program Description

ADJOINT is a yearlong program that provides opportunities for U.S. mathematicians – especially those from the African Diaspora – to conduct collaborative research on topics at the forefront of mathematical and statistical research.

Beginning with an intensive two-week summer session at SLMath (formerly MSRI), participants work in small groups under the guidance of some of the nation’s foremost mathematicians and statisticians to expand their research portfolios into new areas. The two-week summer session will take place June 24 to July 5, 2024 in Berkeley, California. Throughout the following academic year, the program will provide conference and travel support to increase opportunities for collaboration, maximize researcher visibility, and engender a sense of community among participants.  

ADJOINT enriches the mathematical and statistical sciences as a whole by providing a platform for researchers, especially members of the African-American mathematical and statistical communities, to advance their research and careers and deepen their engagement with the broader research community. 

During the workshop, each participant will: 

• conduct research at SLMath within a group of four to five mathematical and statistical scientists under the direction of one of the research leaders 
• participate in professional enhancement activities provided by the onsite ADJOINT Director 
• receive funding for two weeks of lodging, meals and incidentals, and one round-trip travel to Berkeley, CA 

After the two-week workshop, each participant will:

• have the opportunity to further their research project with the team members including the research leader 
• have access to funding (up to $2000 per person) to attend conference(s) or to meet with other team members to pursue the research project, or to present results 
• become part of a network of research and career mentors

Eligibility

Applicants must be a U.S. citizen or permanent resident, possess a Ph.D. in the mathematical or statistical sciences, and be employed at a U.S. institution.

All members must be in residence and actively engaged in the program 8:30 am - 5 pm daily (without teaching, mentoring, or other professional responsibilities) for its duration:  June 24 to July 5, 2024.

Selection Process

The guiding principle in selecting participants and establishing the groups is the creation of diverse teams whose members come from a variety of institutional types and career stages. The degree of potential positive impact on the careers of African-Americans in the mathematical and statistical sciences will be an important factor in the final decisions.

Application Process

Applicants must provide:

• a cover letter specifying which of the offered research projects you wish to be part of; if more than one, please indicate your priorities
• a CV
• a personal statement, no longer than one page, addressing how your participation will contribute to the goals of the program (e.g., why you are a good candidate for this workshop and what you hope to gain)
• a research statement, no longer than two pages, describing your current research interests, and relevant past research activities, and how they relate to the project(s) of greatest interest to you (e.g., what motivates your current interests and what is your relevant research background) 

Due to funding restrictions, only U.S. citizens and permanent residents are eligible to apply.

2024 Research Leaders and Topics

Melody Goodman (NYU School of Global Public Health)
Comparison of probability and non-probability samples of web-based survey data on COVID-19 vaccination

The same survey was collected using a convenience sample (non-probability) and a probability sample with weights. To improve the analytical strength of the data, the qualified responses were weighted by iterative proportional fitting weighting, using multivariate target distributions from the U.S. Census American Community Survey 2018 data for gender, age (18-30 years of age), ethnicity, and race.  The weighted sample size was equivalent to the unweighted number of qualified responses.  The applied weights were clustered around the unweighted value of 1, with a sample balance of 87.3. We will compare differences in demographic characteristics of the samples and estimates of key measures across the samples (probability and nonprobability). The survey is about knowledge, attitudes, and behaviors related to COVID-19 precautions, including vaccination.

Background: Knowledge of working with complex survey samples and using Stata for data analysis.

Aaron Pollack (University of California, San Diego)
Explicit computation of cuspidal modular forms

A modular form is a type of very special smooth function.  One can think of them as being analogues of the exponential function F(x) = e^{2 pi i x} for real numbers x.  This function has three salient properties:
1) it has infinitely many discrete symmetries: F(x) = F(x+n) for any integer n;
2) it satisfies a simple linear differential equation;
3) it is bounded.

What if we change the domain from the real numbers to a more general Lie group? We obtain modular forms.  Specifically, suppose G is a non-compact Lie group, and S in G is an infinite discrete subgroup.  Roughly speaking, a cuspidal modular form for G of level S is a smooth function F that satisfies three properties:
1) F(sg) = F(g) for all s in S;
2) DF = 0, where D is a certain type of linear differential operator;
3) F is bounded.

So, if G is the real numbers and S is the integers, we can count the function F(x) = e^{2 pi i x} as a cuspidal modular form.  But when G is a non-abelian Lie group, it can be extremely difficult to write down even a single example of a cuspidal modular form.  Nevertheless, modular forms are the subject of immense study in number theory and representation theory, partly because they conjecturally connect many different areas of mathematics.  The goal of this project is to do theoretical computation with and numerical computation of certain spaces of modular forms. More specifically,
1) The first goal is to prove that certain classes of cuspidal modular forms are uniquely determined by a finite amount of data, in a precise way.
2) The second goal is to numerically compute some examples of cuspidal modular forms.  (By part 1, only a finite amount of data needs to be computed!)

Background: The main background needed would be some familiarity with Lie groups and Lie algebras.  For motivation, I also recommend reading about classical modular forms, e.g., in Serre’s “A course in arithmetic”, Chapter XII. 

ADJOINT Program Directors

·         Dr. Caleb Ashley, Boston College

·         Dr. Naiomi Cameron, Spelman College

·         Dr. Edray Goins, Pomona College (Onsite Director)

·         Dr. Jacqueline Hughes-Oliver, North Carolina State University

·         Dr. Anisah Nu’Man, Spelman College 

The Simons Laufer Mathematical Sciences Institute (SLMath) has been supported from its origins by the National Science Foundation, joined by the National Security Agency, over 100 Academic Sponsor departments, by a range of private foundations, and by generous and farsighted individuals.