Organizing Committee
- Brianna Donaldson
American Institute of Mathematics - Leslie Hogben
American Institute of Mathematics (AIM) & Iowa State U - Ulrica Wilson
ICERM/Morehouse College
Abstract
This workshop, a formal collaboration between ICERM and the American Institute of Mathematics (AIM), is one in a series of annual REUF workshops. These workshops bring together leading research mathematicians and faculty based at primarily undergraduate institutions to investigate open questions in the mathematical sciences and to equip participants with tools to engage in research with undergraduate students. REUF also serves to jump-start faculty who want to re-engage in research or who are considering a change in their research area.
The workshop will be hosted at ICERM.
The goals of this workshop are to promote undergraduate research and to forge research collaborations among the participating faculty. The majority of the workshop will be spent working on problems in small research groups, reporting on progress, and formulating plans for future work. Note that there are opportunities for participants to continue research activities beyond the workshop week, which will be discussed during the workshop.
Preference will be given to faculty who teach or mentor substantial numbers of minority students underrepresented in mathematics, students with disabilities, or first-generation students.
Workshop Leaders:
- Elizabeth Gross (University of Hawaii at Manoa)
- Helen Grundman (Bryn Mawr College)
- Victor Moll (Tulane University)
Confirmed Speakers & Participants
Talks will be presented virtually or in-person as indicated in the schedule below.
- Speaker
- Poster Presenter
- Attendee
- Virtual Attendee
-
Feryal Alayont
Grand Valley State University
-
Ghanshyam Bhatt
Tennessee State University
-
Cashous Bortner
California State University, Stanislaus
-
Tavish Dunn
Emory University Oxford College
-
Norman Fox
Austin Peay State University
-
Nathan Fox
Canisius College
-
Luella Fu
San Francisco State University
-
Jennifer Garbett
Lenoir-Rhyne University
-
Scott Greenhalgh
Siena College
-
Elizabeth Gross
University of Hawai'i at Mānoa
-
Helen Grundman
Bryn Mawr College
-
Leslie Hogben
American Institute of Mathematics (AIM) & Iowa State U
-
Naomi Krawzik
Sam Houston State University
-
Rachel Lynn
Schreiner University
-
Christopher McClain
West Virginia University Institute of Technology
-
Victor Moll
Tulane University
-
Changningphaabi Namoijam
Colby College
-
Mary Vanderschoot
Wheaton College
-
Ulrica Wilson
ICERM/Morehouse College
-
Derek Young
Mount Holyoke College
Workshop Schedule
Monday, August 7, 2023
-
9:00 - 9:20 am EDTCheck In11th Floor Collaborative Space
-
9:20 - 9:30 am EDTWelcome11th Floor Lecture Hall
- Brendan Hassett, ICERM/Brown University
-
9:30 - 10:00 am EDTWelcome to REUF / IntroductionProgram Overview - 11th Floor Lecture Hall
- Leslie Hogben, American Institute of Mathematics (AIM) & Iowa State U
- Ulrica Wilson, ICERM/Morehouse College
-
10:00 - 10:30 am EDTProject 1 Introduction - Maximum likelihood degree of stochastic block models11th Floor Lecture Hall
- Project Leader
- Elizabeth Gross, University of Hawai'i at Mānoa
Abstract
A popular class of statistical models studied in algebraic statistics are log-linear models. Log-linear models are popular since they have a monomial parameterization and correspond to toric ideals. Toric ideals are polynomial ideals generated by binomials with lots of combinatorial structure, making them great objects for exploration at varying levels of depth. For our project, we will focus on log-linear models that appear in network analysis, in particular, stochastic block models, which are used for clustering tasks in networks. We will study the geometry of maximum likelihood estimation for these models, specifically the maximum likelihood degree. The maximum likelihood degree is the number of complex solutions to the system of likelihood equations, and thus, for part of our project we will explore different computational software to solve such systems and different techniques to bound the number of solutions.
