/CV

Primary LanguageTeX

Andrew Maurer

Contact Information

Education

Mathematics, PhD Candidate

  • University of Georgia, Athens Georgia
  • Advisor: Dr Daniel K Nakano
  • Research Area: Cohomology of Lie superalgebras.

Mathematics, Bachelor of Science. Computer Science, Minor.

  • University of Massachusetts, Amherst Massachusetts
  • Advisor: Dr Farshid Hajir
  • Senior Project: Hasse-Witt invariants of Jacobi Polynomials.

Research

Representations, cohomology, and geometry of Lie superalgebras

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.

Tropical geometry, algebra, and Grassmannians

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.

Talks Given

Cohomology, Support Varieties, and Lie Superalgebras

  • University of Colorado Boulder, Student Algebra Seminar
  • Spring 2016

Tropical Linear Spaces

  • UGA Tropical Geometry VRG
  • Fall 2015

The Tropical Grassmannian

  • UGA Tropical Geometry VRG
  • Fall 2015

Asymptotically Good Families

  • UGA Graduate Student Seminar
  • Spring 2015

Determinantal Complexity of the Permanent

  • UGA Student Algebraic Geometry Seminar
  • Spring 2015

Construction of the Grassmannian for Schubert Calculus

  • UGA Schubert Calculus VRG
  • Fall 2014

Computability with an Eye Towards Elliptic Curves

  • Elliptic Curves Discussion Section
  • Fall 2014

Conferences, Summer Schools, and Workshops Attended

Topological and Geometric Aspects of the Representation Theory of Finite Groups

  • Pacific Institute for the Mathematical Sciences
  • Summer 2016