Workshops on Geometry of Polynomials

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This award provides support for organizing three workshops around the theme of Geometry of Polynomials at Simons Institute - Berkeley. Simons Institute at University of California, Berkeley has taken a leading role in advancing the state-of-the-art in Theoretical Computer Science by bringing together the most prolific and upcoming researchers. This effort will bridge ideas from mathematics and computer science and develop new techniques with broad applicability. Researchers will engage in diverse research areas like combinatorics, probability, statistical physics, optimization and real algebraic geometry. These workshops will be open to all potential participants, and video recordings of presentations will be distributed to the public for comment and engagement. The organizers will invite students and scientists from a diversity of backgrounds to participate.Geometry of polynomials is a topic which has shown a lot of promise recently in solving Asymmetric Traveling Salesman Problems, Constructing Ramanujam Graphs and other problems. The power of this framework stems from the fact that certain classes of these polynomials are general enough to encode a variety of interesting combinatorial, probabilistic and geometric data, and special enough to have useful global properties and structure theory. To further develop, enrich and popularize these techniques, this project will organize three workshops around the topic: (1) Beyond randomized rounding and the probabilistic method (2) Deterministic Counting, Probability and Zeros of Partition Functions and (3) Hyperbolic Polynomials and Hyperbolic Programming.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.