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Fall Semester 2022 Student Probability Seminar

Welcome to the Columbia Student Probability Seminar. In this seminar, we will be studying Macdonald Processes. We will use the classical paper written by Alexei Borodin and Ivan Corwin. Our talks will be held in room 622 on Tuesdays from 3:00pm to 4:00pm(EST). The first talk will start on 10/11/2022.

Schedule of Talks

Date Speaker content
10/11/2022 Jiyue Zeng Basic introductions and review of Brownian motion, stochastic calculus, Ito's formula.
10/25/2022 Zongrui Yang In this talk, we give a brief introduction of symmetric function theory to set up the algebraic backgrounds for the Macdonald process paper. We roughly follow the first half of Macdonald’s book Symmetric functions and orthogonal polynomials. We start with the definition of symmetric functions and conclude with the proof of existence of Macdonald symmetric functions.
11/1/2022 Zongrui Yang We continue the discussion of symmetric functions.
11/22/2022 Hindy Drillick We will follow chapter 2 and cover skew Macdonald functions, nonnegative specializations, and Macdonald measures.
11/29/2022 Zoe Himwich We continue the discussion of Macdonald process.
12/06/2022 Sayan Das We will discuss how random permutations exhibit both KPZ and SLE behavior under appropriate settings.