Irish Mathematical Society
- Cumann Matamaitice na hÉirinn
ICEDIM Seminars
Date: Wednesday, March 13 2024 at
2pm (UTC)
Speaker: Arundhathi Krishnan, Mary Immaculate
College
Title: A Central Limit Theorem in the Framework
of the Thompson Group F
Location: Online
via Zoom [Meeting ID: 974 4383 7621 - Passcode: 443044 ]
Abstract
The classical central limit theorem states that
the average of an infinite sequence of independent and identically
distributed random variables, when suitably rescaled, tends to a
normal distribution. In fact, this classical result can be stated
purely algebraically, using the combinatorics of pair partitions. In
the 1980s, Voiculescu proved an analog of the central limit theorem in
free probability theory, wherein the normal distribution is replaced
by Wigner's semicircle distribution. Later, Speicher provided an
algebraic proof of the free central limit theorem, based on the
combinatorics of non-crossing pair partitions. Since then, various
algebraic central limit theorems have been studied in noncommutative
probability, for instance, in the context of symmetric groups. My talk
will discuss a central limit theorem for the Thompson group F, and
show that the central limit law of a naturally defined sequence in the
group algebra of F is the normal distribution. Our combinatorial
approach employs abstract reduction systems to arrive at this result.
Arundhathi Krishnan got her PhD at the Indian Institute of Technology Madras in 2018. After postdoctoral positions at University College Cork and the University of Waterloo, she joined Mary immaculate College, Thurles as an assistant professor in September 2023. Her research is in operator algebras, with a focus on noncommutative probability. Arundhathi enjoys teaching a range of mathematics modules, and is also a junior mentor in the Operator Algebras Mentor Network.
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