Introduction

September 1, 2013

Welcome! I earned my Ph.D. in mathematics in August 2013 under the guidance of Milen Yakimov and am currently a mathematics lecturer at MIT.

Research

I mainly work with quantum groups---studying the ring theory and the representation theory of quantum Schubert cell algebras. The torus-invariant prime spectra of these noncommutative algebras relate to quantum cluster algebras, total positivity/negativity phenomena, Poisson geometry and Weyl group combinatorics, not to mention various structures from geometric representation theory. I am also interested in and am actively pursuing results regarding GKZ holonomic D-modules and cluster algebras arising from marked surfaces.

Papers and Preprints

J. Geiger and M. Yakimov, Quantum Schubert cells via representation theory and ring theory. To appear Michigan Math. J. arXiv:1203.3780v1

C. Bremer, J. Geiger, J.W. Hoffman, G. Muller, Variations of Hodge structure of toric hypersurfaces arising from root systems. In Preparation.

J. Geiger, K. Mahlburg G. Muller, D. Thurston, Superunital domains of cluster algebras. In Preparation.

Past and Upcoming Events (aka where you may have seen/will see me!)

Snowbird Resort, Utah, MRC Cluster Algebras Program,. June 8-14, 2014

Nankai University (Tianjin, China), To work towards results on l-adic GKZ hypergeometric (perverse) sheaves. December 18-31, 2013

Louisiana State University, 6th Southeastern Lie Theory Workshop Noncommutative Algebraic Geometry and Representation Theory , May 10-12, 2013

Northeastern, Algebra, Combinatorics and Representation Theory: in memory of Andrei Zelevinsky (1953-2013), April 24-28, 2013

MSRI Workshop (Berkeley, CA), Interactions between Noncommutative Algebra, Representation Theory, and Algebraic Geometry, April 8-12, 2013

Tulane University, AMS southeastern sectional meeting, October 13-14, 2012

Louisiana State University, Workshop on Lie groups, Lie algebras, and their representations, October 6-7, 2012

University of California Riverside, Algebraic and Combinatorial approaches to representation theory, May 18-20, 2012

North Carolina State University, Southeastern Lie Theory Workshop on Categorification of Quantum Groups and Representation Theory, April 21-22, 2012

International Workshop (Cortona, Italy), Toric Varieties in Cortona, July 18-29, 2011

Sabhal Mòr Ostaig (Isle of Skye, Scotland) New Developments in Noncommutative Algebra and its Applications, June 26 - July 2, 2011

University of Notre Dame, Mathematical Aspects of Quantization Conference, June 6-10, 2011

Louisiana State University, Workshop on Lie Groups, Lie Algebras and their Representations, February 12-13, 2011

2011 Joint Mathematics Meetings, January 6-9, 2011

AIM workshop Algebraic Systems with only Real Solutions, October 18-22, 2010

North Carolina State University, NSF/CBMS Regional Conference: Nakajima Lectures on Quiver Varieties and Quantum Affine Algebras, May 25-29, 2010

University of Georgia, Southeastern Lie Theory Conference: Homological Methods in Representation Theory, May 22-24, 2010

International Conference Bifurcation Theory, Integrable Systems, and the Bispectral Problem, May 15-19, 2010