Spring 2019

Hyperbolic Polynomials and Hyperbolic Programming

Apr. 30May 3, 2019

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Bernd Sturmfels (UC Berkeley; chair), Michel Goemans (Massachusetts Institute of Technology), Pablo Parrilo (Massachusetts Institute of Technology), Jim Renegar (Cornell University)

Hyperbolic Programming (HP) is a generalization of Semidefinite Programming (SDP). Its feasible regions are convex sets that are constrained by hyperbolic polynomials. These multivariate polynomials, closely related to real stable polynomials, extend the linear matrix inequalities that underlie SDP. They arise in many contexts, including negative correlation in probability and exponential families in statistics. This workshop will center around the question: Is HP really more powerful than SDP? This is closely related to recent advances in real algebraic geometry, due to Scheiderer, that are aimed at characterizing which convex sets are spectrahedral shadows. It is also of great interest in theoretical CS, where many of the best-known algorithms for combinatorial optimization are based on SDPs, and beating SDPs in certain contexts is equivalent to refuting the Unique Games Conjecture. This workshop will bring together researchers from these different fields.

Further details about this workshop will be posted in due course. Enquiries may be sent to the organizers workshop-geometry3 [at] lists [dot] simons [dot] berkeley [dot] edu (at this address).

All events take place in the Calvin Lab auditorium.

Registration is required to attend this workshop. To submit your name for consideration, please register and await confirmation of your acceptance to the workshop before booking your travel. Space may be limited, and you are advised to register early.

Invited Participants: 

Nima Anari (Stanford University), Petter Brändén (KTH Royal Institute of Technology in Stockholm), Katharina Victoria Jochemko (KTH Royal Institute of Technology), Khazhgali Kozhasov (Max Planck Institute for Mathematics in the Sciences), Jean Bernard Lasserre (CNRS - Toulouse), Ali Mohammad-Nezhad (Purdue University), Jiawang Nie (UC San Diego), Dávid Papp (North Carolina State University), Gabor Pataki (University of North Carolina at Chapel Hill), Daniel Plaumann (Technical University of Dortmund), James Saunderson (Monash University), Mohit Singh (Georgia Institute of Technology), Levent Tunçel (University of Waterloo), Caroline Uhler (MIT), Cynthia Vinzant (North Carolina State University)