-
10:30 - 11:00 am EDTCoffee Break11th Floor Collaborative Space
-
11:00 - 11:30 am EDTProject 2 Introduction - A New Variation on Happy Numbers11th Floor Lecture Hall
- Project Leader
- Helen Grundman, Bryn Mawr College
Abstract
The happy function maps a positive integer (expressed in base 10) to the sum of the squares of its digits. A happy number is a positive integer that, under repeated applications of the happy function, maps to 1. The iterative behavior of the happy function and its many variations has been the subject of study for over 75 years. In this project, we'll study a new variation on the classic happy function, working to establish results paralleling those known for the classic happy function and/or its other variations.
-
11:30 am - 12:00 pm EDTProject 3 Introduction - BRACKETS: A NEW METHOD FOR INTEGRATION11th Floor Lecture Hall
- Project Leader
- Victor Moll, Tulane University
Abstract
The evaluation of integrals is one of the subjects taught in Calculus courses. Even tough this appears to be an elementary subject, there is no complete algorithm to compute every integral. The project will be based on a new method to evaluate definite integrals. This is called the method of brackets, invented by Ivan Gonzalez at his Physics Ph.D. thesis at Universidad Santa Maria, Valparaiso, Chile in the context of Feynman diagrams. These diagrams explain the interaction of elementary particles and their parametrization produces very complicated integrals. The evaluation of this integrals give all the fundamental properties of particles. This is a heuristic method, based on a small number of rules, some of which have established rigorously. The project will involve a combinations of symbolic computation and also some theory needed to prove the rules of the method. This is a remarkable method: it reduces the evaluation of definite integrals to the solution of a system of linear equations, usually of very small size.
-
12:00 - 2:00 pm EDTLunch/Free Time
-
2:00 - 2:15 pm EDTSelection of Project GroupsGroup Work - 11th Floor Lecture Hall
-
2:15 - 3:30 pm EDTGroup WorkAssigned Group Work Space
-
3:30 - 4:00 pm EDTCoffee Break11th Floor Collaborative Space
-
4:00 - 5:00 pm EDTGroup WorkAssigned Group Work Space
-
5:00 - 6:30 pm EDTReception11th Floor Collaborative Space
Tuesday, August 8, 2023
-
9:00 - 9:15 am EDTAnnouncementsMeeting - 11th Floor Lecture Hall
-
9:15 - 10:00 am EDTGroup WorkAssigned Group Work Space
-
10:00 - 10:30 am EDTCoffee Break11th Floor Collaborative Space
-
10:30 am - 12:00 pm EDTGroup WorkAssigned Group Work Space
-
12:00 - 2:00 pm EDTLunch/Free Time
-
2:00 - 2:15 pm EDTAnnouncementsMeeting - 11th Floor Lecture Hall
-
2:15 - 3:00 pm EDTGroup WorkAssigned Group Work Space
-
3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
-
3:30 - 5:00 pm EDTGroup WorkAssigned Group Work Space
Wednesday, August 9, 2023
-
9:00 - 9:15 am EDTInterim group reportsMeeting - 11th Floor Lecture Hall
-
9:15 - 9:20 am EDTGroup Photo (Immediately After Interim group reports)Group Photo (Immediately After Talk) - 11th Floor Lecture Hall
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9:20 - 10:00 am EDTGroup WorkAssigned Group Work Space
-
10:00 - 10:30 am EDTCoffee Break11th Floor Collaborative Space
-
10:30 am - 12:00 pm EDTGroup WorkAssigned Group Work Space
-
12:00 - 2:00 pm EDTLunch/Free Time
-
2:00 - 2:15 pm EDTAnnouncementsMeeting - 11th Floor Lecture Hall
-
2:15 - 3:00 pm EDTGroup WorkAssigned Group Work Space
-
3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
-
3:30 - 5:00 pm EDTGroup WorkAssigned Group Work Space
Thursday, August 10, 2023
-
9:00 - 10:30 am EDTGroup Discussion - Undergraduate ResearchMeeting - 11th Floor Lecture Hall
-
10:30 - 11:00 am EDTCoffee Break11th Floor Collaborative Space
-
11:00 am - 12:00 pm EDTGroup Work11th Floor Lecture Hall
-
12:00 - 2:00 pm EDTLunch/Free Time
-
2:00 - 2:15 pm EDTAnnouncementsMeeting - 11th Floor Lecture Hall
-
2:15 - 3:00 pm EDTGroup WorkAssigned Group Work Space
-
3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
-
3:30 - 5:00 pm EDTGroup WorkAssigned Group Work Space
Friday, August 11, 2023
-
9:00 - 9:15 am EDTAnnouncementsMeeting - 11th Floor Lecture Hall
