J. L. Doob Research Assistant Professor

University of Illinois, Urbana-Champaign

I am currently a Postdoctoral Researcher at UIUC working with Sheldon Katz.
My research interests are Algebraic Geometry and Derived
Categories. In particular, I am interested in Bridgeland
stability conditions and connections to birational geometry and
physics. Previously I was a postgraduate student of Arend Bayer at
the University
of
Edinburgh.

I am on leave for the 2017-2018 academic year, and can be
contacted at rtramel@illinois.edu.

- Diagonal
splittings of toric varieties and unimodularity (with
Jed Chou, Milena Hering, Sam Payne, Ben Whitney), to appear in
*Proceedings of the AMS*. - Introduction to Bridgeland stability conditions - Notes for
the Superschool on Derived Categories and D-branes, to appear
in
*PIMS Industrial Proceedings*. - Bridgeland stability on surfaces with curves of negative self-intersection.
- The genus of projective curves on complete intersection surfaces.

- Enumerative Geometry, Mirror Symmetry, and Physics, July 2017
- I-70 Algebraic Geometry Symposium, November 2016
- Superschool on Derived Categories and D-branes, July 2016
- AMS Spring Sectionals, April 2016
- Summer Research Institute on Algebraic Geometry, June 2015
- Graduate Student Bootcamp, June 2015
- Geometry
from
Stability Conditions, February 2015

- BrAg, September 2014
- Introductory School on Derived Categories, September 2014
- Summer School on Derived Categories, June 2014
- Categorically Cardiff, October 2013
- MIT-RTG Mirror Symmetry Workshop, May 2013
- Characteristic p Methods in Algebraic Geometry, April 2013
- Graduate Student Workshop on Moduli Spaces and Bridgeland Stability, March 2013
- Homological Projective Duality and Non-Commutative Geometry, October 2012
- Young Mathematicians Conference, July 2012
- AGTP: School on Algebraic Geometry and Theoretical Physics, June 2012
- Georgia Algebraic Geometry Symposium, May 2012
- VIGRE Algebraic Geometry Summer School, May 2012
- AGNES, March 2012
- AGNES, October 2011

- Math 418: Abstract Algebra 2 (Spring 2017)
- Math 417: Abstract Algebra 1 (Fall 2016)
- Math 418: Abstract Algebra 2 (Spring 2016)

Students considering a graduate degree in Mathematics should
consider applying for an REU
program. These are opportunities to gain research
experience and to get paid doing it!

In 2012, I was a mentor at the University of Connecticut REU
under the supervision of Milena Hering. Our students presented
at the Young Mathematicians
Conference in Ohio, and wrote a paper (to appear
in *Proceedings of the AMS*) on their work.

Math students at UIUC can also gain research experience through
the Illinois
Geometry Lab.

- Battleship Game for Practicing Multiplication in Sn
- Symmetry Groups via the Orbit-Stabilizer Theorem (helpful to build models for this activity)
- RSA Encryption and Fermat's Little Theorem