Workshops on Geometry of Polynomials

该奖项提供了支持组织三个研讨会围绕在西蒙斯研究所多项式几何的主题-伯克利。加州大学伯克利分校的西蒙斯研究所通过汇集最多产和即将到来的研究人员，在推进理论计算机科学的最新发展方面发挥了主导作用。这一努力将弥合数学和计算机科学的思想，并开发具有广泛适用性的新技术。研究人员将从事不同的研究领域，如组合学，概率，统计物理，优化和真实的代数几何。这些研讨会将向所有潜在的参与者开放，并将向公众分发发言录像，以征求意见和参与。主办方将邀请来自不同背景的学生和科学家参加。多项式几何是一个最近在解决非对称旅行商问题，构建Ramanujam图和其他问题方面表现出很大希望的主题。 这个框架的力量源于这样一个事实，即这些多项式的某些类别足够普遍，可以编码各种有趣的组合，概率和几何数据，并且足够特殊，可以具有有用的全局性质和结构理论。为了进一步发展、丰富和推广这些技术，该项目将围绕这一主题组织三次讲习班：（1）除了随机舍入和概率方法（2）确定性计数，配分函数的概率和零点及（3）双曲多项式和双曲规划。该奖项反映了NSF的法定使命，并已被认为是值得支持的，通过评估使用基金会的知识优点和更广泛的影响审查标准。

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.