Fall 2014

Solving Polynomial Equations

Monday, Oct 13, 2014 to Thursday, Oct 16, 2014 

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Frank Sottile (Texas A&M University; chair), Jonathan Hauenstein (University of Notre Dame), Pascal Koiran (École Normale Supérieure de Lyon)

Polynomial equations and inequalities are ubiquitous in the mathematical sciences and their applications. This workshop will focus on recent algorithmic advances, both numeric and symbolic, on novel domains of application, and on fundamental issues of complexity in algebraic geometry. One recent advance concerns Smale's 17th problem which asks for the solution of polynomial equations in polynomial time in the average case. Understanding and solving systems of sparse polynomials (fewnomials) offers challenging problems. The real τ-conjecture (on the number of real roots of a sum of products of sparse polynomials) establishes a fascinating new link between real algebraic geometry and fundamental complexity lower bound questions. Another topic for this workshop is convex algebraic geometry, which fuses convex optimization theory and real algebraic geometry. We will also discuss current software tools such as Bertini, Singular, SAGE, and Macaulay2, and how these may aid researchers in the CS community.

Enquiries may be sent to the organizers workshop_alggeom2 [at] (at this address.)

Invited Participants: 

Hirotachi Abo (University of Idaho), Saugata Basu (Purdue University), Frédéric Bihan (Université de Savoie), Grigoriy Blekherman (Georgia Institute of Technology), Daniel Brake (University of Notre Dame), Jaroslaw Buczynski (Polish Academy of Sciences), Peter Bürgisser (Technische Universität Berlin), Felipe Cucker (City University of Hong Kong), Alicia Dickenstein (Universidad de Buenos Aires), Klim Efremenko (University of Chicago), David Eisenbud (Mathematical Sciences Research Institute), Ioannis Emiris (University of Athens), Kousha Etessami (University of Edinburgh), Cameron Farnsworth (Texas A&M University), Michael Forbes (Massachusetts Institute of Technology), Shuhong Gao (Clemson University), Fulvio Gesmundo (Texas A&M University), Elizabeth Gross (San Jose State University), Yonghui Guan (Texas A&M University), Jonathan Hauenstein (University of Notre Dame), Nickolas Hein (University of Nebraska at Kearney), María Isabel Herrero (Universidad de Buenos Aires), Serkan Hosten (San Francisco State University), Pavel Hrubeš (Academy of Sciences of the Czech Republic), Jesko Hüttenhain (Technische Universität Berlin), Christian Ikenmeyer (Texas A&M University), Neeraj Kayal (Microsoft Research India), Pascal Koiran (École Normale Supérieure de Lyon), Teresa Krick (Universidad de Buenos Aires and CONICET), Kaie Kubjas (Aalto University), Mario Kummer (Universität Konstanz), Joseph Landsberg (Texas A&M University), Jean-Bernard Lasserre (CNRS - Toulouse), Anton Leykin (Georgia Institute of Technology), Wei Li (Academy of Mathematics and Systems Science, Chinese Academy of Sciences), Lek-Heng Lim (University of Chicago), Ricky Liu (University of Michigan), Satya Lokam (Microsoft Research India), Gregorio Malajovich (Universidade Federal do Rio de Janeiro), Dhagash Mehta (North Carolina State University), Nikki Meshkat (North Carolina State University), Mateusz Michalek (Polish Academy of Sciences), Peter Bro Miltersen (Aarhus University), Ketan Mulmuley (University of Chicago), Simone Naldi (CNRS - Toulouse), Matthew Niemerg (Colorado State University), Luke Oeding (Auburn University), Mariann Ollar (University of Pennsylvania), Giorgio Ottaviani (Università di Firenze), Pablo Parrilo (Massachusetts Institute of Technology), Youming Qiao (University of Technology, Sydney), Jose Rodriguez (University of Notre Dame), J. Maurice Rojas (Texas A&M University), Zvi Rosen (UC Berkeley), Benjamin Rossman (National Institute of Informatics), Mohab Safey El Din (Université Pierre et Marie Curie), Éric Schost (Western University), Anne Shiu (Texas A&M University), Michael Shub (City University of New York), Frank Sottile (Texas A&M University), Bernd Sturmfels (UC Berkeley), Agnes Szanto (North Carolina State University), Sébastien Tavenas (École Normale Supérieure de Lyon), Leslie Valiant (Harvard University), Cynthia Vinzant (University of Michigan), Charles Wampler (General Motors Research and Development Center), Ryan Williams (Stanford University), Virginia Vassilevska Williams (Stanford University), Ke Ye (University of Chicago).