SPUR PROGRAM - Summer Program for Undergraduate Research
REU PROGRAM - Research Experience for Undergraduates
These
summer programs provide the opportunity for undergraduate students of
mathematics to participate in leading-edge research. This year, one
project is designated "REU" and the other project is designated "SPUR."
The difference between REU and SPUR projects is the funding support
that is available.
We
welcome all students to apply including U.S., Permanent Resident, and
International students whether your home institution is within the U.S.
or outside the U.S. Please read carefully the information below under
details and support/costs. Certain criteria apply for international
students with their home institution outside the U.S.
REU PROGRAM
PROJECT TITLE: Theoretical aspects of deep learning
Directed by Alex Townsend, ajt253@cornell.edu (https://math.cornell.edu/alex-townsend) and Professor Yeona Kang, Howard University, yeona.kang@howard.edu
Project details/abstract: Techniques
in neural networks and deep learning are behind revolutionary
advancements in the last decade, from facial recognition to playing
world-class chess and protein folding. There is now a significant need
for mathematical theory to keep up with practical success in this area.
In this REU program, we will be studying the theoretical aspects of
approximation power, convergence vs. stability, and frequency-biasing,
when applied to neural networks. We will be particularly interested in
how these techniques can be used in the context of learning differential
equation models from data and medical imaging. This REU program is
organized with Howard University. Undergraduates will be jointly
mentored by Prof. Yeona Kang at Howard University.
SPUR PROGRAM
PROJECT TITLE: Loop groups and Verlinde algebra
Directed by Yiannis Loizides, yl3542@cornell.edu (https://math.cornell.edu/yiannis-loizides)
Project details: This
project will focus on some questions related to the loop group of
SU(2): the space of 2 by 2 unitary matrices of determinant 1 whose
entries are trigonometric polynomials. We will learn a bit about loop
groups, Riemann surfaces, topological quantum field theory, and the
Verlinde algebra (which links these things together). One aim will be to
carry out calculations closely related to the Verlinde algebra, and to
interpret the results in terms of the geometry of SU(2). Another aim
will be to develop and implement methods for computing some invariants
of "moduli spaces" associated to Riemann surfaces, and then to prove
identities suggested by the examples. Previous exposure to abstract
algebra, topology and maybe even representations of SU(2) would be
helpful, though not essential.
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(posted 2021/01/21, listed until 2021/03/06)