Photo by Cameron Franc

Jenna Rajchgot Postdoc Assistant Professor University of Michigan, Ann Arbor Email: rajchgot [at] umich [dot] edu Office: 1834 East Hall

I am a Postdoc Assistant Professor at the University of Michigan in Ann Arbor, supervised by Karen Smith. In the Fall of 2012, I was a research member at the Mathematical Sciences Research Institute in Berkeley, CA. I completed my Ph.D. at Cornell University under the supervision of Allen Knutson.

You can find out about my research, teaching, and other mathematical activities below.

Research

Broadly speaking, my research interests lie at the intersection of algebraic geometry, combinatorics, and commutative algebra. For example, I use torus actions and/or degenerations to study certain algebraic varieties using combinatorial techniques. Specific topics that I've been thinking about include Frobenius splitting and Hilbert schemes of points (usually in the plane).

Thesis:

The title of my thesis is Compatibly split subvarieties of the Hilbert scheme of points in the plane. The document can be found here.

[Brief summary: We explicitly describe all compatibly split subvarieties of the Hilbert scheme of n points in the plane for small values of n, and we provide some partial results for arbitrary n. We then restrict to a specific affine open patch (for arbitrary n) and find all compatibly split subvarieties, their defining ideals, and Gröbner degenerations to Stanley-Reisner schemes. The associated simplicial complexes are used to prove that certain compatibly split subvarieties of this open patch are Cohen-Macaulay.
Also included is some background material on the Hilbert scheme of points in the plane, Frobenius splitting, moment polyhedra (in the algebraic setting), and Gröbner bases/degenerations.]

Slides for a talk based on my thesis can be found here.

Teaching (at Michigan)

This semester I'm teaching Math 214. The course webpage is here.

Past teaching (at Cornell):

Activities

Conferences and Workshops:

• Schubert Calculus Summer School. Osaka City University, Osaka, Japan. July 17-20, 2012.
• CMS Winter Meeting. Toronto, Ontario, December 10-12, 2011
• AGNES. Stony Brook, October 28-30, 2011
• Route 81. Cornell University, September 24, 2011
• Cluster Algebras and Lusztig's Semicanonical Basis. University of Oregon, June 2011.
• Southern Ontario Groups and Geometry. Fields Institute, April 2011.
• Route 81. Syracuse University, October 2010.
• Frobenius Splitting. University of Michigan, Ann Arbor, May 2010.
• Southern Ontario Groups and Geometry. Fields Institute, October 2009.
• Workshop in Geometric Representation Theory and Extended Affine Lie Algebras. University of Ottawa, June 2009.

Past and Future Visits:

• Algebra and Number Theory Seminar. UC Santa Cruz, March 13, 2012.
• Algebra-Geometry-Combinatorics Seminar. UIUC, January 31, 2012.
• Commutative Algebra Seminar. University of Michigan, January 12, 2012.

Other

"A Exam":

I took my "A-exam" in June 2010. As part of it, I gave a presentation on the Hilbert scheme of points in the affine plane. These slides are far from comprehensive but they may be helpful for someone with minimal knowledge of the subject. For better, more complete treatments, see some of the references listed on the last slide.

Cornell Numb3rs project:

If you know (or you are!) an elementary or high school student who is interested in math and enjoys watching television, you may be interested in the Cornell Numb3rs project. On these webpages, the mathematical ideas that appear in the episodes are explained and activities for students are suggested. (Many of the math graduate students at Cornell took part in this project. I was responsible for episodes 505 through 508.)