SIUC Physics Seminar
School of Physics and Applied Physics, Southern Illinois University--Carbondale
2025 February 7 Friday 4:00 PM:
Physics Seminar in Neckers 440
Title: Modular Representations of the Special Linear Groups over a Finite Field
Speaker: Devjani Basu
Affiliation: Southern Illinois University--Carbondale
Abstract:
Symmetry exists around us, and the set of symmetries forms a group.
Representation theory is the study of linear group actions. The modular representations of
a group are the representations over the field with characteristic p>0, p a prime.
This poses a different problem than studying the ordinary representations over the
complex field ℂ. Around 1940, Richard Brauer had a pivotal role in developing the
modular representation theory to study the classification of simple finite groups.
Presently, it has far reaching applications. This includes, but not restricted to the
study of Langlands Problem, the so-called grand unified theory of Mathematics.
The problems in modular representation theory become more interesting when
the characteristic p of the field on which the representations are defined, divides the
order of the group. Special linear groups are groups of matrices with determinant
1, and of finite order if they are defined over a finite field. The overarching goal is
to describe all the irreducible modular representations of such a group, explicitly,
i.e., as vector spaces. In this talk, we will explore some time-honored methods and
some new techniques to achieve our goal.
Biography:
I am a fifth year PhD student of Mathematics at SIUC.
My research interest lies primarily in representation theory but encompasses
number theory and algebraic geometry. Presently, I am writing my PhD thesis
under the supervision of Prof. Kwangho Choiy. When I am not working on my thesis,
I like to read popular science books, and think about applications of
representation theory in Quantum Physics.
I am mostly found talking about Calculus to undergrads around the campus.
Education:
B.S. (Statistics) University of Calcutta, India
M.S. (Statistics) Presidency College, Kolkata, India
M.S. (Mathematics) Southern Illinois University Carbondale, Illinois, USA
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by K V Shajesh
(kvshajesh@gmail.com).