Loading...
Organizing Committee
American Institute of Mathematics
American Institute of Mathematics (AIM)
ICERM/Morehouse College
Abstract
Research Experiences for Undergraduate Faculty (REUF) is a program for undergraduate faculty who are interested in mentoring student research. REUF specifically supports involvement in research with undergraduates by faculty at colleges and universities that emphasize undergraduate education. Each annual cycle includes a week-long REUF workshop during the summer and additional activities for participants afterwards to support continuation of research engagement. In addition, participants become members of the long-term REUF community.
The goals of REUF are to provide faculty participants with a research experience investigating open questions in the mathematical sciences; to equip participants to engage in research with undergraduate students at their home institutions; to foster long-term research collaborations among some of the faculty participants; and to establish a network of faculty at primarily undergraduate institutions together with faculty at research universities who support collaboration and undergraduate research.
REUF is a program of the American Institute of Mathematics (AIM) and the Institute for Computational and Experimental Mathematics (ICERM), made possible by the support from the U.S. National Science Foundation (NSF).
The goals of REUF are to provide faculty participants with a research experience investigating open questions in the mathematical sciences; to equip participants to engage in research with undergraduate students at their home institutions; to foster long-term research collaborations among some of the faculty participants; and to establish a network of faculty at primarily undergraduate institutions together with faculty at research universities who support collaboration and undergraduate research.
REUF is a program of the American Institute of Mathematics (AIM) and the Institute for Computational and Experimental Mathematics (ICERM), made possible by the support from the U.S. National Science Foundation (NSF).
Loading...
Loading participant list in background...
Workshop Schedule
Monday, June 09, 2025
9:00 - 9:20 AM EDT
Check In
11th Floor Collaborative Space
9:20 - 9:30 AM EDT
Welcome
11th Floor Lecture Hall
Brendan Hassett, ICERM/Brown University
9:30 - 10:00 AM EDT
Welcome to REUF/ Introduction
Opening Remarks - 11th Floor Lecture Hall
Leslie Hogben, American Institute of Mathematics (AIM)
Ulrica Wilson, ICERM/Morehouse College
10:00 - 10:30 AM EDT
Project 1 Introduction
11th Floor Lecture Hall
Alison Marr, Southwestern University
10:30 - 11:00 AM EDT
Coffee Break
11th Floor Collaborative Space
11:00 - 11:30 AM EDT
Project 2 Introduction
11th Floor Lecture Hall
Brant Jones, James Madison University
11:30 AM - 12:00 PM EDT
Project 3 Introduction
11th Floor Lecture Hall
Haydee Lindo, Harvey Mudd College
12:00 - 12:30 PM EDT
Project 4 Introduction
11th Floor Lecture Hall
Edray Goins, Pomona College
12:30 - 2:15 PM EDT
Lunch/Free Time
2:15 - 2:30 PM EDT
Selection of Project Group
Meeting - 11th Floor Lecture Hall
2:30 - 3:30 PM EDT
Group Work
Assigned Group Work Space
3:30 - 4:00 PM EDT
Coffee Break
11th Floor Collaborative Space
4:00 - 5:00 PM EDT
Group Work
Assigned Group Work Space
5:00 - 6:30 PM EDT
Reception
11th Floor Collaborative Space
Tuesday, June 10, 2025
9:00 - 9:15 AM EDT
Announcements
Meeting - 11th Floor Lecture Hall
9:15 - 10:00 AM EDT
Group Work
Assigned Group Work Space
10:00 - 10:30 AM EDT
Coffee Break
11th Floor Collaborative Space
10:30 AM - 12:00 PM EDT
Group Work
Assigned Group Work Space
12:00 - 2:00 PM EDT
Lunch/Free Time
2:00 - 3:00 PM EDT
Group Work
Assigned Group Work Space
3:00 - 3:30 PM EDT
Coffee Break
11th Floor Collaborative Space
