NSF Award Search: Award # 1653002 - REU Site: Research in Geometry, Algebra, and Analysis

Award Abstract # 1653002

REU Site: Research in Geometry, Algebra, and Analysis

NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	KENT STATE UNIVERSITY
Initial Amendment Date:	April 30, 2017
Latest Amendment Date:	April 30, 2017
Award Number:	1653002
Award Instrument:	Standard Grant
Program Manager:	Tiziana Giorgi DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences
Start Date:	May 1, 2017
End Date:	April 30, 2021 (Estimated)
Total Intended Award Amount:	$259,200.00
Total Awarded Amount to Date:	$259,200.00
Funds Obligated to Date:	FY 2017 = $259,200.00
History of Investigator:	Jenya Soprunova (Principal Investigator) soprunova@math.kent.edu Mikhail Chebotar (Co-Principal Investigator)
Recipient Sponsored Research Office:	Kent State University 1500 HORNING RD KENT OH US 44242-0001 (330)672-2070
Sponsor Congressional District:	14
Primary Place of Performance:	Kent State University PO Box 5190 Kent OH US 44242-0001
Primary Place of Performance Congressional District:	14
Unique Entity Identifier (UEI):	KXNVA7JCC5K6
Parent UEI:
NSF Program(s):	WORKFORCE IN THE MATHEMAT SCI
Primary Program Source:	01001718DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s):	9250
Program Element Code(s):	733500
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

A motivated and diverse group of undergraduates will be recruited to work on research problems in a variety of topics in mathematics including geometry and analysis. The purpose of the program is to provide mathematics research experiences in a nurturing atmosphere for talented and motivated undergraduates. Students will work on projects arising naturally in the research of the Mathematics Department faculty. The student participants will learn how to discuss and present mathematical ideas, write project reports, explore with mathematical software, and engage in mathematical research. The emphasis of the program is on independent work under close supervision of a project advisor. The program will provide an intense research graduate school-like experience and lead students to awareness and appreciation for potential connections between different fields of mathematics. The program will be advertised nationally with a particular effort to reach underrepresented groups. The expectation is that many of the REU students will decide to pursue graduate studies in mathematics or related fields.

Most of the projects will require only a limited background, allowing the participants to get right to work extending their knowledge of the subject while working on research questions. This will also allow for the recruitment of well-prepared students at earlier stages of their studies, including freshmen and sophomores. Motivations for the projects will come from a variety of fields, including algebraic geometry, coding theory, convex geometry, group theory, harmonic analysis, lattice point geometry, Lie algebras, linear algebra, number theory, operator theory, and ring theory. All the projects will deal with unsolved research problems. Based on previous experience, the expectation is that many of the projects will lead to publications in refereed journals.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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Beaupré, Aria and Hoopes-Boyd, Emily and O'Brien, Grace "On the images of generalized polynomials evaluated on matrices over an algebraically closed skew field" Linear Algebra and its Applications , v.610 , 2021 https://doi.org/10.1016/j.laa.2020.10.021 Citation Details

BEIKE, NICOLAS F. and CARLETON, RACHEL and COSTANZO, DAVID G. and HEATH, COLIN and LEWIS, MARK L. and LU, KAIWEN and PEARCE, JAMIE D. "EXTENDING RESULTS OF MORGAN AND PARKER ABOUT COMMUTING GRAPHS" Bulletin of the Australian Mathematical Society , 2021 https://doi.org/10.1017/S0004972721000332 Citation Details

Borisov, Nikita and Julius, Hayden and Sikora, Martha "On maps preserving square roots of idempotent and rank-one nilpotent matrices" Journal of Algebra and Its Applications , 2020 https://doi.org/10.1142/S0219498822501237 Citation Details

Catalano, Louisa and Chang-Lee, Megan "On maps preserving rank-one nilpotents" Linear and Multilinear Algebra , 2020 10.1080/03081087.2019.1707753 Citation Details

CATALANO, LOUISA and CHANG-LEE, MEGAN "ON THE CONNECTION BETWEEN DIFFERENTIAL POLYNOMIAL RINGS AND POLYNOMIAL RINGS OVER NIL RINGS" Bulletin of the Australian Mathematical Society , v.101 , 2020 10.1017/S0004972719000923 Citation Details

Catalano, Louisa and Hsu, Samuel and Kapalko, Regan "On maps preserving products of matrices" Linear Algebra and its Applications , v.563 , 2019 10.1016/j.laa.2018.10.029 Citation Details

Chen, Fei Yu and Hagan, Hannah and Wang, Allison "Differential polynomial rings in several variables over locally nilpotent rings" International Journal of Algebra and Computation , v.30 , 2020 10.1142/S0218196719500668 Citation Details

Chen, Fei Yu and Hagan, Hannah and Wang, Allison "On skew polynomial rings over locally nilpotent rings" Communications in Algebra , v.47 , 2019 10.1080/00927872.2018.1499929 Citation Details

COSTANZO, DAVID G. and LEWIS, MARK L. and SCHMIDT, STEFANO and TSEGAYE, EYOB and UDELL, GABE "THE CYCLIC GRAPH OF A Z -GROUP" Bulletin of the Australian Mathematical Society , 2020 https://doi.org/10.1017/S0004972720001318 Citation Details

Ginsburg, Victor and Julius, Hayden and Velasquez, Ricardo "On maps preserving Lie products equal to a rank-one nilpotent" Linear Algebra and its Applications , v.593 , 2020 10.1016/j.laa.2020.02.007 Citation Details

Jin, Steven and Shin, Jooyoung "Iterated differential polynomial rings over locally nilpotent rings" Communications in Algebra , v.49 , 2021 https://doi.org/10.1080/00927872.2020.1797075 Citation Details

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PROJECT OUTCOMES REPORT

Disclaimer

This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.

Kent State University held an annual mathematics REU program in summers 2018, 2019, and 2020. The program provided support to 27 students, of which thirteen were female and four were from minority groups. Among this cycle's alumni, there are already two Goldwater scholarship recipients and two graduate NSF fellowship recipients.

The program provided an intense graduate-school-like research experience where students worked on projects arising naturally in KSU faculty's research. All projects dealt with unsolved research problems and have so far resulted in eleven research papers that have appeared in peer-reviewed journals. The results have been presented at different venues, including AMS and AMS-MAA meetings, and YMC conference.

Each of the projects involved some participation of KSU's graduate students who are experts in the mathematics related to the given project, giving REU students a glimpse into a potential future in graduate school. Based on the exit surveys, our program helped many of the students better understand what they want to do after they graduate. Almost all of them expect to go into math-related careers with most planning to go to graduate school in mathematics or related fields.

Communication between students involved in different projects was encouraged. The students learned how to discuss their mathematical ideas, give oral presentations, and write research papers. Some of the projects relied at least in part on computer exploration. Students acquired experience working with mathematical software, such as GAP, MATLAB, and Maple.

Recreational group activities were a regular and important part of the program, with one of the aims of the program being that participants get to know each other on a personal level and form a cohesive group that stays in touch after the program finishes.

Last Modified: 07/30/2021
Modified by: Evgenia Soprunova

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