Cornell University, Department of Mathematics

Program ID: 104-UNDERGRADUATESUMMERRESEARCH [#1075]
Program Title: Cornell Summer Research Programs for Undergraduates
Program Type: Undergraduate program
Program Location: Ithaca, New York 14853, United States [map]
Application Deadline: 2021/03/06 11:59PMhelp popup finished (2021/01/21, finished 2021/06/09, listed until 2021/03/06)
Program Description:   URMs  

*** this program has been closed and new applications are no longer being accepted. ***

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.



Diversity and Inclusion are a part of Cornell University's heritage. We are a recognized employer and educator valuing AA/EEO, Protected Veterans, and Individuals with Disabilities. We also recognize a lawful preference in employment practices for Native Americans living on or near Indian reservations.

Application Materials Required:
Submit the following items online at this website to complete your application:
And anything else requested in the program description.

Further Info:
https://math.cornell.edu/undergraduate-research
 
310 Malott Hall
Ithaca, NY 14850

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