3:30 - 5:00 PM EDT
Group Work
Assigned Group Work Space
Wednesday, June 11, 2025
9:00 - 9:15 AM EDT
Interim Group Reports
Group Presentations - 11th Floor Lecture Hall
9:15 - 9:20 AM EDT
Group Photo (Immediately After Talk)
11th Floor Lecture Hall
9:20 - 10:00 AM EDT
Group Work
Assigned Group Work Space
10:00 - 10:30 AM EDT
Coffee Break
11th Floor Collaborative Space
10:30 AM - 12:00 PM EDT
Group Work
Assigned Group Work Space
12:00 - 2:00 PM EDT
Lunch/Free Time
2:00 - 2:15 PM EDT
Announcements
Meeting - 11th Floor Lecture Hall
2:15 - 3:00 PM EDT
Group Work
Assigned Group Work Space
3:00 - 3:30 PM EDT
Coffee Break
11th Floor Collaborative Space
3:30 - 5:00 PM EDT
Group Work
Assigned Group Work Space
Thursday, June 12, 2025
9:00 - 10:30 AM EDT
Group Discussion - Undergraduate Research
Other - 11th Floor Lecture Hall
10:30 - 11:00 AM EDT
Coffee Break
11th Floor Collaborative Space
11:00 AM - 12:00 PM EDT
Group Work
Assigned Group Work Space
12:00 - 2:00 PM EDT
Lunch/Free Time
2:00 - 2:15 PM EDT
Announcements
Meeting - 11th Floor Lecture Hall
2:15 - 3:00 PM EDT
Group Work
Assigned Group Work Space
3:00 - 3:30 PM EDT
Coffee Break
11th Floor Collaborative Space
3:30 - 5:00 PM EDT
Group Work
Assigned Group Work Space
Friday, June 13, 2025
9:00 - 9:15 AM EDT
Announcements
Meeting - 11th Floor Lecture Hall
9:15 - 10:00 AM EDT
Group Work
Assigned Group Work Space
10:00 - 10:30 AM EDT
Coffee Break
11th Floor Collaborative Space
10:30 AM - 12:00 PM EDT
Group Work
Assigned Group Work Space
12:00 - 2:00 PM EDT
Lunch/Free Time
2:00 - 2:30 PM EDT
Project 1 Presentation
Group Presentations - 11th Floor Lecture Hall
2:30 - 3:00 PM EDT
Project 2 Presentation
Group Presentations - 11th Floor Lecture Hall
3:00 - 3:30 PM EDT
Coffee Break
11th Floor Collaborative Space
3:30 - 4:00 PM EDT
Project 3 Presentation
Group Presentations - 11th Floor Lecture Hall
4:00 - 4:30 PM EDT
Project 4 Presentation
Group Presentations - 11th Floor Lecture Hall
Request Reimbursement
This section is for general purposes only and does not indicate that all attendees receive funding. Please refer to your personalized invitation to review your offer.
- ORCID iD
- As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
- Acceptable Costs
- 1 roundtrip between your home institute and ICERM
- Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
- Ground Transportation to and from airports and ICERM.
- Unacceptable Costs
- Flights on non-U.S. or non-E.U. airlines
- Flights on U.K. airlines
- Seats in economy plus, business class, or first class
- Change ticket fees of any kind
- Multi-use bus passes
- Meals or incidentals
- Advance Approval Required
- Personal car travel to ICERM from outside New England
- Multiple-destination plane ticket; does not include layovers to reach ICERM
- Arriving or departing from ICERM more than a day before or day after the program
- Multiple trips to ICERM
- Rental car to/from ICERM
- Flights on a Swiss, Japanese, or Australian airline
- Arriving or departing from airport other than PVD/BOS or home institution’s local airport
- 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
- Travel Maximum Contributions
- New England: $350
- Other contiguous US: $850
- Asia & Oceania: $2,000
- All other locations: $1,500
- Note these rates were updated in Spring 2023 and supersede any prior invitation rates.
- Reimbursement Requests
Request Reimbursement with Cube
Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.
- Reimbursement Tips
- Scanned original receipts are required for all expenses
- Airfare receipt must show full itinerary and payment
- ICERM does not offer per diem or meal reimbursement
- Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via Google Maps PDF
- Keep all documentation until you receive your reimbursement!
