue University), Alessandra Bernardi (University of Bologna), Grigoriy Blekherman (Georgia Institute of Technology), Jaroslav Buczynski (Polish Academy of Sciences), Peter Bürgisser (Technical University of Berlin; chair), Matthias Christandl (ETH Zürich), Jan Draisma (Technische Universiteit Eindhoven ), David Eisenbud (Mathematical Sciences Research Institute and UC Berkeley), Ioannis Emiris (University of Athens), Elizabeth Gross (San Jose State University), Jonathan Hauenstein (North Carolina State University), Neeraj Kayal (Microsoft Research India), Teresa Krick (Universidad de Buenos Aires ), Joseph M. Landsberg (Texas A&M University), Lek-Heng Lim (University of Chicago), Ricky Liu (University of Michigan), Gregorio Malajovich (Universidade Federal do Rio de Janeiro), Laurent Manivel (University of Montreal), Ketan Mulmuley (University of Chicago), Luke Oeding (Auburn University), Giorgio Ottaviani (University of Florence), Pablo Parrilo (Massachusetts Institute of Technology), Youming Qiao (University of Technology, Sydney), Jose Rodriguez (North Carolina State University), Michael Shub (City University of New York), Frank Sottile (Texas A&M University), Bernd Sturmfels (UC Berkeley), Leslie Valiant (Harvard University), Jerzy Weyman (Northeastern University), Virginia Vassilevska Williams (Stanford University).
Research Fellows: 
Klim Efremenko (Tel Aviv University), Michael Forbes (Massachusetts Institute of Technology), Maria Isabel Herrero (Universidad de Buenos Aires), Christian Ikenmeyer (Texas A&M University), Kaie Kubjas (Aalto Science Institute), Mateusz Michalek (Polish Academy of Sciences), Matthew Niemerg (Colorado State University), Benjamin Rossman (National Institute of Informatics), Cynthia Vinzant (University of Michigan).
Visiting Graduate Students: 
Cameron Farnsworth (Texas A&M University), Fulvio Gesmundo (Texas A&M University), Yonghui Guan (Texas A&M University), Samuel Hopkins (Cornell University), Mario Kummer (University of Konstanz), Simone Naldi (LAAS-CNRS, Toulouse), Zvi Rosen (UC Berkeley).


Sept. 2Sept. 5, 2014
Organizers: Joseph M. Landsberg (Texas A&M University)
Sept. 15Sept. 19, 2014
Organizers: Ketan Mulmuley (University of Chicago; chair), Peter Bürgisser (Technical University of Berlin), Laurent Manivel (University of Montreal), Leslie Valiant (Harvard University)
Oct. 13Oct. 17, 2014
Organizers: Frank Sottile (Texas A&M University; chair), Jonathan Hauenstein (North Carolina State University), Pascal Koiran (ENS Lyon)
Nov. 10Nov. 14, 2014
Organizers: Lek-Heng Lim (University of Chicago; chair), Henry Cohn (Microsoft Research New England), Jason Morton (Pennsylvania State University), Giorgio Ottaviani (University of Florence)
Nov. 18Nov. 21, 2014
Organizers: Cynthia Vinzant (University of Michigan; chair), Alessandra Bernardi (University of Bologna), Anton Leykin (Georgia Institute of Technology), Luke Oeding (Auburn University), Claudiu Raicu (Princeton University)

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.