- Department of Mathematics
Boyd Graduate Research Studies
University of Georgia
Athens, Georgia 30602 - andrew.b.maurer@gmail.com
- andrewmaurer.github.io
- University of Georgia, Athens Georgia
- Advisor: Dr Daniel K Nakano
- Research Area: Cohomology of Lie superalgebras.
- University of Massachusetts, Amherst Massachusetts
- Advisor: Dr Farshid Hajir
- Senior Project: Hasse-Witt invariants of Jacobi Polynomials.
I am studying the relative cohomology ring of a Lie superalgebra relative to a reductive even subalgebra. I conjecture that this relative cohomology ring is finitely generated, which I hope can be showed via a spectral sequence argument. Once this is established I will investigate the natural mappings of support varieties in the spirit of Friedlander and Parshall's "Support varieties for restricted Lie algebras."
This research relies heavily on work by Benson, Boe, Carlson, Friedlander, Gruson, Hochschild, Kujawa, Nakano, Parshall, and Serre.
The Grassmannian is often identified with the image of the Plucker embedding into projective space. This variety is isomorphic to the GIT quotient of the space of d x n matrices by the natural action of GL(d). There has been much interest in defining tropical analogues of the Grassmannian, with several constructions due to Speyer and Sturmfels. With Dr Noah Giansiracusa, I have been working on an analogue that mimics the GIT construction. We have discovered many interesting similarities, and many interesting differences when compared to the classical theory.
This research relies heavily on work by Fink, G Giansiracusa, N Giansiracusa, Rincon, Speyer, and Sturmfels.
- University of Colorado Boulder, Student Algebra Seminar
- Spring 2016
- UGA Tropical Geometry VRG
- Fall 2015
- UGA Tropical Geometry VRG
- Fall 2015
- UGA Graduate Student Seminar
- Spring 2015
- UGA Student Algebraic Geometry Seminar
- Spring 2015
- UGA Schubert Calculus VRG
- Fall 2014
- Elliptic Curves Discussion Section
- Fall 2014
- Pacific Institute for the Mathematical Sciences
- Summer 2016