Sivasankar Nair

Sivasankar Nair

I obtained my Ph.D. from the Département de Mathématiques et de Statistique of the Université de Montréal. My supervisor was Prof. Matilde Lalín, and I am interested in special values of L-functions and Mahler measures. I was one of the many people working in Number Theory in the vibrant city of Montréal! I was previously a Master's student at UBC, supervised by Prof. Sujatha Ramdorai and Prof. Vinayak Vatsal, and an undergraduate student at IIT Kanpur.

Email: siva.sankar.nair[AT]umontreal.ca

Publications

• Random walks through the areal Mahler measure: steps in the complex plane
  (with Matilde Lalín, Berend Ringeling and Subham Roy)
  Quarterly Journal of Mathematics, 76 (2025), no. 4, pp. 1315-1353, [arxiv]
• The Mahler measure of a multivariate polynomial family with non-linear degree
  (with Matilde Lalín and Subham Roy)
  Acta Arithmetica, 216 (2024), no. 1, pp. 35-61. [pdf]
• The Mahler measure of a family of polynomials with arbitrarily many variables
  Journal of Number Theory, 275 (2025), pp. 214-272, [arxiv].
• An invariant property of Mahler measure
  (with Matilde Lalín)
  Bulletin of the London Mathematical Society, 55 (2023), no. 3, pp. 1129-1142. [pdf]
• Families of non-θ-congruent numbers with arbitrarily many prime factors
  (with Vincent Girard and Matilde Lalín)
  Colloquium Mathematicum, 152 (2018), no. 2, pp. 255-271. [pdf]

Research talks

• The Mahler measure of some polynomial families, CNTA XVI, Fields Institute, June 2024 [slides].
• Regulators, polylogarithms and the Mahler measure of some polynomial families, MOBIUS Seminar, UdeM, April 2024.
• The Mahler measure of a family of polynomials with arbitrarily many variables
  • CMS Winter Meeting, Montréal, December 2023, [slides].
  • MM(P): Mahler Measures of Polynomials, Radboud University, Nijmegen, October 2023, [slides].
  • Maine-Québec Number Theory Conference, University of Maine, October 2023.
  • MOBIUS Seminar, UdeM, May 2023.
• An invariant property of Mahler measures [slides]
  • CMS Winter Meeting, Toronto, December 2022.
  • Québec-Maine Number Theory Conference, Université Laval, October 2022.
  • Department Seminar, Indian Institute of Technology Kanpur, July 2022.
• A family of polynomials with Mahler measure 28ζ(3) ⁄ 5π², Maine-Québec Number Theory Conference, October 2021 [slides]
• The Mahler measure of some three-variable polynomials, Montréal Online Biweekly Inter-University Seminar (MOBIUS), July 2021 [slides]

Other talks

• π and sums of squares, Séminaire étudiant en mathématiques, UdeM, March 2024 [slides]
• Recherche en théorie des nombres, Symposium SAMARI , UdeM, mars 2024 [diapositives]
• An overview of quadratic forms, Séminaire étudiant en mathématiques, UdeM, March 2023 [slides]

Miscellaneous