# Arshay Sheth

## About me

I am a second year PhD student working under the supervision of Prof. David Loeffler and a member of the Number Theory Group at the University of Warwick. I am especially interested in topics such as special values of L-functions, Euler systems, p-adic variation of automorphic forms, and explicit class field theory.

I completed my undergraduate studies at the National University of Singapore and my masters studies at Leiden University and the University of Regensburg as part of the ALGANT program.

## Contact Details

Email address: arshay.sheth@warwick.ac.uk

## Publications

*A statistical comparison of flood-related economic damage in Indian states with reflections on policy implications*(published version) (pdf) (joint with P. Bansal, J. Chuah, S. Das and R. Wasson), International Journal of Disaster-Risk Reduction, Volume 72, April 2022.

## Teaching

- 2022/2023 Term 1: Teaching assistant for MA3A6 Algebraic Number Theory and MA4L6 Analytic Number Theory.
- 2021/2022 Term 2: Teaching assistant for MA257 Introduction to Number Theory .
- 2021/2022 Term 1: Teaching assistant for MA3A6 Algebraic Number Theory.

## Talks in research seminars and conferences

*p-adic variation of the Asai-Flach Euler system,*Number Theory seminar, Indian Institute of Science, Bengaluru, India, 17th August 2022.*p-adic variation of the Asai-Flach Euler system,*Summer school on Motives and Arithmetic Groups, Strasbourg, France, 13th June 2022.

## Writings

Theses:

- Masters thesis: The Brumer-Stark Conjecture
- Undergraduate thesis: Local Class Field Theory

Expository articles:

Notes/slides for talks in learning seminars/ study groups:

- Etale cohomology and the Weil conjectures: A survey for a study group on Hasse-Weil zeta functions.
- A Historical Introduction to Transcendental Number Theory for a talk in the Warwick Postgraduate seminar.
- Heegner Points for a study group on CM theory and RM theory.
- The Absolute Galois Group of C(t) for a learning seminar on Galois Groups and Fundamental Groups.
- Transformation formulae and Theta Relations for a learning seminar on Theta functions, complex abelian varieties and their moduli spaces.
- The Atiyah-Janich Theorem for a learning seminar on Topological K-theory .
- The Commutativity Theorem and Segre & Chern classes of vector bundles for a learning seminar on intersection theory.
- Simply Connected Lie Groups & the Exponential Map and Representations of sl(2,C) for a learning seminar on Lie theory.
- Orientation & Integration and Stokes' theorem for a learning seminar on de Rham cohomology