1. (with D. Batra, R. Khraishi) Conformal Predictions for Longitudinal Data, preprint (2023).
2. (with G. Cowan, R. Khraishi) Modelling customer lifetime value in the retail banking industry, preprint (2023).
3. (with R. Khraishi, R. Okhrati, D. Batra, C. Hamill, T. Ghasempour, A. Nowlan) An Introduction to Machine Unlearning, (2022).
4. Algebraicity of metaplectic L-functions, (arXiv link), J. Number Theory 219 (2021), 109-161.
5. (with T. Bouganis) On the Rankin–Selberg method for vector-valued Siegel modular forms, (arXiv link), Int. J. Number Theory 17 (2020), no. 5, 1207-1242.
6. p-adic L-functions on metaplectic groups (arXiv link), J. London Math. Soc., 102 (2020), 229-256.
7. The p-adic L-function for half-integral weight modular forms, manuscripta math., 161 (2020), 61-91.

• Proof assessment in STACK with Parsons problems, MERGE Seminar, University of Trieste, Italy (Mar. 2024).
• Proof assessment in STACK using SortableJS, International Meeting of the STACK Community 2024, OTH Amberg-Weiden, Amberg, Germany (Mar. 2024).
• Garrett’s conjecture for metaplectic Eisenstein series, Young Researchers in Algebraic Number Theory 2018, The University of Sheffield, UK (Nov. 2018).

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• International Meeting of the STACK Community 2024, OTH Amberg-Weiden, Amberg, Germany (Mar. 2024).
• Young Researchers in Algebraic Number Theory 2018, The University of Sheffield, UK (Nov. 2018).
• 32nd Automorphic Forms Workshop, Tufts University, Medford, Massachusetts, USA (Mar. 2018).
• Iwasawa 2017, The University of Tokyo, Tokyo, Japan (Jul. 2017).

STACK

STACK is open-source software that is used for automated digital assessment of mathematics within universities and schools globally. To get get started writing questions, install STACK and then use the author quick-start guide.

There are increasing ways to assess proof questions in STACK and my work so far has helped enable assessing proofs as drag-and-drop reordering questions through a parsons block. This was released in Dec. 2023 in STACK v4.5.0. See the documentation for how to write and assess these types of questions in STACK.

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Lean

The Lean theorem prover is an automated theorem prover that has grown rapidly as a tool for research and for education in both mathematics and AI. Mathlib is an open-source library for Lean containing a large and growing body of mathematical theory in Lean.

A great place to start learning is the Natural Number Game. After that, a good next step would be to install Lean and follow Imperial College London's "Formalising Mathematics 2024" course on GitHub, as well as reading Mathematics in Lean.

I have a GitHub repository formalising the proof of the local compactness of the adele ring of a number field here.

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FLINT

The images below and on the home page were made using the C library Arb, which is now part of FLINT (Fast Library for Number Theory). They show the complex plots of modular forms, including the half-integral weight Dedekind eta function, and other elliptic functions as well as L-functions. The images use colour to plot the phase of the output complex number of the function for each complex input, being forgetful of magnitude.

As well as facilitating the production of high resolution images of intricate complex objects through the use of ball arithmetic, FLINT has been used for computational research purposes such as the highest-known (as of January 2024) verification of the Riemann Hypothesis, Dave Platt & Tim Trudgian (2020).

Member of the STACK Professionals Network, University of Edinburgh/IDEMS International

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