Class meets every Monday 10AM to 12 PM in KAP 427
Organizer: Sergey Lototsky.
Office: KAP 248D.
Phone: (213) 740-2389.
Office Hours: MWF 2-3pm.
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: Mark Duggan, Hyun-Jung Kim, Alperen Ozdemir, Jian Wang, Fanhui Xu.
What we did
January 9: Introduction and general discussion. A possible question to think about and discuss throughout the semester: what can we say about the eigenvalues of a square matrix with iid Levy processes as entries? While we might not be able to say much, we should learn, and try to connect, some ideas about Levy processes, random matrices, Tracy-Widom distributions, Malliavin calculus, and maybe large deviations and optimal control.
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January 16: MLK Day.
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January 23: A (long) presentation by Fanhui on Levy processes, followed by a (short) presentation by Alperen on (random) Wigner matrices.
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January 30: A white-board presentation by Alperen on period-two Markov chains on the symmetric group.
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February 6: A presentation by Hyun-Jung on the parabolic Anderson model.
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February 13: A computer presentation by Alperen on period-two Markov chains on the symmetric group (practice for the oral exam).
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February 20: Presidents Day.
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February 27: A presentation by Hyun-Jung on Bernoulli traps.
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March 6: A presentation by Jian on time series, in particular, the unit root processes.
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March 13: Spring Break.
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March 20: A practice presentation by Fanhui for the oral exam
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March 27: Practice presentations by Hyun-Jung and Fnahui for an upcoming conference.
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April 3: A presentation by Mark on KL divergence.
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April 10: A discussion of career plans of participating students.
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April 17: A discussion of random matrices with Levy processes as entries.
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April 24: A presentation by Jian on large deviations/optimal control approach to the study of coupled diffusions with a small parameter.