I am Alex, a fourth year grad student at Boston University.
Previously I worked at TU Kaiserslautern (on the MPIR Library), and studied at the Universities of Cambridge and Warwick.

I am interested in many things, but mostly number theory and related topics right now. I would try to be more specific, but honestly there is just too much cool stuff out there.

My PhD supervisor is Jennifer Balakrishnan.

Here is a picture of me.

And below are some things you might actually have come here looking for.

If you want to send me an email, go ahead! Just replace the .github.io part of this web address with @gmail.com.

I am running the BUNTES learning seminar this semester: the topic is Abhyankar's conjecture.

Preprints:

- Square root time Coleman integration on superelliptic curves (abstract) (preprint)
- Elliptic curves with good reduction outside of the first six primes (with Benjamin Matschke) (abstract)
- Computing classical modular forms (with Jonathan Bober, Andrew R. Booker, Edgar Costa, John Cremona, Maarten Derickx, David Lowry-Duda, Min Lee, David Roe, Andrew V. Sutherland, and John Voight) (abstract) (arXiv)
- Two Recent p-adic Approaches Towards the (effective) Mordell Conjecture (with Jennifer Balakrishnan, Francesca Bianchi, Brian Lawrence, Steffen Müller, Nicholas Triantafillou and Jan Vonk) (abstract) (arXiv)

- Explicit Coleman Integration in Larger Characteristic (abstract) (arXiv) doi:10.2140/obs.2019.2.85
- Computing Zeta Functions of Cyclic Covers in Large Characteristic (with Vishal Arul, Edgar Costa, Richard Magner and Nicholas Triantafillou) (abstract) (arXiv) doi:10.2140/obs.2019.2.37

Notes from Céline Maistret's class, on *Ranks and Parity of Ranks of Curves and Abelian Surfaces*:

Web notes on Ranks and Parity of Ranks of Curves and Abelian Surfaces

Pdf notes on Ranks and Parity of Ranks of Curves and Abelian Surfaces

Notes from Ali Altuğ's class, on *Equidistribution in Number theory*:

Web notes on Equidistribution in Number theory

Pdf notes on Equidistribution in Number theory

Notes from Ali Altuğ's class on *Automorphic forms and the Arthur-Selberg trace formula*:

Web notes on Automorphic forms and the Arthur-Selberg trace formula

Pdf notes on Automorphic forms and the Arthur-Selberg trace formula

My Part III Essay on *Serre's conjecture*; supervised by Jack Thorne
(source on GitHub, comments welcome!)

For (some old) lecture notes see Mjolnir.

Current: None

Past:**MA225 Multivariable Calculus (BU Fall 2017) (TA)**

**MA123 Calculus 1 Section A2 (BU Summer 1 2017) (Lecturer)**

**EK102 Linear Algebra (BU Spring 2017) (TA)**

**MA121 Calculus I for Life and Social Scientists (BU Fall 2016) (TA)**

**CS137 Discrete Maths and its Applications 2 (Warwick 2014) (TA)**

Past:

Explicit computation with Coleman integrals, Journées Arithmétiques XXXI 2/7/19 (slides)

Explicit computation with Coleman integrals, Boston University - Keio University workshop 27/6/19 (slides)

Explicit Coleman Integration in Larger Characteristic, ANTS XIII UW-Madison 17/7/18 (paper above) (slides)

The Kodaira-Parshin construction, STAGE Fall 2018

Quaternion Algebras, and Descent and Canonical Models BUNTES Fall 2018

The (inescapable) p-adics, a lightning talk at the BU Math retreat (slides)

A Smörgåsbord of Dessins d'Enfants, and Dessins, integer points on elliptic curves and
a proof of the ABC conjecture BUNTES Spring 2018

The Tannakian formalism cannot hurt you STAGE Spring 2018

Various in BUNTES 2017 (Abelian varieties: Complex theory, Étale cohomology, the Rosati involution)

Ribet's converse to Herbrand's theorem: Cuspstruction, at STAGE Spring 2017, (notes on my blog: part I, part II)

Serre's Conjecture, at Ulm University Oberseminar (based on part III essay)

Singular Moduli, at Warwick Imperial Autumn Meeting 2014 & Cambridge Part III seminar series (slides)

Riemann Hypotheses, at Warwick Mathematics Society talks (slides)

Geometric approaches to solving Diophantine equations, at Tomorrow's Mathematicians Today 2013, (slides)