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Summertime at the Mathematics Research Communities (MRCs)

Sarah Bryant

So much energy! That’s what I experienced at the 2023 MRCs, starting with the shuttle ride out to Beaver Hollow Conference Center, where I saw joyful reunions between old friends and eager introductions among new colleagues.

Set in the forests of upstate New York, the MRCs offer a summertime retreat from the day-to-day world that allows for immersion in cutting-edge research. Each conference is extremely hands-on and collaborative. Organizers post materials well ahead of the MRC week to ensure that participants are ready to hit the ground running, and they do. Walking around the conference center, I saw whiteboards and flipcharts full of definitions, proof sketches, conjectures, and calculations: usually with a huddle of mathematicians talking through an idea.

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But MRCs aren’t all math. The setting and structure allow you to walk a trail, sit in nature, jump in a rowboat. There’s even an excursion to nearby Niagara Falls. Conversations during these moments are just as valuable as those that happen in working sessions. Graduate students and early-career faculty can discuss careers, work-life balance, coping with setbacks, and other important topics among themselves and with organizers. And in addition to research breakout groups, the MRCs include complementary activities such as career-focused, soft-skills training opportunities.

On my academic journey, I never participated in a program like the MRCs, and I wish I had. As a graduate student, I often felt isolated in my work. I have come to learn that the most enjoyable parts of math, and life, involve collaboration. I am so glad this experience is available now for early-career researchers, as I know it has the potential to change a mathematician’s career trajectory positively. Many MRC participants maintain their working collaboration groups and mentoring networks throughout the year and well beyond.

Who should apply? Applicants should be ready to engage in collaborative research and should be “early career”—either expecting to earn a PhD within two years or having completed a PhD within five years of the date of the summer conference. Exceptions to this limit on the career stage of an applicant may be made on a case-by-case basis. Applicants who identify as members of underrepresented groups and gender minorities are especially encouraged to apply.

The following MRC sessions are scheduled for summer 2024. Lead organizers are denoted with an asterisk. To learn more and apply by February 15, 2024, visit http://www.ams.org/programs/research-communities/mrc.

MRC 2024, Week 1: Algebraic Combinatorics (Organizers: Susanna Fishel, Rebecca Garcia, Pamela Harris*, Rosa Orellana, Catherine H. Yan)

Algebraic combinatorics combines tools and techniques from both algebra and combinatorics to study discrete structures and their properties. This branch of math has strong ties to representation theory, computing, knot theory, mathematical physics, symmetric functions, and invariant theory.

This MRC seeks to advance the frontiers of cutting-edge algebraic combinatorics, including through explicit computations and experimentation, and to strengthen the research networks of those working in this branch. Postdocs and sufficiently advanced graduate student researchers will work together in small groups on open problems in algebraic combinatorics and closely related areas, including representation theory, special functions, and enumerative combinatorics.

Applicants should have a background in algebra and/or combinatorics. Please mention any programming experience, although it’s not required.

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MRC 2024, Week 2: Mathematics of Adversarial, Interpretable, and Explainable AI (Tegan Emerson, Emily King*, Dustin Mixon, Tom Needham, Karamatou Yacoubou Djima)

Some of the most active areas of research in machine learning today are adversarial artificial intelligence (AI), explainable AI, and interpretable AI. In explainable AI, methods are developed to “open up” black boxes like neural networks, while interpretable AI creates white box methods with possibly lower accuracy. It is possible to “trick” a trained neural network into outputting an error; adversarial AI is the study of such phenomena, which could yield dangerous outcomes. Most progress in these areas has been empirical and rooted in computer science, but there is a growing body of literature that suggests that fresh insights are available in fields that are traditionally considered to be pure mathematics, such as algebra, geometry, topology, and analysis.

The goal of this MRC is to introduce early career mathematicians, coming from a variety of subdisciplines, to these cutting-edge research areas and to show them how they can use their own expertise to make substantial contributions. The establishment of a diverse community of mathematicians working in this research area would be timely, since the role of AI in industry is increasing exponentially, and the demand for theoretical understanding of these algorithms is reflective of this.

MRC 2024, Week 3a: Climate Science at the Interface of Topological Data Analysis and Dynamical Systems Theory (Davide Faranda, Théo Lacombe, Nina Otter, Kristian Strommen*)

A central challenge in climate science is understanding how global warming will affect mid-latitude weather. This MRC will address that question using topological data analysis (TDA), with a broader goal of fostering new collaborations between TDA, climate science, and dynamical systems theory.

The MRC will consider questions both practical—improving algorithms and software—and theoretical, such as analyzing dynamical properties of topological features. We welcome applicants from academia and industry with a wide range of backgrounds. Tutorials on TDA, climate science, and dynamical systems will take place before the research week.

MRC 2024, Week 3b: Homotopical Combinatorics (Andrew Blumberg, Michael Hill, Kyle Ormsby*, Angélica Osorno, Constanze Roitzheim)

This MRC will bring together early-career researchers with interests in combinatorics, algebraic topology, and abstract homotopy theory. Familiarity with abstract homotopy theory or with modern methods of algebraic topology will allow deeper engagement with some problems, but is not required; much of the subject can be approached purely combinatorially.

Relevant readings will be provided before the workshop, and an online collaboration platform will be used to discuss material and to build community. At the workshop, participants will work in teams on research programs, engage with lectures from senior faculty participants about aspects of homotopical combinatorics, and have open feedback sessions for further discussion.

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