- Reimbursement Timing
6–8 weeks after all documentation is sent to ICERM. All reimbursements are reviewed by multiple Brown University offices.
- Reimbursement Deadline
Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. No submissions are accepted after six months.
Projects
Magic labelings on directed graphs
Alison Marr (Southwestern University)
This project will explore the properties and structures of various types of magic labelings applied to directed graphs. We will investigate conditions under which directed graph components (vertices, directed edges, or both) can be assigned unique and consecutive labels from the positive integers such that ingoing and/or outgoing sums are consistent across all vertices (or edges). The goal is to discover new results on a certain type of magic labeling for directed graphs and to generate additional magic or antimagic labeling questions for directed graphs that faculty and undergraduate students can further explore.
Combinatorics of sequential best choice models
Brant Jones (James Madison University)
The game of best choice (also known as the secretary problem) has been studied since at least the 1950's and was widely popularized in a 1960 column of Martin Gardner. In the classical setup, a player conducts "interviews" with a fixed number of "candidates." Immediately after each interview, the player ranks the current candidate against all of the candidates that have been considered so far. The player must then decide whether to accept the current candidate and end the game or, alternatively, whether to (irrevocably) reject the current candidate and continue playing in the hope of obtaining a better candidate in the future. This problem features an exploration–exploitation tradeoff: each interview reveals more information about the candidate pool, yet acting on this information (by selecting a candidate) ends the game.
We are interested in optimal strategies for these games as well as the probability that a player selects the best candidate. Crucially, most of the classical analyses assume that candidate rankings are uniformly distributed (so each possible permutation occurs with probability 1/n!). In this project, we use a new combinatorial perspective on the game that allows us to relax this assumption and discover new facets of the best choice game.
We are interested in optimal strategies for these games as well as the probability that a player selects the best candidate. Crucially, most of the classical analyses assume that candidate rankings are uniformly distributed (so each possible permutation occurs with probability 1/n!). In this project, we use a new combinatorial perspective on the game that allows us to relax this assumption and discover new facets of the best choice game.
Traces and other closures
Haydee Lindo (Harvey Mudd College)
The well-known trace map on matrices can be generalized to a map on any module, M, over a commutative ring, R. Its image, the trace ideal of the R-module M, is the ideal generated by the homomorphic images of M in R. Within commutative algebra, these trace ideals have recently experienced an uptick in attention, in part, because the naturalness of their construction ensures the ubiquity of their applications. In this project we will specifically explore the relationship between various notions of closure, for example, being a trace ideal, reflexive, integrally closed, or stable. We will focus on settings in which these notions coincide, for example in Arf rings, with an eye to characterize these and related rings that have a well-established history within singularity theory.
Roots of Polynomials and their Galois Groups via Belyi Maps and Fuchsian Differential Equations
Edray Goins (Pomona College)
In the early 1500's, work of Scipione del Ferro, Gerolamo Cardano, Nicolo Tartaglia illuminated a way to express the roots of a cubic polynomial in terms of square and cubic roots. Nearly 200 years later, Paolo Ruffini showed in 1799 while Niels Henrik Abel showed in 1823 that similar results do not hold for quintic polynomials. Indeed, we cannot express the roots of a quintic in terms of radicals. However, Charles Hermite showed in 1858 how to express the roots of a quintic using hypergeometric functions, completing a circle of ideas first initiated by Ernst Kummer in 1836. A coherent theory to solve all polynomials of degree at most five was completed by a series of authors including Hermann Schwarz in 1873, Lazarus Fuchs in 1876, and Felix Klein in 1884.
In this project, we explore Hermite's construction using the modern language of Belyi maps. We will explore how to relate roots of polynomials using Belyi maps; express the roots of polynomials by inverting such maps through the use solutions to hypergeometric differential equations; and create animations of Galois groups of the polynomials using monodromy.
In this project, we explore Hermite's construction using the modern language of Belyi maps. We will explore how to relate roots of polynomials using Belyi maps; express the roots of polynomials by inverting such maps through the use solutions to hypergeometric differential equations; and create animations of Galois groups of the polynomials using monodromy.
