I am interested in arithmetic geometry and algebraic number theory. As a PhD student, I studied abelian varieties under the supervision of Yuri Zarhin. More specifically, my thesis project concerned Jacobians of hyperelliptic curves defined over certain fields, and how the absolute Galois group acts on their points of prime power order. This has implications concerning the size of the endomorphism rings of such Jacobians. I am particularly interested in how results proven topologically for coverings of Riemann surfaces can be used to obtain arithmetic results in a purely algebraic setting.

Here are links to my publications and preprints:

Images of 2-adic representations associated to hyperelliptic Jacobians

(published in Journal of Number Theory 151: 7-17, 2015)

Dyadic Torsion of Elliptic Curves (published in

Dyadic Torsion of 2-Dimensional Hyperelliptic Jacobians (posted to ArXiv)

Boundedness results for 2-adic Galois images associated to hyperelliptic Jacobians

(posted to ArXiv

A note on 8-division fields of elliptic curves

(published in

Prime-to-

(posted to ArXiv)

An abelian subfield of the dyadic division field of a hyperelliptic Jacobian (posted to ArXiv and submitted, with minor edits, to Mathematica Slovaca)

And here is a link to my dissertation (minor edits have been made since officially submitting it):

Hyperelliptic Jacobians and their associated \ell-adic Galois representations

Here are some notes on various background topics which I wrote up just for fun:

Notes on Riemann's Existence Theorem -- proving the algebraic statement of RET from the analytic statement of RET, mostly following Volklein

Polarization of complex abelian varieties

Symplectic representations of braid groups

Explicit construction of hyperelliptic Jacobians

Semistable models of elliptic curves over residue characteristic 2 -- this describes an explicit and elementary algorithm I found for obtaining semistable models at 2, may be turned into a full article

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