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.

Invited Participants

Dimitris Achlioptas (UC Santa Cruz), Bibhas Adhikari (IIT Kharagpur), AmirMahdi Ahmadinejad (Stanford University), Nima Anari (Stanford University), Federico Ardila (San Francisco State University), Petter Brändén (KTH Royal Institute of Technology in Stockholm), Sarah Cannon (UC Berkeley), Charlie Carlson (University of Colorado Boulder), Yeshwanth Cherapanamjeri (UC Berkeley), Péter Csikvári (Eötvös Loránd University), Ewan Davies (QuSoft, CWI and University of Amsterdam), Papri Dey (Max Planck Institute (MIS, Leipzig)), Mareike Dressler (UC San Diego), Shirshendu Ganguly (UC Berkeley), F Alberto Grunbaum (UC Berkeley), Leonid Gurvits (City University of New York), Bill Helton (UC San Diego), Olga Holtz (UC Berkeley and Technische Universität Berlin), Fotis Iliopoulos (UC Berkeley), Katharina Victoria Jochemko (KTH Royal Institute of Technology), Konstantin Kakaes (MIT Technology Review), Ravi Kannan (Microsoft Research India), Alexandra Kolla (University of Colorado Boulder), Khazhgali Kozhasov (Max Planck Institute for Mathematics in the Sciences), Jean Lasserre (CNRS - Toulouse), Rachel Lawrence (UC Berkeley), Jingcheng Liu (UC Berkeley), Rafael Mendes de Oliveira (University of Toronto), Ali Mohammad-Nezhad (Purdue University), Rad Niazadeh (Stanford University), Jiawang Nie (UC San Diego), Mike Ogiugo (University of Ibadan, Nigeria), Dávid Papp (North Carolina State University), Gabor Pataki (University of North Carolina at Chapel Hill), Will Perkins (University of Illinois at Chicago), Daniel Plaumann (Technical University of Dortmund), Prasad Raghavendra (UC Berkeley), Mohan Ravichandran (Mimar Sinan University), Guus Regts (University of Amsterdam), Zvi Rosen (Florida Atlantic University), David Ruelle (IHES), Nick Ryder (UC Berkeley), Amin Saberi (Stanford University), Peter Sarnak (IAS), James Saunderson (Monash University), Tselil Schramm (MIT), Boris Shapiro (KTH Royal Institute of Technology), Alistair Sinclair (UC Berkeley), Mohit Singh (Georgia Institute of Technology), Rainer Sinn (Freie Universität Berlin), Nikhil Srivastava (UC Berkeley), Piyush Srivastava (Tata Institute of Fundamental Research), Levent Tunçel (University of Waterloo), Caroline Uhler (MIT), Cynthia Vinzant (North Carolina State University), David Wagner (University of Waterloo), Yitong Yin (Nanjing University), Josephine Yu (Georgia Institute of Technology)


The workshops in the "Geometry of Polynomials" program are supported in part by the National Science Foundation under Award No. 1835986.

We are required by the NSF Proposal & Award Policies & Procedures Guide (Chapter II.E.7), effective January 28, 2019, to provide all event participants with information on the University’s policy on sexual and other forms of harassment or sexual assault as well as directions on how to report any violations of this policy. For purposes of this requirement, “other forms of harassment” is defined as “non-gender or non-sex-based harassment of individuals protected under federal civil rights laws, as set forth in organizational policies or codes of conduct, statutes, regulations, or executive orders.” This information is available here.