Arun Soor’s Webpage

I am a DPhil (Maths) student at in the Mathematical Institute, University of Oxford.

My supervisor is Prof. Konstantin Ardakov. I am interested in representations arising from the cohomology of modular curves, and using geometric representation theory to understand them.

I did my BA and MMath at Oxford. My part C dissertation “Crystal Graphs and the representation theory of the symmetric group” was supervised by Prof. Kevin McGerty.

Preprints

• A. Soor. Quasicoherent sheaves for dagger analytic geometry, 2023. arXiv:2311.03101.

Publications

• T. Assiotis, B. Bedert, M. A. Gunes, and A. Soor. Moments of generalized Cauchy random matrices and continuous-Hahn polynomials. Nonlinearity, 34(7):4923–4943, 2021. arXiv:2009.04752.

• T. Assiotis, B. Bedert, M. A. Gunes, and A. Soor. On a distinguished family of random variables and Painlevé equations. Probability and Mathematical Physics, 2:613–642, 2022. arXiv:2009.04760.

• T. Assiotis, M. A. Gunes, and A. Soor. Convergence and an explicit formula for the joint moments of the circular Jacobi β-ensemble characteristic polynomial. Mathematical Physics Analysis and Geometry, 2021. arXiv:2110.05406.

• P. Velvaluri, A. Soor, P. Plucinsky, R. Lima de Miranda, R. D. James, and E. Quandt. Origami-inspired thin-film shape memory alloy devices. Scientific Reports, 11(1):10988, 2021.

News Articles

• H. Liu, P. Plucinsky, F. Feng, A. Soor, and R. D. James. Origami and the structure of materials. SIAM news January/February 2022.

Seminars

• In the academic year 2023-2024, I am co-organizing the Oxford Junior Number Theory Seminar, together with James Taylor and Zachary Feng.

Study group talks, etc. (Use notes at your own risk).

• ”(\varphi, \Gamma)-modules”. Montreal functor study group, Oxford (March 2024). Notes.

• “Galois representation associated to a weight 2 modular form”. Global reciprocity study group, Oxford (March 2024). Notes.

• “Some perspectives on differential operators”. Geometric Langlands study group, Oxford (May 2023). Notes.

• “Localisation of locally analytic representations”. Oxford junior algebra (February 2023).

• “Period morphism and tower”. Rapoport-Zink spaces study group, Oxford (February 2023). Notes.

• “Divisors on Y/φ^ℤ”. Fargues-Fontaine curve study group, Oxford (November 2022).

• “Eichler-Shimura isomorphism”. Galois representations and modularity reading group, Oxford (November 2022). Notes.

• I gave a series of talks about locally analytic vectors of completed cohomology from May-June 2022. Notes.

• “Joint moments of characteristic polynomials of random unitary matrices”, Oxford junior number theory (March 2022). Slides.

• “Weil groups, Weil-Deligne representations and class field theory”. Langlands reading group, Oxford (February 2022).

• “Hodge-Tate representations”. p-adic Hodge theory reading group, Oxford (February 2022). Notes.

• “Origami with conformal and helical symmetry”, a 20-minute talk I gave at the SIAM MS21 conference (May 2021). Slides.

Teaching

Lecturer II, Magdalen college

• HT24: College tutorials (Magdalen) for A5 Topology, Prelims Dynamics. Tutor for C2.6 Introduction to Schemes.
• MT24: College tutorials (Magdalen) for A2 Metric Spaces & Complex Analysis, Prelims Geometry
• TT23: College tutorials (Magdalen) for ASO Group theory, ASO Multidimensional Analysis, Prelims Constructive Mathematics
• HT23: College tutorials (Magdalen) for A5 Topology, Prelims Dynamics. Tutor for C2.6 Introduction to Schemes.
• MT22: College tutorials (Magdalen) for A2 Metric spaces & Complex analysis. TA for C3.6 Modular Forms, TA for B3.1 Galois Theory.
• TT22: College tutorials (Magdalen) for ASO number theory, revision classes for A2 Metric Spaces & Complex Analysis
• HT22: TA for B3.4 Algebraic Number Theory.
• MT21: TA for B2.1 Introduction to Representation Theory.

Conferences attended

• The Automorphic Side of the p-adic Langlands Programme 31 July 2023-4 August 2023, Wuppertal, Germany.
• Number theory meets p-adic representations, A conference on the occasion of Peter Schneider’s 70th birthday, 13-17 February 2023, Münster, Germany.
• Topology and Arithmetic around the Langlands Programme, 7-11 June 2022, Stockholm University, Stockholm, Sweden.
• Arizona Winter School 2022, Automorphic forms beyond GL_2, 5-9 March 2022, University of Arizona, Tucson, Arizona.

Experience

• From 2020-2021 I was the president of the Invariants, Oxford’s student maths society.

Miscellaneous

Origami: Lion, Collie, Spiral.