Maria K. Cameron

University of Maryland, Department of Mathematics

Research Experience for Undergraduates

Modern topics in pure and applied mathematics

An intense 8-week summer program for undergraduate students will be run at the University of Maryland, College Park, MD, for three years: 2022, 2023, and 2024. Research topics in six different fields of contemporary pure and applied mathematics will be offered. Each year, two research topics will be advertised and a total of 12 undergraduates will be recruited nationwide. The projects will come from hot research areas where a lot of exploration is yet to be done. This will enable the undergraduates to exploit their creativity and advance knowledge in the corresponding fields. The REU program will start with two weeks of teaching the undergraduates the necessary background. Then each team of six undergrads will be split into a few subgroups to work on specific projects within each topic. Each team will include a UMD graduate assistant who will help the faculty team leader mentor the undergrads. Besides technical training and research activities, the REU program will involve three weekly seminars: the Update Seminar where the undergrads will give oral presentations on their projects, the Exposure Seminar where professors from the UMD and nearby universities will give expository talks on their research, and the Lunchtime Workshop where topics such as how to apply for graduate schools and research fellowships, how to write a paper and give a talk will be discussed. The REU program will be concluded with the Symposium where each undergraduate participant will give a talk. Additionally, each undergrad will need to write a report that will be converted into a paper in a peer-reviewed journal. Selected participants will be given an opportunity to present their work in conferences such as the Joint Mathematics Meeting.

Summer 2023 REU

REU 2023 team: (first row, left to right) Santiago Martinez (University of Maryland), Maria Cameron (the REU director, UMD) Rayyan El Ghandour (Walter Johnson High School, MD), Abjini Chattopadhyay (Blair High School, MD), Amy Xu (Walt Whitman High School, MD), Seyed Banihashemi (MATH graduate student, UMD); (second row, left to right) Stanley Jian (Columbia University), Aren Martinian (UC Berkeley), Bill Chen (Northwestern University), Alkis Boukas (Cornell University), Julien Kaufmann (University of Notre Dame), Etienne Phillips (North Carolina State University), Christian Zickert (the algebra group professor, UMD), Leo Chang (Northwestern University); (row three, left to right) Adam Moubarak (Stevens College), Daniel Xu (Columbia University), Arnav Mehta (UC Berkeley), Roy Lam (Cornell University), Valerie Wray (AMSC graduate student, UMD), Vasanth Pidaparthy (MATH graduate student, UMD); (row four, left to right) Luis Suarez (MATH graduate student, UMD), Perrin Ruth (AMSC graduate student, UMD), Luca Nijim (University of Notre Dame)

Dates of the Summer Program:

June 12, 2023 -- August 4, 2023

Program outline

June 12: 10:00 AM -- 4:00 PM Kick-off. Room: MATH 3206 and the graduate lounge
June 13 -- June 23. Tutorials. Room: TBA
Mondays June 26, July 3, 10, 24, 12:00 PM -- 1:30 PM. Lunchtime workshop. MATH Lounge
Wednesdays June 28, July 5,12, 19, 26, 2:00 PM -- 3:00 PM. Exposure Seminar. Room: MATH 3206
Thursdays June 15, 22, 29, July 6, 13, 20, 27, 4:00 PM -- 5:00 PM. : Joint seminar with other STEM REUs, Room: MATH3206
Fridays June 30, July 7, 14, 21, 28, 1:30 PM -- 3:30 PM. Update Seminar. Room: MATH 3206
Monday, July 17. Visit to NSA is CANCELED
Monday, July 31. Joint lunch with other STEM REUs and graduate directors
Wednesday, August 2, 12 PM -- 2 PM. Poster Competition. Rotunda of the Math Building.
Friday, August 4. 10:00 AM -- 4:00 PM. Symposium. Room: MATH 3206

