# Research

I graduated from the University of Wisconsin, working under the direction of Tonghai Yang, in 2011. I am now a Ritt Assistant Professor at Columbia University. My research interests include various aspects of number theory and representation theory. I like when results and techniques from the latter can be used to prove things about the former.

## Publications and Preprints

Appendix to "The Quantum Variance of the Modular Surface" by Peter Sarnak and Peng Zhao

(with G. Savin) Matching of Hecke operators for Exceptional dual pair correspondences Journal of Number Theory 146 (2015)

"Trilinear forms and subconvexity of the tiple product L-function" (Submitted) This version (new as of 4/6/2012) has been somewhat modified from prior versions. The main differences are that a more elaborate explanation of Ichino's result is given, and the proof of Theorem 5.1 (which was previously called Theorem 4.7) has been amended.

(with G. Savin) "Structure of internal modules and a formula for the spherical vector of minimal representations" Journal of Algebra 312 (2007)

## Notes

### Conferences

Instructional Conference on Representation Theory and Arithmetic at Northwestern

School on Equidistribution of Finite Volume Orbits on Homogeneous Spaces at Mathematisches Forshungsinstitut, Oberwolfach

### Talks

Slides from talk given at joint meetings of American and Korean Mathematical Societies

### Other

Notes taken on lectures given by Dick Gross on Representation theory and number theory at Columbia University Fall 2011.

Notes taken with Rob Rhoades on automorphic forms on GL(2) based on class taught by Yannan Qiu.

Notes on class on Gross-Zagier formula taught by Tonghai Yang.

Notes on class on elliptic curves and modular forms taught by Jordan Ellenberg.

Notes on relation between classical and adelic Eisenstein series

Notes on invariant pairing between a representation and its contragradient

Quadratic extensions of a local field