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Organizing Committee
Purdue University
Occidental College
ICERM/Brown University
University of Michigan
Simons Laufer Mathematical Sciences Institute
ICERM/Morehouse College
Abstract
The NSF Mathematical Sciences Institutes Diversity Committee hosts the 2024 Blackwell-Tapia Conference and Award Ceremony. The conference and prize honor Dr. David Blackwell, the first African-American member of the National Academy of Science, and Dr. Richard Tapia, winner of the National Medal of Science in 2010, two seminal figures who have inspired generations of Black, Latinx, and Indigenous students and researchers in the mathematical sciences.
The Blackwell-Tapia Prize recognizes a mathematical scientist who has made outstanding contributions to research in their field of expertise and served as a role model for mathematical scientists and students from underrepresented groups, or has contributed in significant ways to addressing the underrepresentation of minorities in math.
The 2024 recipient of the Blackwell-Tapia Prize is Dr. Illya Hicks, Professor and Department Chair of Computational Applied Mathematics and Operations Research at Rice University.
Goals of the conference are to:
The Blackwell-Tapia Prize recognizes a mathematical scientist who has made outstanding contributions to research in their field of expertise and served as a role model for mathematical scientists and students from underrepresented groups, or has contributed in significant ways to addressing the underrepresentation of minorities in math.
The 2024 recipient of the Blackwell-Tapia Prize is Dr. Illya Hicks, Professor and Department Chair of Computational Applied Mathematics and Operations Research at Rice University.
Goals of the conference are to:
- recognize and showcase mathematical excellence by underrepresented researchers,
- build on efforts to increase diversity in mathematics,
- inform students and mathematicians about career opportunities in mathematics, especially outside academia, and
- provide networking opportunities for mathematical researchers at all points in the higher education/career trajectory.
Brought to you by the Mathematical Sciences Institutes Diversity Initiative with funding from the U.S. National Science Foundation. Additional funding has been provided by the Alfred P. Sloan Foundation, the Brown University Department of Mathematics, and the Brown University Office of Institutional Equity and Diversity.
David H. Blackwell & Richard Tapia
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Workshop Schedule
Friday, November 15, 2024
12:30 - 1:00 PM EST
Check In
11th Floor Collaborative Space
1:00 - 1:10 PM EST
Welcome
11th Floor Lecture Hall
Brendan Hassett, ICERM/Brown University
1:10 - 1:55 PM EST
Working with genomic data in Computational Biology
11th Floor Lecture Hall
Speaker
Emilia Huerta-Sanchez, Brown University
Session Chair
Rodrigo Banuelos, Purdue University
2:05 - 2:50 PM EST
Lipschitz graphs covering large subsets of fractals
11th Floor Lecture Hall
Speaker
Bobby Wilson, University of Washington
Session Chair
Rodrigo Banuelos, Purdue University
Abstract
In this talk we will discuss the extent to which one can cover a large subset of a purely unrectifiable set with a Lipschitz graph. In particular, we will present tools from harmonic analysis (Favard Length) and ergodic theory that make it possible to identify regular arrangements of points lying inside of any given one-dimensional set in the plane.
2:50 - 3:10 PM EST
Coffee Break
11th Floor Collaborative Space
3:10 - 3:55 PM EST
GMRES Convergence and Spectral Properties for Preconditioned KKT Matrices with Extensions to Generalized Block Matrices
11th Floor Lecture Hall
Speaker
Josef Sifuentes, University of Texas Rio Grande Valley
Session Chair
Brendan Hassett, ICERM/Brown University
Abstract
Several important preconditioners for saddle point problems yield linear systems for which the GMRES iterative method converges exactly in just a few iterations. However, these preconditioners all involve inverses of large submatrices. In practical computations such inverses are only approximated, and more iterations are required to solve the preconditioned linear system. How many more iterations? In this talk, we present perturbation analysis results for GMRES that leads to rigorous upper bounds on the number of iterations as a function of the accuracy of the preconditioner to the ideal and spectral properties of the constituent matrices. We also derive a thorough analysis of the spectral properties of these common saddle point preconditioners. Generalizations of these preconditioners have been proposed, however their convergence properties have not been described. Our spectral analysis of these generalized systems allow us to finally prove tight convergence bounds for these preconditioned systems.
4:05 - 4:50 PM EST
My Unlikely Journey: From the Barrios of Los Angeles to the White House and the National Medal of Science
11th Floor Lecture Hall
Virtual Speaker
Richard Tapia, Rice University
Session Chair
Brendan Hassett, ICERM/Brown University
Abstract
In this talk, Prof. Tapia will discuss how he became a leader in underrepresentation issues at the campus, state, and national levels, and will discuss challenges he’s faced throughout this journey from being born in Los Angeles to parents who immigrated from Mexico to his trip to the White House to receive the 2010 National Medal of Science from President Obama. The National Medal of Science is the highest award given by the United States government and Richard Tapia is the first Latino to win this prestigious award.
5:00 - 6:30 PM EST
Welcome Reception & Poster Session
Poster Session - Poster Session - 11th Floor Lecture Hall; Reception - 11th Floor Collaborative Space
Saturday, November 16, 2024
8:30 - 9:00 AM EST
Continental Breakfast
Continental Breakfast - 11th Floor Collaborative Space
9:00 - 9:45 AM EST
Green-elastic solids with gradient elastic boundaries
11th Floor Lecture Hall
Speaker
Casey Rodriguez, University of North Carolina
Session Chair
Ulrica Wilson, ICERM/Morehouse College
Abstract
In this talk, we explore new developments in the field of gradient elasticity. We begin by providing an intuitive introduction to the theory, which extends classical elasticity by incorporating higher-order spatial derivatives that capture microstructural effects. These contributions become particularly important at small spatial scales, offering a more refined description of deformation that classical models cannot account for. We then present a novel theory of three-dimensional Green-elastic bodies with gradient elastic material boundary surfaces and highlight its application to modeling brittle fracture.
