Sivasankar Nair

Sivasankar Nair

I recently 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.

Bureau 6192, Pavillon André Aisenstadt
Département de Mathématiques et de Statistique
Université de Montréal
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)
  submitted (2025). [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