After a hiatus, we plan to reboot the REU program for Summer 2021 (May 31 - July 23) either in-person (if deemed safe) or virtually. Students will likely work in groups of 2 (or more, pending local funding) with a faculty adviser from SUNY Potsdam or Clarkson University. Participants will receive a stipend of $4,400. If the program is in-person, participants will receive free housing in an on campus apartment or dorm room with access to cooking facilities, as well as $375 in funds to support travel expenses to/from Potsdam. We are seeking applicants, in particular from students from groups traditionally under-represented in mathematics.
Interested applicants should submit their application materials, including:
Contact information (email, phone, mailing address)
Expected date of graduation
Preference of topic
300-500 word statement of interest
2 letters of recommendation (that address your interest and positive experiences in mathematics, work ethic, and ability to work in a group)
Unofficial transcript
Please send application materials, including letters of reference, via Mathprograms.org. Applications already submitted via email do not need to be resubmitted.
The deadline for submitting all application materials is March 29, 11:59 p.m. Applicants must be US citizens or permanent residents, and plan to be enrolled in an undergraduate program in the Fall 2021 semester.
Links
in embedded graphs (Joel Foisy, SUNY Potsdam)
A
spatial embedding of a graph is a way to place a graph in space, so
that vertices are points and edges are arcs that meet only at
vertices. Mathematicians have studied graphs that are intrinsically
linked: that is, in every spatial embedding, there exists a pair of
disjoint cycles that form a non-splitable link. Sachs and Conway and
Gordon showed that the complete graph on 6 vertices is intrinsically
linked. More recently, people have studied graphs that have
non-split links with more than 2 components, as well as knotted
cycles, in every spatial embedding. Building off a previous REU
group’s work, we’ll first examine certain graphs that can be
embedded in the plane that can help us better understand graphs that
have a non-split 3 component link in every spatial embedding. We
will use tools from graph and knot theory. Experience in these areas
is not required. (minimum requirement: good experience in at
least one proof intensive math class)
Numerical
solutions to high-dimensional stochastic differential equations
(Guangming Yao, Clarkson University)
Mathematical
models described by partial differential equations (PDEs) have been
a necessary tool to model nearly all physical phenomena in science
and engineering. Due to the growth of the complexity in emerging
technologies, the increase in the complexity of the PDEs for
realistic problems become inevitable. Some of the complexities are,
for example, complicated domains, high-dimensional spatial domains,
multiscale, large-scale problems, etc. This project will develop a
new algorithm for solving partial differential equations (PDEs) in
high dimensions by solving associated backward stochastic
differential equations (BSDEs) using neural networks [*], as is done
in deep machine learning. Another option is to employ radial basis
functions [*] to reduce the dimensions in the numerical simulation.
The project can be future enhanced by adding complicated
computational domains, large scale problems with or without
multiscale feature. If a particular student became interested in
parallel computing, there could be a productive a collaboration
between this REU site and the NSF REU Site: High Performance
Computing with Engineering Applications, led by the Department of
Electrical and Computer Engineering, Clarkson University, Potsdam,
NY.
The process of dealing with realistic PDE
models with various behaviors of the solutions will help students to
understand the key concepts in computational science, including
accuracy, efficiency, convergence and stability. Numerical
simulation requires programming in MATLAB or Python to test
efficiency and accuracy of the proposed algorithms by solving
various applied problems such as the Allen-Cahn equation[*], and
nonlinear pricing models for financial mathematics[*], the
Black-Scholes equations [*], the Boltzmann transport equations [*]
for modeling phonon distribution functions in high dimensional space
(higher than 6 dimensions), and/or more advanced PDE models for
COVID-19[*]. Fundamental concepts in computational mathematics and
numerical analysis can be introduced at beginning, followed by
particular focuses of students’ choices of PDE models.
(A course in differential equations required. Familiarity with MATLAB or similar software recommended, though students with a willingness to learn some coding are encouraged to apply)
(*reference available on request)
Dr.
Joel Foisy, Department of Mathematics
SUNY Potsdam
44
Pierrepont Avenue
Potsdam, New York, U.S.A. 13676
Phone:
(315) 267 - 2084
Email: foisyjs@potsdam.edu