Kick-off. Slides

Monday, June 12, MATH 3206

10 AM -- 10:20 AM: Opening Remarks
10:20 AM -- 10:50 AM: Maria Cameron, Data-driven methods and model reduction for the study of rare events in stochastic systems
10:55 AM -- 11:25 AM: Christian Zickert, Cluster algebras and polylogarithm relations
11:30 AM -- 12:00 PM: Antonio De Rosa, Geometric measure theory in optimal transport, geometric flows, and minimal surfaces
12:05 PM -- 12:35 PM: Rodrigo Trevino, Statistical mechanics for quasicrystals
12:40 PM -- 1:40 PM: Lunch
1:40 PM -- 2:10 PM: A tour around relevant buildings
2:10 PM -- 4:00 PM: Meeting with research leaders

UMD Calendar: Campus Closures

We will follow the UMD Academic Calendar (scroll to the bottom of the page.)

June 19, Monday: Juneteenth Holiday. Campus closed.
July 4, Tuesday: Independence Day Holiday. Campus closed.

Exposure Seminar.

Wednesdays, 2--3 PM, MATH 3206

June 28: Jonathan Rosenberg, The Bernoulli numbers: how they were first discovered and some of their amazing applications
July 5: Bill Goldman, Lines of Cubic Surfaces
July 12: Yanir Rubinstein, Mahler and Bourgain Conjectures - Geometry, Number Theory, and Convex/Complex Analysis
July 19: Rodrigo Trevino, Swedish royalty and space travel
July 26: Abba Gumel, Mathematics of Epidemics

Joint REU Seminar.

Thursdays, 4--5 PM, MATH 3206

June 15: Erin Molly, Models and methods for reconstructing population-level evolutionary histories and relationships to tumor phylogenetics
June 22: Najib El-Sayed, Computational Biology
June 29: Maria Cameron, Quantifying Rare Events in Stochastic Systems
July 6, note special time 3--4 PM: Dana Dachman-Soled, Types of Cybersecurity Attacks
July 13: Evan Golub, How to do bad science SPECIAL LOCATION: IRIBE 4105
July 20: Victor Yakovenko, Statistical Mechanics of Money
July 27: Emily Kaplitiz, Neurodivergence

Lunchtime Workshop

Mondays, 12--1:30 PM, MATH lounge

June 26: How to give a talk
July 3, 10: How to apply to a graduate school and for graduate research fellowships
July 24: How to prepare a poster and write the final report.

Poster Competition

Wednesday, August 2, Rotunda

Click to see more photos

Alkis Boukas and Bill Chen: "Neural Networks and Neural Operators for the Committor Problem"
Amy Xu: "SIR Model on Random Graphs"
Arnav Mehta and Roy Lam: "Machine-Learned Collective Variables that Represent Molecular Dynamics"
Leo Chang, Stanley Jian, Aren Martinian, and Adam Moubarak: "Ellipticity Condition Implications for the Study of Anisotropic Minimal Surfaces"
Leo Chang, Stanley Jian, Aren Martinian, and Adam Moubarak: "Notions of Convexity and Ellipticity Conditions"
Etienne Phillips and Ziwei Tan: "The Space of Cluster Polylogarithms"
Julien Kaufmann and Daniel Yuan: "Quadrangular Polylogarithms"
Daniel Xu, Luca Nijim, and Abjini Chattopadhyay: "Data-Driven Studies of Noisy Chaotic Oscillators"
Rayyan El Ghandour: "Numerical Estimaties of Hausdorff Dimensions"

Results

Winner: Leo Chang, Stanley Jian, Aren Martinian, and Adam Moubarak, mentored by Dr. Antonio de Rosa: Ellipticity Condition Implications for the Study of Anisotropic Minimal Surfaces.
Runner-up: Alkis Boukas, Bill Chen, mentored by Dr. Maria Cameron: Neural Networks and Neural Operators for the Committor Problem.

The hike in the Great Falls park on the Virginia side, July 4, 2023

Great Falls, VA, Scenic Outlook

Great Falls, VA, on the trail

The website for the REU 2022.

Contact:

Maria Cameron, mariakc@umd.edu