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.
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 .
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.
Brief summary: Via a purely geometric approach, we give a counterexample to the Hasse principle on a degree 2 K3 surface over the rationals which arises from a 3-torsion transcendental Brauer class, thereby answering a question of Skorobogatov from 2014 in the affirmative. Although a degree 3 Azumaya algebra can always be written as a cyclic algebra, we do not need to write down such a representative to compute invariants.
In the summer of 2012 I worked as a teaching assistant at the Summer Program for Women in Math (SPWM) at George Washington University.
UNDER CONSTRUCTION. Below are some photos from some math-related travel, plus photos from my two main hobbies: baking and painting.