Skip to main content

Focused Collaborative Research

The American Institute of Mathematics

Research Communities

AIM Research Communities (ARCs) are virtual collaborative efforts involving at least 40 people, organized around a particular area of research in the mathematical sciences. The purpose of an AIM Research Community is to support the ongoing research activities of its participants. It is expected that Research Communities have a long lifetime and grow over time. Most ARCs accept applications when they are starting and some accept applications periodically; please check the webpage associated with each ARC for information about how to apply to that ARC.  There are three main types of ARCs:  

  • The primary outcome of a Research Group  ARC is the production of research results and their dissemination via publications. Such ARCs often resemble an AIM workshop, but expanded in time, reduced in intensity, and held completely online.   This type of ARC often continues for years.

  •  A Research Learning Community ARC usually provides guided collaborative learning for graduate students and other junior researchers, often with mini-courses, tutorials, reading groups, etc.  This type of ARC usually lasts between one semester and one year..

  • A Research Network  ARC focuses on supporting the development of a particular research area through building a network, often bringing together experts in different areas who can help bridge gaps and strengthen collaborations among those with different scientific backgrounds.  This type of ARC often continues for years. 

For more information, please contact Leslie Hogben, Director of Research Communities, hogben@aimath.org.

Proposing an ARC

Proposals for ARCs include:

  • a description of the ARC’s motivation, focus and goals;

  • a discussion of the mathematics involved in the ARC;

  • a list of organizers (at least 2, at most 4);

  • a list of potential participants;

  • the mathematics subject classification and a list of references.

AIM is currently accepting proposals for AIM Research Communities, with a deadline of November 1. Proposals can be submitted using the research community proposal form . Groups considering proposing a Research Community may find it helpful to meet with Leslie Hogben (hogben@aimath.org) before submitting a proposal.

AIM Quantum Research Community
Orly Alter, Ortwin Hess, Valerio Pascucci
Started Jan 2026 – Jan 2028
View →

In 1960, the quantum mechanist Eugene P. Wigner famously wrote about "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." He was referring to the …

Arizona Winter School research community
Renee Bell, Brandon Levin, Anthony Varilly-Alvarado
Started Apr 2025 – Apr 2027
View →

is a virtual companion to the Arizona Winter School, centered around two short courses each Fall aimed at advanced undergraduate and beginning graduate students broadly …

Consortium of digital ecosystems for mathematics
Steven Clontz, David Lowry-Duda, Christelle Vincent
Started Apr 2025 – Apr 2027
View →

is dedicated to the advancement of mathematical research through the development of high-quality sociotechnical infrastructure, including mathematics software, databases, documentation, communities, and more. We work …

Ecology meets infectious diseases
Folashade Agusto, Eric Numfor, Michael Robert
Started Apr 2025 – Apr 2027
View →

provides training in mathematical modeling of infectious diseases, ecological dynamics, and eco-epidemiological systems. Over the course of one year, starting in August 2025, the community …

Fourier restriction conjecture and related problems
Alan Chang, Zane Kun Li, Po-Lam Yung
Started Mar 2022 – Mar 2028
View →

Please see the community's website at https://sites.google.com/view/aim-frc/.

Graph Polynomials and Invariants
Aihua Li, Sarita Nemani
Started Jan 2026 – Jan 2028
View →
Inverse eigenvalue problems for graphs
Mary Flagg, Jephian Lin, Bryan Shader
Started Feb 2021 – Mar 2031
View →

This AIM Research Community (ARC), sponsored by AIM and the NSF, began in 2021 and focuses on combinatorial and linear algebraic problems related to inverse …

Mathematics and climate research network
Kate Meyer, James Broda, Kaitlin Hill
Started Jan 2024 – Dec 2028
View →

provides intellectual support and mentoring to researchers at all career stages who are eager to identify and tackle mathematical questions raised by the urgent climate …

Representation theory and noncommutative geometry
Pierre Clare, Nigel Higson, Birgit Speh
Started Jan 2021 – Dec 2028
View →
Rethinking Number Theory
Heidi Goodson, Allechar Serrano Lopez, Jen Berg
Started Jan 2022 – Dec 2027
View →

Please see the community's website at https://sites.google.com/view/rethinkingnumbertheory/.

Latinx mathematicians research community
Jesus De Loera, Pamela Harris
Jun 2021 – Jun 2026
View →
Little school dynamics
Kimberly Ayers, Han Li, David McClendon
Feb 2021 – Dec 2025
View →
Link homology
Nicolle Gonzalez, Eugene Gorsky, Matthew Hogancamp
May 2021 – Apr 2025
View →
4-dimensional topology
Miriam Kuzbary, Maggie Miller, Juanita Pinzon-Caicedo
Feb 2021 – Feb 2025
View →
Big ideas in dynamics
Benjamin Call, Noelle Sawyer
Feb 2023 – Feb 2024
View →

focuses on collaborative learning among graduate students in dynamical systems, specifically smooth dynamics, ergodic theory, and homogeneous dynamics. There are three main goals to this …

Complex and Arithmetic Dynamics Research Environment
Laura DeMarco, Patrick Ingram, Joseph Silverman
Jan 2022 – Jan 2023
View →