University of Alabama Department of Mathematics

2026 Alabama Summer Undergraduate Math Workshop

The Department of Mathematics was pleased to host the 2026 Alabama Summer Undergraduate Math Workshop, a four-day program designed to support and inspire undergraduate students in mathematics.

The workshop featured plenary lectures, mini-courses, problem-solving sessions, and professional development activities, providing participants with valuable opportunities to deepen their mathematical knowledge and explore academic and career pathways. Students also had the chance to showcase their work through short research presentations and poster sessions, fostering collaboration and scholarly exchange among peers.

We thank all participants, speakers, organizers, and mentors who contributed to the success of this enriching event and helped create a vibrant mathematical community.

For more information about the workshop, please visit: https://sites.ua.edu/btosun/asumw/

Luke Bowman and Eoin O’Hearn Offered Fulbright Award for 2026-2027

Congratulations to Luke Bowman and Eoin O’Hearn on their recognition in the Fulbright U.S. Student Program competition for 2026–2027.

Luke, who recently completed his B.S. in Mathematics, is among ten University of Alabama students who have been offered Fulbright awards this year. He will serve as an English Teaching Assistant in Germany. Bulent Tosun had the pleasure of teaching Luke in my MATH 301 course last spring and was impressed by his strong academic abilities and thoughtful engagement in the classroom.

Eoin, another outstanding Mathematics student and participant in the AMP in Mathematics program, has been named a Fulbright finalist and may still receive an award if additional funding becomes available. Bulent Tosun had the opportunity to work closely with Eoin both as a student and through AMP in Mathematics. He is a truly remarkable scholar and an exceptional person, and this recognition is well deserved.

Congratulations to both Luke and Eoin on these significant achievements.

More information is available here:

UA students offered Fulbright awards for 2026-2027 The Fulbright Program selected 10 University of Alabama students for various awards for the 2026-2027 academic year.

Congratulations to Dr. Simon Bortz on NSF Grant Award

Congratulations to Dr. Simon Bortz, who has been awarded a three-year grant from the National Science Foundation’s Analysis Program within the Division of Mathematical Sciences in support of his project, “Quantitative Parabolic Rectifiability, Parabolic Partial Differential Equations and Boundary Value Problems.”

The project studies evolution equations that govern heat flow, diffusion, and transport, that is, processes described mathematically by parabolic partial differential equations. A central question of the project is how the shape and roughness of a region’s boundary influence the behavior of solutions of these parabolic equations inside the region. A particular focus is on regions that are allowed to deform over time. The project aims to identify sharp criteria connecting the geometry of these evolving boundaries to the analytic behavior of solutions.

Please join us in congratulating Dr. Bortz on this outstanding achievement and wishing him continued success with this important research.

Dr. Jia Zhao Serves as Co-PI on NSF Research Grant

Congratulations to Dr. Jia Zhao, assistant professor of mathematics, who will serve as a co-principal investigator (Co-PI) on a three-year, $525,021 research grant from the National Science Foundation (awarded through the Division of Mathematical Sciences). The project is titled “FDT-BioTech: Biosignals Fusion-Informed Neuromusculoskeletal Reconstruction in Immersive Digital Twin for Personalized Stroke Gait Rehabilitation Using Lower-Limb Exoskeletons.”

The interdisciplinary project is led by Dr. Qiang Zhang as PI, with Drs. Fei Hu, Jia Zhao, and Mizanur Rahman serving as Co-PIs. The research team will develop a personalized digital-twin framework that integrates mathematical modeling, biosignal data, artificial intelligence, and wearable robotics to improve lower-limb rehabilitation for individuals who have experienced a stroke.

More info can be found at: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2625825

Dr. Michael Perlman Awarded NSF Research Grant

Congratulations to Dr. Michael Perlman, who has been awarded a three-year grant from the National Science Foundation’s Algebra and Number Theory Program within the Division of Mathematical Sciences, in support of his project, “Group Actions and Hodge Theory in Commutative Algebra.”

The project sits at the confluence of algebraic geometry, commutative algebra, and representation theory, and investigates the singularities of algebraic varieties possessing rich group symmetry, such as toric varieties, Schubert varieties, and orbit closures of reductive groups. Drawing on cohomological methods, Hodge theory, and the representation theory underlying these symmetries, the project develops new tools to compute homological invariants that are otherwise notoriously intractable, shedding light on the geometry of singularities and their place within a broader mathematical landscape.

Congratulations to Dr. Prashanth Sridhar on NSF Grant Award

Congratulations to Dr. Prashanth Sridhar on being awarded a three-year grant from the National Science Foundation for his project, Novel Homological Structures in Commutative Algebra and Their Applications.

This award recognizes the significance of Dr. Sridhar’s research and will support innovative work exploring new homological structures in commutative algebra and their applications. We congratulate Dr. Sridhar on this outstanding achievement and wish him continued success in advancing mathematical research.

Dr. Prashanth Sridhar Receives The Simons Foundation Award

Congratulations to Dr. Prashanth Sridhar on receiving a prestigious grant award from the Simons Foundation.

The award is through the Simons Foundation’s Mathematics & Physical Sciences (MPS) Travel Support for Mathematicians program, which is designed to foster collaboration in mathematics by supporting travel and related research expenses over a five-year period.