-
9:15 - 10:00 am EDTGroup WorkAssigned Group Work Space
-
10:00 - 10:30 am EDTCoffee Break11th Floor Collaborative Space
-
10:30 am - 12:00 pm EDTGroup WorkAssigned Group Work Space
-
12:00 - 2:00 pm EDTLunch/Free Time
-
2:00 - 2:30 pm EDTGroup Presentations - 1Group Presentations - 11th Floor Lecture Hall
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2:30 - 3:00 pm EDTCoffee Break11th Floor Collaborative Space
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3:00 - 3:30 pm EDTGroup Presentations - 2Group Presentations - 11th Floor Lecture Hall
-
3:30 - 4:00 pm EDTGroup Presentations - 3Group Presentations - 11th Floor Lecture Hall
All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC-4).
All event times are listed in .
ICERM local time in Providence, RI is Eastern Daylight Time (UTC-4). Would you like to switch back to ICERM time or choose a different custom timezone?
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 airlines
- 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 superseded any prior invitation rates. Any invitations without travel support will still not receive travel support.
- 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 pdf of Google Maps result
- Keep all documentation until you receive your reimbursement!
- Reimbursement Timing
-
6 - 8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.
- Reimbursement Deadline
-
Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.
Projects
Maximum likelihood degree of stochastic block models
Elizabeth Gross (University of Hawai'i at Mānoa)
A popular class of statistical models studied in algebraic statistics are log-linear models. Log-linear models are popular since they have a monomial parameterization and correspond to toric ideals. Toric ideals are polynomial ideals generated by binomials with lots of combinatorial structure, making them great objects for exploration at varying levels of depth. For our project, we will focus on log-linear models that appear in network analysis, in particular, stochastic block models, which are used for clustering tasks in networks. We will study the geometry of maximum likelihood estimation for these models, specifically the maximum likelihood degree. The maximum likelihood degree is the number of complex solutions to the system of likelihood equations, and thus, for part of our project we will explore different computational software to solve such systems and different techniques to bound the number of solutions.
A New Variation on Happy Numbers
Helen Grundman (Bryn Mawr College)
The happy function maps a positive integer (expressed in base 10) to the sum of the squares of its digits. A happy number is a positive integer that, under repeated applications of the happy function, maps to 1. The iterative behavior of the happy function and its many variations has been the subject of study for over 75 years. In this project, we'll study a new variation on the classic happy function, working to establish results paralleling those known for the classic happy function and/or its other variations.
Brackets: A New Method for Integration
Victor Moll (Tulane University)
The evaluation of integrals is one of the subjects taught in Calculus courses. Even tough this appears to be an elementary subject, there is no complete algorithm to compute every integral. The project will be based on a new method to evaluate definite integrals. This is called the method of brackets, invented by Ivan Gonzalez at his Physics Ph.D. thesis at Universidad Santa Maria, Valparaiso, Chile in the context of Feynman diagrams. These diagrams explain the interaction of elementary particles and their parametrization produces very complicated integrals. The evaluation of this integrals give all the fundamental properties of particles. This is a heuristic method, based on a small number of rules, some of which have established rigorously. The project will involve a combinations of symbolic computation and also some theory needed to prove the rules of the method. This is a remarkable method: it reduces the evaluation of definite integrals to the solution of a system of linear equations, usually of very small size.