We congratulate the undergraduates below, each of whom has obtained support to perform research mentored by a Math Department faculty member this summer. We are pleased to be able to support several of these talented students with Painter Fellowships, which are principally funded by a generous endowment from the Painter family. Each supported researcher is listed below with a short description of his or her project.

Sam Brunacini (mentor Jason DeBlois) is working in hyperbolic geometry, coding a program to construct Escher-like “circle limit” tilings of the Poincare disk, with prescribed combinatorics and using any given starting image. Sam is supported by a Painter Fellowship.

Neil Maclachlan (mentor Bard Ermentrout) is working in mathematical neuroscience, using numerical simulations with coupled ODE to study the dynamics of the activity of excitatory and inhibitory neurons arranged in a two-dimensional grid. Neil is supported by the TECBio REU hosted by the Pitt School of Medicine’s Department of Computational and Systems Biology.

Ryder Pham (mentor Carl Wang-Erickson) is working in number theory, studying 7-torsion in the class group of integer quadratic forms using elliptic curves and the Birch and Swinnerton-Dyer conjecture. Ryder is supported by a SURA (Summer Undergraduate Research Award) from Pitt’s Office of Undergraduate Research.

David Philips (mentor Thomas Gilton) is working in mathematical logic, applying the compactness theorem to first order logic and the Peano axioms. David is supported by a Painter Fellowship.

Sasha Sluis-Cremer and Lark Song (mentor Tom Hales) are working in discrete geometry, proving their conjecture for the densest packing of specific convex shapes, using an optimal control approach that Dr. Hales developed to attack the Reinhardt conjecture. Sasha is supported by a Brackenridge Fellowship sponsored by the Frederick Honors College, while Lark is supported by a Painter Fellowship.

Freddy Tang (mentor Juan Manfredi) is working on partial differential equations on graphs of $p$-Laplacian type, which are used in the mathematical theory of semi-supervised learning. Freddy is looking in detail to the case of directed trees. He is supported by a Painter Fellowship.

Annie Wang (mentor Catalin Trenchea) is working in fluid dynamics, using the Navier-Stokes and transport equations to model the convective motion of microorganisms suspended in water. Annie is supported by a Painter Fellowship.

Jen Wang (mentor Jeffrey Wheeler) is working in combinatorics and optimization, on problems related to the max-flow min-cut theorem for flow networks. Jen is supported by a Painter Fellowship.

We also congratulate Adam Hicks, a Mathematics and Economics double major, for receiving a Brackenridge Fellowship for his project titled “Sea Level Rise and the UK

Housing Market”. The entire list of Brackenridge Fellows can be found here:

https://www.pitt.edu/pittwire/features-articles/brackenridge-fellows-2023-undergraduate-research