Class meets every Friday 1-3PM in KAP 427
Organizer: Sergey Lototsky.
Office: KAP 248D.
Phone: (213) 740-2389.
Office Hours: MW 10:30am-12pm.
Walk-ins and appointments at other time are welcome.
The objective this semester: To discuss current research projects and future plans of participating students.
Participating students: Chinmoy Bhattacharjee, Chandrasekhar Karnam, Haining Ren, Kira Sushkoff-Nguyen, Xiaojing Xing, Weisheng Xie, Fan Yang.
What we did
August 29 Introduction and plans for the semester
September 5 Presentation by Fan on basics of dynamical systems (ergodic theorems, entropy, SRB measure, Arnol’d’s cat map, Smale’s horse shoe).
September 12 The second part of Fan’s presentation: asymptotic of return time to cylinder sets, Bowen balls, and metric balls.
September 19 Xiaojing’s presentation on optimal dividend payment for an insurance company when the claim arrival times are not exponentially distributed.
September 26 Haining’s presentation on the connections between the cycle structure of a random permutation and factorization of polynomials over finite fields.
October 3 Weisheng’s presentation on fractional Brownian motion.
October 10 Kira’s presentation on Stein’s method and concentration inequalities.
October 17 Weisheng’s presentation on Malliavin calculus for Gaussian processes.
October 24 Weisheng’s presentation on stochastic differential equations driven by fractional Brownian motion.
October 31 Chinmoy’s presentation on Stein’s method and exchangeable pairs for general distributions, and an open problem on the number of increasing subsequences of a given length in a random permutation.
November 7 Haining’s presentation on a limit theorem for the cycle structure of a unimodal permutation.
November 14 Chandrasekhar’s presentation on time-inconsistent problems in stochastic control.
November 21 Fan’s presentation on the properties of the Arnold cat map and the related results and open problems in dynamical systems.
November 28 Thanksgiving break – no meeting.
December 5 Department’s end-of-semester party, followed by the talk of our recent graduate Stephen DeSalvo at the probability seminar; the talk is about limit shapes of restricted integer partitions under non-multiplicative conditions.