This recognition reflects Dr. Sridhar’s contributions to the mathematical sciences and provides valuable opportunities to strengthen research collaborations and advance innovative work in the field. Congratulations on this well-deserved achievement!

Algebra, MathBio, and Numerical PDE Group Presentations: On Wednesday July 1st 11AM-2:15PM in GP227 the local REU groups will present the projects they have worked on during the summer.

The schedule is as follows:

11AM-11:50AM Algebra group: Vu Minh Khang Ho, Hans Laren, and Nathan McWilliams (Mentors: Dr. Perlman and Dr. Polstra)
11:50 – 12:15 PM Break/pizza
12: 15 – 1:05 MathBio/Numerical PDE: Spence Hanegan (Mentors: Dr. S. Shao and Dr. Zhao)
1:15- 2:05 Computational Modeling: Warren Chen, Levi Maxwell, and Jonathan Wisnoff (Mentors: Dr. Wang and Dr. J. Zhao)
You can find (two of) the abstracts below.

The abstract for the MathBio/Numerical PDE group:

Title: Physics-informed Neural Networks for the Poisson-Boltzmann Equation

Abstract: The electrostatic potential of proteins is necessary for computing the solvation free energy used for biomolecular modeling and drug discovery. However, the widely used Poisson-Boltzmann Equation (PBE) for solving electrostatic potential presents significant numerical challenges such as singular atomic charges, nonlinear terms, and sharp dielectric interfaces. Applying Physics-Informed Neural Networks (PINN) to the PBE provides a promising alternative to traditional mesh-based schemes. Existing PINN approaches address the PBE’s piecewise-defined nature by using cPINN or xPINN architectures; however, the resulting loss functions are complex and can lead to training instability and poor computational efficiency. We developed a PINN method that employs a Sobolev extension to represent a piecewise continuous function in $\mathbb{R}^n$ as a continuous function in $\mathbb{R}^{n+1}$. This reformulates the PBE as a continuous problem, a setting more suited to neural network approximation. We analyze and validate this approach against the Kirkwood Sphere PBE benchmark and a diverse set of proteins.

The abstract for the Computational Modeling group:

Title: Mathematical Modeling of Human Behavior in Epidemics Using Population Networks, Game Theory, and Digital Twins

Abstract: Human behavior strongly shapes epidemic transmission and the impact of public health interventions. This REU project examines this issue through three related projects focused on social contacts, behavioral responses, and campus-scale simulation.

(1) The first project reconstructs realistic population contact networks from previously collected contact data. Using simulated annealing and network rewiring, it produces network structures that preserve important features of empirical contact patterns and can be used in epidemic simulations. (2) The second project develops a game-theoretic model of behavioral decision-making during an epidemic. Individuals choose between compliance and noncompliance with public health guidance according to a logit equilibrium that accounts for perceived infection risk, economic burden, government mandates, peer influence, and restriction fatigue. (3) The third project develops an interactive digital twin of the University of Alabama campus for simulating epidemic scenarios and evaluating intervention strategies. The simulator provides a campus-scale platform incorporating epidemic dynamics, behavioral assumptions, and policy interventions.

Overall, these projects offer complementary approaches to modeling human behavior in epidemics and provide building blocks for a future integrated framework combining contact networks, behavioral decision-making, and digital twin simulation.

Congratulations to Luke Bowman and Eoin O’Hearn on their recognition in the Fulbright U.S. Student Program competition for 2026–2027.

Luke, who recently completed his B.S. in Mathematics, is among ten University of Alabama students who have been offered Fulbright awards this year. He will serve as an English Teaching Assistant in Germany. Bulent Tosun had the pleasure of teaching Luke in my MATH 301 course last spring and was impressed by his strong academic abilities and thoughtful engagement in the classroom.

Eoin, another outstanding Mathematics student and participant in the AMP in Mathematics program, has been named a Fulbright finalist and may still receive an award if additional funding becomes available. Bulent Tosun had the opportunity to work closely with Eoin both as a student and through AMP in Mathematics. He is a truly remarkable scholar and an exceptional person, and this recognition is well deserved.

Congratulations to both Luke and Eoin on these significant achievements.

More information is available here:

UA students offered Fulbright awards for 2026-2027 The Fulbright Program selected 10 University of Alabama students for various awards for the 2026-2027 academic year.

We are pleased to announce that Aakash Gurung will present the results of his REU project. The title and abstract are included below.

Please join us for this presentation and support Aakash as he shares his research. We look forward to seeing you there.

Title: Measuring Flatness in Parabolic Geometry

Abstract : How can we tell whether a rough-looking set is secretly made out of nice geometric pieces? For example, what distinguishes the geometric “niceness” of a hexagon from the roughness of a Koch snowflake? A common strategy in geometric measure theory is to zoom in at many points and many scales and ask: does the set look almost flat?

We study the same question in a parabolic space-time geometry, where space and time scale differently. This changes what “flat” should mean: for parabolic hypersurfaces, the right flat models are vertical planes. We measure how flat a set looks by assigning, at each point and scale, a number that records its distance from the best-fitting vertical plane. These numbers are called parabolic beta numbers.

Our project studies a parabolic beta-number characterization of rectifiability. More precisely, we investigate when finiteness of the parabolic beta square function is equivalent to the ability to build a rough set, up to negligible error, from regular parabolic Lip(1,1/2) graph pieces. Toward the end, we briefly discuss how this fits into a broader program involving principal values and the Riesz transform.