# Introduction

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.

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.

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.

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.

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