Student Probability Seminar

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An introduction to the approximate conic kinematic formula

Speaker: Haoxiang Huang, CIMS

Location: Warren Weaver Hall 517

Date: Monday, October 25, 2021, 11:30 a.m.

Synopsis:

What is the probability that a randomly rotated convex cone shares a ray with a fixed convex cone? This is a classical problem in conic integral geometry and naturally arises in random convex optimization problems. We first answer this question in the conic integral geometry framework by introducing conic kinematic formula. While the formula is exact, its applications are limited due to its complicated structure. We will then introduce its approximate version called "approximate conic kinematic formula" which is more powerful in applications. Finally, we will end the talk by discussing some of its applications in random convex optimization problems and high dimensional statistics (if time permitted).