Jaclyn Lang
E-mail: jaclyn[dot]lang[at]maths[dot]ox[dot]ac[dot]uk
Office: N3.14
Address: Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
OX2 6GG
Oxford
United Kingdom
I am currently a Titchmarsh Research Fellow at the University of Oxford. Starting in Fall 2021 I will be an assistant professor at Temple University in Philadelphia. Previously, I was an NSF postdoc at Université Paris 13 with Jacques Tilouine and a postdoc at the Max Plank Institute for Mathematics. I finished my Ph.D. at UCLA in 2016 under the supervision of Haruzo Hida. I am interested in algebraic number theory, especially Galois representations, modular forms, elliptic curves, and motives. You can find a copy of my CV here.
Publications and Preprints
- Big images of two-dimensional pseudorepresentations, (pdf; arXiv; Oberwolfach report; slides)
With A. Conti, A. Medvedovsky
- A inf is infinite dimensional, (published version; arXiv)
With J. Ludwig
- Chow motives associated to certain algebraic Hecke characters, Transactions of the American Mathematical Society, Series B. Vol. 5, (2018) 102--124. (published version; arXiv)
With L. Flapan
- On the image of the Galois representation associated to a non-CM Hida family, Algebra and Number Theory, Vol. 10, No. 1 (2016) 155-194. (published version; arXiv; slides; poster)
- Shadow lines in the arithmetic of elliptic curves, Directions in number theory; Assoc. Women in Math. Ser., 3, Springer, (2016), 33-55. (published version; arXiv)
With J. Balakrishnan, M. Çiperiani, B. Mirza, R. Newton
- Function fields with class number indivisible by a prime l, Acta Arithmetica, Vol. 150 (2011), 339-359. (published version; arXiv)
With M. Daub, M. Merling, A. Pacelli, N. Pitiwan, M. Rosen
Funding I've received
Math programs I have participated in:
- *Women in Numbers -- Europe: 3 2019
Project Group: Local fields and Galois groups with Ramla Abdellatif, Agnès David, Supriya Pisolkar, Beth Romano, Marine Rougnant, Lara Thomas, and Hanneke Wiersema
- MSRI Graduate Summer School 2017; Automorphic forms and the Langlands program
Teaching assistant; (unofficial website)
- CRM Graduate Summer School 2014, Counting Arithmetic Objects
- *Women in Numbers: 3 2014
Project Group: Shadow Lines with Jennifer Balakrishnan, Mirela Çiperiani, Bahare Mirza, and Rachel Newton
- MSRI Graduate Summer School 2013, New Geometric Techniques in Number Theory
- Arizona Winter School 2013, 2014
- Program in Mathematics for Young Scientists (PROMYS) I was a counselor in 2010.
- Part III of the Mathematical Tripos at the University of Cambridge. While doing Part III, I was a student at Churchill College. 2009-2010
- Park City Mathematics Institute 2009
- *Institute for Advanced Study Program for Women in Mathematics 2008
- *Nebraska Conference for Undergraduate Women in Mathematics 2008
- SMALL REU I was a participant in 2008. I worked with Allison Pacelli on a problem in algebraic number theory. Our paper can be found above.
- *Summer Program for Women in Mathematics (SPWM) I was a participant in 2007 and a teaching assistant in 2012.
*Program specifically for women
Other writings
Here are majors papers I've written for various degrees. I provide them mainly as samples for current students in similar programs.
- Images of Galois representations associated to p-adic families of modular forms, PhD dissertation at UCLA (June 2016); under the supervision of Haruzo Hida
- Two-Descent on the Jacobians of Hyperelliptic Curves, Part III essay at the University of Cambridge (April 2010); under the supervision of T. Fischer
- Properties of Class Groups of a Family of Cyclic Cubic Fields, thesis for MA at Bryn Mawr College (May 2009); under the supervision of H. G. Grundman
Resources for undergraduate and high school students
- Here is a list of lots of cool opportunities for undergraduates to study math. Disclaimer: I wrote this shortly after I was an undergrad and so some of the programs may no longer exist.
- When I was a PROMYS counselor, I gave a lecture for high school students about p-adics. Here are the notes for that.
- I gave a talk about absolute values and p-adic numbers to the high school group of the Los Angeles Math Circle. Here are the worksheets associated with that. This is related to the above set of notes.
Website last updated: 17 December 2020