Algebra Group
Lenny Chastkofsky
Faculty: Brian Boe and Dan Nakano
Graduate students: Bobbe Cooper, Kenyon Platt, Wenjing Li, Carrie Wright, Irfan Bagci, Ben Connell, Jae-Ho Shin
Post-Doc: Ben Jones
We will be studying Cohomology of Lie Algebras in characteristic p. Kostant's Theorem gives a description of the cohomology in characteristic 0. Previously, the group had come up with a new proof that the cohomology is the same as in characteristic 0 for large enough primes, and that there is always extra cohomology for small enough primes. By using Magma to compute many examples, the group is close to coming up with a conjecture as to precisely when these exceptions occur. We will work on refining this conjecture, and think of how we might prove it.
Algebraic Geometry Group
Elham Izadi Graduate Students: Maxim Arap, Tyler Kelly, Lev Konstantinovskyi, Al Lapointe, Jeremy Praissman, Lucius Schoenbaum, Benjamin Wyser
Undergraduates: Kyle Istvan and Jasmine Mathis
The group is investigating properties of Fano varieties of linear spaces in various hypersurfaces.
Circle Packing Group
Faculty: Will Kazez and Malcolm Adams
Graduate Students: Jennifer Belton, Xiaoyan Hu, Yang Liu, Matt Mastin, Whitney Montgomery
Undergraduate students: Nona Dowling,Casey Murphy, Meredith Perrie, Josh Wood.
Circle Packing VIGRE group will be first studying the Koebe-Andreev-Thurston Theorem. We will start with some basic facts about Circle Packing and constant curvature geometries in dimension two. We will then learn some foundational tools in the field, basic examples and explore applications and further research directions.
Tropical Geometry Group
Faculty: Dino Lorenzini, Gordana Matic, Robert Varley
Graduate students: Michael Berglund, Lev Konstantinovskiy, Maxim Arap, Kevin Kennedy, Leopold Matamba, Jennifer Muskovin, Brandon Samples, Kate Thompson, Maury LeBlanc
Undergraduate: Eric Cho(not for credit), Joe Brown
The aim of the group is to study this new and rapidly developing and its applications in the fields of interest to the participants: algebraic geometry, arithmetic geometry, topology, mathematical physics, quantum theory. We also aim to work on a circle of problems related to curves and to moduli spaces, motivated by several open problems in classical algebraic geometry and number theory.