Contact Information:

Phone: (540) 231-1649 FAX: (540) 231-2606 Office: VBI 245-15 Hours: by appt. Address: Virginia Bioinformatics Institute Washington Street, MC 0477 Virginia Tech Blacksburg, VA 24061

Professional:

• Curriculum Vitae
• Research Statement (or just the summary page)
• Teaching Statement (or the extended version)
• An extended abstract of my thesis project

Teaching:

• Math Emporium (Fall 2011)
  I'm on the floor this semester, so come by with any questions related to Emporium classes.
• Private tutoring
  I'm available to tutor freshman- through graduate-level courses. Some restrictions apply. My default rate is $20/hour but this is negotiable. I am glad to work with groups of n students at a per-student rate of $(2 + 27·(²⁄₃)ⁿ)/hour.

Research:

• Matrix Schubert varieties for the affine Grassmannian (Extended Abstract; Advisor: Mark Shimozono)
  The goal of my thesis project is to obtain an explicit combinatorial formula for a polynomial homology class of an affine Schubert variety. We begin with an embedding of the affine Grassmannian into the infinite Grassmannian, which restricts to an embedding of an affine Schubert variety into a finite Grassmannian. We borrow a lift-and-close procedure to produce a matrix variety, reformulating the problem in equivariant cohomology. The monomials of the cohomology class may be read off RC–like diagrams which suggest an expansion into Stanley symmetric functions. Several low-order calculations support the conjecture, based on the fact that k-Schur functions describe the Schubert basis for the affine Grassmannian, that the corresponding polynomial homology class is a k-Schur function.
• Modeling and Simulation in Systems Biology (Supervisor: Reinhard Laubenbacher)
  A motivated and highly collaborative team of undergrads and i performed a longitudinal study of the Mathematical Reviews publishing database, beginning with a suite of statistical and graph-theoretic metrics taken across a sliding window. We identified and described stark differences among subcommunities of researchers within mathematics (for instance the "pure" and "applied" communities) and two major structural shifts in the evolution of the research network. Our first paper is submitted and our second is in preparation.

Affiliations:

• Applied Discrete Mathematics Group
  My research has been professionally and emotionally supported by our research team at VBI.
• Focused Research Group: Affine Schubert Calculus
  My research was partially supported by an NSF grant for this FRG, my advisor being a principal researcher. I am grateful to the NSF for funding my Summer Research Assistantships and travel to several conferences.
• SIAM Student Chapter
  The Student Chapter hosts semiregular talks by local and visiting speakers. Corollary: SIAM
• Math Club
  I was Graduate Representative for several years.
• AMS
  The Notices and the Bulletin are available for electronic subscription.

Gatherings:

• Complex Networks: Dynamics on Networks (SAMSI)
• 21th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC) (RISC)
• Summer School and Conference in Geometric Representation Theory and Extended Affine Lie Algebras (U Ottawa)
• Graduate Student Combinatorics Conference 2009 (U Kentucky)
• Combinatorial, Enumerative and Toric Geometry (MSRI)
• 20th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC) (Viña del Mar, Chile)
• Workshop on Representation Theory, Geometry and Combinatorics (UC Berkeley)
• Topics In Combinatorial Representation Theory (MSRI)

Papers:

• "Matrix Schubert Varieties for the Affine Grassmannian" (with Mark Shimozono), in preparation.
• "More Names for (7,3,1)" (with Bud Brown), in preparation.
• "Evolutionary Events in the Mathematics Research Collaboration Network" (with Reinhard Laubenbacher et al), submitted.
• "Fibonacci's Forgotten Number" (with Bud Brown), College Mathematics Journal 39 (March 2008), 112–120.
• "On Projective Planes & Rational Identities" (advisor: Dan Farkas), Master's Thesis (2005).
• "Reaction-Controlled Diffusion: Monte Carlo Simulations" (with Beth Reid and Uwe Täuber), Physical Review E 68, 046121 (2003), 1–19.