Jen Berg

About

I am currently an RTG Lovett Instructor at Rice University. I received my PhD in 2016 at the University of Texas at Austin and my B.S. at UIUC in 2010. I grew up in Chicago, IL. These days, my main interests outside of math include cooking/baking, painting, attending concerts, reading, playing board games, various additional arts & crafts projects, and bouldering.

Research

I am interested in algebraic number theory and arithmetic geometry. In particular, I work on obstructions to the Hasse principle. My current projects involve studying Brauer-Manin obstructions to integral and rational points on certain families of surfaces and higher dimensional varieties. My thesis advisor was Felipe Voloch. My postdoc mentor is Tony Várilly-Alvarado .

Upcoming and Recent Travel

  • May 27 - June 1, 2018. Rational and Integral Points Via Analytic and Geometric Methods. CMO, Oaxaca, Mexico.
  • November 15, 2017. BC NG & AT Seminar . Boston College, Boston, MA.
  • September 29 - Oct. 1, 2017. Open Source Computation and Algebraic Surfaces. BIRS. Banff, AB, Canada.
  • September 9-10, 2017. AMS Fall Central Sectional Meeting. Denton, TX.
  • July 2-8, 2017. Rational Points 2017. Schney, Germany.
  • June 1-3, 2017. Re:boot Number Theory 2017. Durham, NC.
  • May 15-19, 2017. ECHORAP. Emory University, Atlanta, GA.
  • April 28-30, 2017. Atkin Memorial Lectures. UIC, Chicago, IL.
  • April 21-23, 2017. TAGS (Texas Algebraic Geometry Symposium). Rice University, Houston, TX.
  • April 8-9, 2017. AWM Research Symposium. Los Angeles, CA.

Publications

  1. Insufficiency of the Brauer-Manin Obstruction for Rational Points on Enriques Surfaces, with F. Balestrieri, M. Manes, J. Park, and B. Viray. Directions in Number Theory, September, 2016.
  2. Congruences for Ramanujan's f and Omega Functions Via Generalized Borcherds Products,with A. Castillo, R. Grizzard, V. Kala, R. Moy, C. Wang. The Ramanujan Journal, August 2013.
  3. p-groups Have Unbounded Realization Multiplicity, with Andrew Schultz. Proceedings of the American Mathematical Society, August 2012.

In Preparation

  1. Obstructions to the integral Hasse principal for generalized affine Chatelet surfaces
  2. Summary: We enumerate the possible Brauer groups that can occur for affine varieties of the form x^2 - ay^2 = c P(t) under mild conditions on the Galois group of the polynomial P(t). In the case when P(t) is dihedral of degree n, the Brauer groups are cyclic of order n, generated by a non-cyclic algebra. We construct an explicit representative for the generator of the Brauer group, and provide an algorithm for computing the Brauer Manin set. In particular, we address the curious examples of the varieties x^2 + y^2 + t^4 = m for m =22,43,67,70,78,93... which have points over the rationals, points over the p-adic integers for all p, but no integral points. We prove that the failure of existence of integral points cannot be explained by a Brauer-Manin obstruction.

In Progress

  1. Transcendental 3-torsion on degree 2 K3 surfaces arising from special cubic fourfolds

Conferences Organized

  • RTG Lectures in Arithmetic Geometry at Rice (with Anastassia Etropolski and Anthony Várilly-Alvarado)

Contact

  • Office: Herman Brown Hall (HBH) 408
  • Office Hours: TBA. Or by appointment
  • Email: jb93 [at] rice [dot] edu

Teaching

This Semester

At Rice

  • Spring 2017: Math 306, Math 499
  • Fall 2016: Math 101, Math 499

At UT Austin

  • Fall 2015: Learning Assistant and Calc Lab coordinator.
  • Spring 2014: Won Natural Sciences Council TA Award!
  • Spring 2014: Graded Prelim Algebra M380D for Felipe Voloch.
  • Fall 2013: SI for M408N for Prof. Anna Spice.
  • Spring 2013: M408C for Prof. John Dollard
  • Fall 2012: M305G for Dr. Amanda Hager, Graded for M373K for Sean Keel
  • Spring 2012: M408D for Prof. Ray Heitmann
  • Fall 2011: M408C for Prof. Kathy Davis
  • Spring 2011: On departmental fellowship.
  • Fall 2010: M408K for Dr. Elif Seckin

In the summer of 2012 I worked as a teaching assistant at the Summer Program for Women in Math (SPWM) at George Washington University. If you are an undergraduate woman interested in math, check it out!

Photos

UNDER CONSTRUCTION. Below are some photos from some math-related travel, plus photos from my two main hobbies: baking and painting.