9:55 - 10:40 AM EST
Stochastic Optimization: Complexity-Based Analysis and Development Engineering Applications
11th Floor Lecture Hall
Speaker
Caleb Bugg, Reaching Our Sisters Everywhere (ROSE) Inc.
Session Chair
Ulrica Wilson, ICERM/Morehouse College
Abstract
This work combines two lines of work related to stochastic optimization, one focused on theoretical contributions to the field, and the other focused on modelling and philosophical contributions to the field. In the first line of work, we contribute to the theoretical underpinnings of two models that draw from data analysis, mathematical and statistical modeling, and optimization. In particular, there are several classes of machine learning problems which interface with stochastics and optimization, and, with the use of stochastic process theory and associated notions of complexity, we can recharacterize some of the theoretical expectations of these problems, which importantly model uncertainty. The improved results are gained from problem reformulations, improved analytical techniques, and a concerted effort to use the most recent advances in complexity analysis and their associated generalizations, and has implications for the construction and analysis of societal scale models. In the second line of work, we demonstrate why the techniques in stochastic optimization help form a mathematical and statistical basis that can solve large-scale societal problems over time, with precise engineering intervention focus.
10:40 - 10:45 AM EST
Group Photo (Immediately After Talk)
11th Floor Lecture Hall
10:45 - 11:10 AM EST
Coffee Break
11th Floor Collaborative Space
11:10 - 11:55 AM EST
Panel Discussion
11th Floor Lecture Hall
Panelist
Ron Buckmire, Occidental College
Panelist
Juan Meza, Simons Laufer Mathematical Sciences Institute
Panelist
Omayra Ortega, Sonoma State University
Panelist
Nathaniel Whitaker, ICERM/ University of Massachusetts Amherst
Moderator
Brendan Hassett, ICERM/Brown University
12:00 - 1:30 PM EST
Lunch Provided by ICERM
Lunch/Free Time - 11th Floor Collaborative Space
1:30 - 2:15 PM EST
A Perspective on the Mathematics of Intelligence: Adaptive Cycles, Homeostasis, and Nonlocal Interactions
11th Floor Lecture Hall
Speaker
Cynthia Flores, California State University, Channel Islands
Session Chair
Ron Buckmire, Occidental College
Abstract
This talk explores a mathematical approach to understanding intelligence by focusing on adaptive cycles and nonlocal interactions, particularly in systems affected by damage. We begin with an introduction to nonlocal analysis—mathematics that considers influences beyond immediate neighbors—and how this approach provides insights into damage in materials, such as the propagation of corrosion. We will explore how to extend this idea to intelligent systems—both natural and artificial. Continuing our discussion on intelligence, we will consider a Koopman Operator approach to identifying adaptive cycles, aiming to capture the homeostasis seen in ecological and biological systems. Through frequency analysis and Koopman operators, we’ll explore how systems can learn and adapt to changing conditions by capturing natural rhythms and cycles. This presentation is designed to be accessible to undergraduate audiences, inviting an interdisciplinary discussion on applications spanning neuroscience and mathematical biology.
2:25 - 3:10 PM EST
Trace Ideals in Commutative Algebra
11th Floor Lecture Hall
Speaker
Haydee Lindo, Harvey Mudd College
Session Chair
Ron Buckmire, Occidental College
Abstract
The well-known trace map on matrices can be generalized to a map on any module over a commutative ring. The image of such a map is a trace ideal. In particular, given a ring R, the trace ideal of an R-module M is the ideal generated by the homomorphic images of M in R, and this construction has recently garnered new attention within commutative algebra. In this talk we will outline some recent developments in the theory of trace ideals, with some applications to endomorphism rings, rigid modules, and classifications of commutative rings.
3:10 - 3:30 PM EST
Coffee Break
11th Floor Collaborative Space
3:30 - 4:15 PM EST
Unexpected Connections
11th Floor Lecture Hall
Speaker
William Christian, .
Session Chair
Tatiana Toro, Simons Laufer Mathematical Sciences Institute
4:25 - 5:10 PM EST
Graphs and Discrete Optimization
11th Floor Lecture Hall
Speaker
Illya Hicks, Rice University
Session Chair
Tatiana Toro, Simons Laufer Mathematical Sciences Institute
Abstract
Graphs or networks are everywhere! Network analysis has garnered significant attention as an effective tool for studying and solving problems related to complex, natural, and engineered systems. Indeed, the novel network models derived from these problems have led to many interesting insights. In this talk, we will explore some connections that arise in political redistricting, electrical grids, and quantum computing.
6:00 - 7:00 PM EST
Cocktail Hour
Cocktail Hour - Graduate Hotel
7:00 - 9:00 PM EST
Banquet
Banquet - Graduate Hotel
Lecture Videos
Josef Sifuentes
University of Texas Rio Grande Valley
November 15, 2024 • 12:00 AM
Casey Rodriguez
University of North Carolina
November 16, 2024 • 12:00 AM
Caleb Bugg
Reaching Our Sisters Everywhere (ROSE) Inc.
November 16, 2024 • 12:00 AM
Cynthia Flores
California State University, Channel Islands
November 16, 2024 • 12:00 AM