# Melissa Emory: Assistant Professor

## Department of Mathmatics

Home Page of the Math DepartmentI am a faculty adviser for the Oklahoma State University Chapter of The Association for Women in Mathematics

### Contact info

Office : MSCS 526

Office hours: Office hours M 2:30-3:30PM at the MLSC, W 10:30-11:30PM in MSCS 526, F 10:30-11:30 MSCS 526, or by appointment

Email: melissa.emory@okstate.edu

Please reach out if you are interested in joining my research group

### Teaching

Fall 2023: MATH 2153 Calculus II and MATH 4713 Number Theory and MATH 2890 Honors Topics in Calculus II

Spring 2023: Math 4453/5453 Mathematical Interest Theory

### Research

My research interests include automorphic forms and representations, number theory, and representation theory. My thesis work combined with [3] below formulated a global Gan-Gross-Prasad conjecture for general spin groups and verified the conjecture for the first three cases. Beyond Endoscopy is a strategy proposed by Langlands to prove the principle of functoriality. A first step in the strategy was achieved by Ali Altug who worked over the rationals. I am currently working on a project (joint with M.Espinosa-Lara, D. Kundu and T. Wong) to generalize Altug's work to an arbitrary number field. I am also currently working on the endoscopic classification of representations for the general Spin group (joint with S. Takeda). I then plan on formulating and proving a local GGP conjecture for general Spin groups. My work on Sato-Tate distributions for higher genus curves is also continuing (joint with H. Goodson).

Publications and Preprints

6. Contragredients and a multiplicity one theorem for general Spin groups with S. Takeda, Math Ziet (2023). Preprint arXiv:2104.04814

5. Sato-Tate distributions of y^2=x^p-1 and y^2=x^{2p}-1 with H. Goodson, J. Algebra (2022).Preprint arXiv:2004.10583

4. On Sato-Tate groups of trinomial hyperelliptic curves with H. Goodson and A. Peyrot , International Journal of Number Theory (April 2021), 2175-2206. Preprint arXiv:1812.00242

3. On the global Gan-Gross-Prasad conjecture for general spin groups, Pacific Journal of Mathematics 306-1 (2020), 115--151. Preprint arXiv:1901.01746

1. The Diophantine equation x^4+y^4=D^2z^4 in quadratic fields, Integers 12 (2012), article A65

### About me

I am an Assistant Professor at Oklahoma State University. Previously I was a NSF Postdoctoral Fellow at the University of Toronto with mentor James Arthur. I earned my PhD from the University of Missouri in 2018 with advisor Shuichiro Takeda.

My Vita