Research

 

Current Research

My research area is algebraic representation theory and Lie theory, and I am particularly interested in the use of sheaf theory within this area.  More specifically, much of my work relates to the Springer Correspondence and perverse sheaves on the nilpotent cone.  My PhD advisor was Pramod Achar, and my current research mentor is William Graham.  I also have an ongoing collaboration with Laura Rider.

2014:

          March 21 - 23        AMS Sectional Meeting in Knoxville, TN

                                               Organized Special Session on Geometric and Combinatorial

                                               Methods in Representation Theory.

                                                  Co-organizer: William Graham


          May 16 - 17           Southeastern Lie Theory Workshop 2014 at UGA

                                               Local co-organizer with Dan Nakano and Andrew Talian


          May                       Representations of Reductive Groups:  A conference dedicated to

                                               David Vogan on his 60th birthday.


          September 20 - 21     AMS Sectional Meeting in Eau Claire, WI

                                                Spoke in Special Session on Analysis and Geometry on Lie

                                                Groups and

                                                Spoke in Special Session on Cohomology and Representation

                                                Theory of Groups and Related Structures



2013:

          April 13 - 14            AMS Sectional Meeting in Boulder, CO

                                                Spoke in Special Session on Geometric Methods in the

                                                Representation Theory of Reductive Groups


          May 10 - 12            Southeastern Lie Theory Workshop at LSU


          July 1 - 13               Atlas Workshop and Conference on Reductive Groups

                                                 University of Utah, Salt Lake City


          September 16 - 20  Summer School on Character Sheaves with Applications to

                                                 Representation Theory, Kaiserslautern, Germany


2012:

          January 3 - 8             Joint Mathematics Meeting, Boston, MA

                                                 Spoke in Special Session on Linear Algebraic Groups:

                                                 Their Arithmetic, Geometry, and Representations


          April 21 - 22             Southeastern Lie Theory Workshop at NC State


          September 22-23        AMS Sectional Meeting in Rochester, NY

                                                 Spoke in Special Session on Geometric, Categorical, and

                                                 Combinatorial Methods in Representation Theory



2011:

          January 5 - 9            AMS-MAA Joint Meeting in New Orleans, LA


          January 21               “Spaltenstein Day” at EPFL in Lausanne, Switzerland


          January 24 - 28        Chevalley Groups, Reflection Groups and Braid Groups in honor

                                                 of Jean Michel and François Digne in Les Houches, France

                                                 at Ecole du Physique


          February 12 - 13       Workshop on Lie Groups, Lie Algebras, and their

                                                 Representations at LSU    


          March 28 - April 1     HIM Workshop on the Interaction of Representation Theory with

                                                 Geometry and Combinatorics in Bonn, Germany


          June 1- 4                   Southeastern Lie Theory Workshop 2011 at UVA in

                                                 Charlottesville, VA


          October 22 - 23        AMS Western Sectional Meeting, University of Utah

                Talk:  “Graham’s Variety and Perverse Sheaves on the Nilpotent Cone”


2010:

          May 9 - 21                VIGRE Summer School at the University of Georgia on Lie and

                                                 Representation Theory


          May 22 - 24              Southeastern Lie Theory Workshop 2010 at the Univerisity of

                                                 Georgia

                 Contributed Talk: "Graham's Variety and Perverse Sheaves on the Nilpotent Cone"


          October 15 - 17        Southern Regional Algebra Conference, Univeristy of Louisiana

                                                 at Lafayette


2009:

          Jan 12 - Feb 20        Algebraic Lie Theory Program at the Isaac Newton Institute in

                                                 Cambridge, UK


          March 20 - 22          Southern Regional Algebra Conference 2009 in Mobile, AL


          May 27 - 31             Workshop on Geometry Related to the Langlands

                                                 Programme (Fields Institute) at University of Ottawa


          October 9 - 11         Southeastern Lie Theory Workshop 2009 at NC State in Raleigh


          October 24 - 27       Representation Theory and Mathematical Physics Conference in

                                                 honor of Greg Zuckerman at Yale University


2008:

          March 28 - 30          AMS Sectional Meeting at LSU in Baton Rouge, LA

Conferences Attended

    REUs:

            Summer 2004         Mississippi State University in Starkville, MS under R.

                                                  Shivaji in the area of Diffential Equations

            Summer 2005         James Madison University in Harrisonburg, VA under Jason

                                                  Rosenhouse in the area of Graph Theory

 

    Papers:            

            1.   D. Lanphier, C. Miller, J. Rosenhouse, and A. Russell, Expansion Properties of Levi Graphs, Ars Combinatoria, 80 (2006), 3 - 9.


            2.   Tammy Ladner, Anna Little, Ken Marks, Amber Russell, Positive Solutions to a Diffusive Logistic Equation with Constant Yield Harvesting, Rose-Hulman Undergraduate Math Journal (2005), ISSN Vol. 6, Issue 1, 2005 [php]

Undergraduate Research

Upcoming Conferences

Papers:

2015:

          January 10 - 13    Joint Mathematics Meeting, San Antonio, TX


William Graham and Amber Russell, Staggered Sheaves and K-Theory of Toric Varieties.

                In preparation.


Laura Rider and Amber Russell, Perverse Sheaves on the Nilpotent Cone and Lusztig’s

                Generalized Springer Correspondence.  Preprint.  arXiv:1409.7132


Amber Russell, Graham’s Variety and Perverse Sheaves on the NIlpotent Cone, In revision.

                arXiv:1111:2343

HIM, Bonn, Germany


Cologne, Germany




 

Newton Institute, Cambridge, UK


Mont Blanc, France


Les Houches, France


Königswinter, Germany

Schloss Drachenburg, Germany