The Department of Mathematics at Pomona College will offer an eight-week summer residential program to conduct research in Algebraic Geometry & Number Theory. The program, entitled PRiME (Pomona Research in Mathematics Experience), will run from from **Sunday June 11 through Saturday August 5, 2023.** The program is being sponsored by the National Science Foundation (DMS-2113782). PRiME is an REU/Learning Community consisting of 15 undergraduates, 5 graduate students, and 5 faculty to conduct research in groups, vertically integrate mentoring, and provide professional development for students and staff alike.

Faculty in residence for the program will be:

**Alex Barrios**, Assistant Professor of Mathematics at the University of St. Thomas**Luis David Garcia Puente**, Professor of Mathematics and Computer Science at Colorado College**Edray Herber Goins**, Professor of Mathematics at Pomona College**Haydee Lindo**, Assistant Professor of Mathematics at Harvey Mudd College**Lori D. Watson**, Assistant Professor of Mathematics at Trinity College

More information about the 2023 Research Projects can be found here.

Algebraic Geometry is among the most distinguished fields in the mathematical sciences. Widely respected mathematical prizes such as the Abel Prize, the Breakthrough Prize in Mathematics, and the Fields Medal have been disproportionately awarded to researchers in Algebraic Geometry. Unfortunately, this subdiscipline is notorious for its dismally low numbers of underrepresented minorities. A report from the American Mathematical Society on new 2017-2018 doctorate recipients states that 269 of 1,960 math PhDs in the U.S. were in Algebra and Number Theory. Among the US citizens in this group, just 34 were Hispanic or Latino, 27 were Black or African American, 6 were American Indian or Alaska Native, and 2 were Native Hawaiian or Other Pacific Islander.

Pomona College will offer an eight-week summer residential program to conduct research in Algebraic Geometry and Number Theory (AG&NT), with the express intent to diversify the field. The program, entitled "Pomona Research in Mathematics Experience (PRiME)", will host fifteen undergraduates recruited in a national competition, five graduate students, two junior faculty/postdoctoral fellows, and three senior faculty members. PRiME will present new mathematical ideas and techniques, highlight research in AG&NT, provide enhanced mentoring opportunities, identify potential role models and strengthen professional networks for all participants in the program. These components, individually and wholly, will produce significant broader impacts by fostering the current and future professional skills of a diverse group of participants.

PRiME was incredible and an unforgettable experience. It made me feel comfortable and capable of doing mathematics. Prior to PRiME I was unsure and felt un-supported and alone in math. I had no mentorship or friends within math. Everyone seemed to already have a leg up on me and that was demoralizing but after PRiME I feel capable and empowered to do mathematics.- PRiME Participant

PRiME's goals are to:

- to provide a nationally recruited group of undergraduates with an 8-week intensive summer research experience in AG&NT and lead to new results worthy of publication or presentation at national meetings;
- to position undergraduates to enter post-baccalaureate degree programs in the mathematical sciences;
- to provide intensive mentoring and mentor training for faculty, postdocs, and grad students via vertically integrated clusters; and
- to establish an extended cross-generational network and community of underrepresented minorities in AG&NT.

PRiME will meet these goals through four key elements.

**Research with Undergraduate Participation:**Five research groups meeting daily, each forming an REU-like unit consisting of one faculty member, one graduate student, and three undergraduates. Their research projects will delve into the ranks of elliptic curves; compute information about Belyi maps for the L-Series and Modular Forms Database (LMFDB); write open-source software to visualize*Dessin d'Enfants*; and create animations to illustrate the action of monodromy corresponding to branched covers of curves. More information about the 2023 Research Projects can be found here.**Mentoring Clusters:**There will be three mentoring clusters, each consisting of two graduate students, one junior faculty/postdoctoral fellow, and one senior faculty member. Each week, the mentoring clusters will have lunch at least once to discuss topics such as the academic job market, writing funding proposals, and forming potential research collaborations. The mentoring clusters are meant to provide a space for graduate students, postdoctoral fellows, and junior faculty to receive one-on-one mentoring with senior faculty.**Professional Development:**There will be various development activities for both undergraduates and staff (graduate students and faculty) on Fridays. Undergraduates will attend a series of workshops run by local faculty to prepare for the Graduate Record Examination, gain LaTeX proficiency, and strengthen graduate school and fellowship applications. Every other week, the staff will have focused, literature-based discussions led by local faculty who are experts in the field, whereas the remaining weeks there will be highly technical seminars on advanced mathematical topics given by graduate students and junior faculty/postdoctoral fellows for the senior faculty in attendance.**Community Building:**There will be a lecture series during Friday afternoons featuring underrepresented minority faculty. Each talk in the Colloquium will be made publicly available via YouTube. The students and staff will have the opportunity to have dinner with the presenters, discussing the presenter's journey from undergraduate to the professoriate. Speakers will be encouraged to stay for Saturday outings to help build community and facilitate social interactions.

During the summer, each of the undergraduate participants will:

- Complete a research project done in collaboration with other PRiME students.
- Give a presentation at MAA's MathFest and write a technical report.
- Attend a series of colloquium talks given by leading researchers in their fields.
- Attend workshops aimed at developing skills and techniques needed for research careers in the mathematical sciences.

In order to successfully complete this project, undergraduate participants will:

- Meet at least 10 hours every week for a minimum of 8 weeks.
- Be introduced to advanced topics relevant for their research such as: Abstract Algebra, Complex Analysis, Differential Geometry, Graph Theory, and Number Theory.
- Learn how to use an computational mathematical packages such as Sage, Mathematica, or Matlab.
- Learn how to use LaTeX, a mathematical typesetting language.
- Write a technical paper explaining the details of the project.
- Design a poster giving an overview of the project.

Undergraduate participants in the PRiME program will receive:

- a stipend of $4,000 upon successful completion of the program;
- travel to and from Claremont CA, housing at Pomona College, and meals in the dining halls; and
- a $1,500 allowance for travel to future conferences.

Students must be undergraduates in good standing, although preference will be given to applicants who will begin either their junior or senior year in the Fall of 2023. National Science Foundation (NSF) funding also requires that participants must be either US Citizens or Permanent Residents. Unfortunately, we are not accepting applications from students who may provide their own funding.

Applications for the PRiME program should be submitted through the NSF Common App. For a complete application, you will need to submit

- Two letters of recommendation addressing your ability to conduct research and your ability to work with others.
- An unofficial transcript or list of math courses and grades. An official transcript may be required upon admission to the program.
- A cover letter addressing your interest in the PRiME program. Please address what you hope to get out of participating in PRiME and also which of the research topics you would prefer to participate in.

For full consideration, applications should be received no later than ~~February 15, 2023~~ ** February 24, 2023**. Decisions will be announced by March 1, 2023. Questions should be directed to Edray Goins at edray.goins@pomona.edu.

*February 24, 2023:*Deadline for submitting applications to PRiME.*March 1, 2023:*Admission decisions will be announced.*March 8, 2023*(Common Reply Date for REUs): Students will inform PRiME Staff of their decision to attend.*June 11, 2023:*PRiME begins!

This material is based on work supported by the National Science Foundation under Grant No. DMS-2113782. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Contact edray.goins@pomona.edu for more information.