Andreani Petrou

 

Andreani Petrou, Ph.D. student
e-mail: andreani.petrou@oist.jp
 

My research focuses on the study of knot invariants through a physics lense. In particular, I study the HOMFLY-PT and Kauffman polynomials and relations between them, using a physics-inspired tool, called the Harer-Zagier  transform. This is a version of the Laplace transform that maps polynomials, such as the HOMFLY-PT polynomial, into rational functions. This is a promising tool, since knots for which the latter is factorisable, share many nice properties with torus knots, including closed formulas for their polynomials. Among my future research goals, will be to consider the geometrical significance of this algebraic property, i.e. the Harer-Zagier factorisability, in the context of 3-manifolds. Moreover, I am interested in exploring potential applications to condensed matter physics and quantum computing.

 

Publication

  • with Shinobu Hikami, “Harer–Zagier transform of the HOMFLY–PT polynomial for families of twisted hyperbolic knots”, J. Phys. A: Math. Theor. 57 (2024) 205204. https://doi.org/10.1088/1751-8121/ad421b

Pre-prints

  • with Shinobu Hikami, “The HOMFLY-PT polynomial  and HZ factorisation”, arXiv:2412.04933
  • with Shinobu Hikami, “Character Expansion and the Harer–Zagier Transform of Knot Polynomials”, arXiv:2505.10629 

 

Conference Presentations

  • “Knots, Links and the Harer–Zagier factorisability”, World of GroupCraft V, online, 1 Sept. 2025 (available on YouTube)
  • “Knots, Links and the Harer–Zagier factorisability”, WPI–AIMR & WPI–SKCM2 International & Interdisciplinary Math–Materials Workshop, Tohoku University, 28 July 2025
  • “Knots, Links and the Harer–Zagier factorisability”, Silver Workshop VII, University of Tokyo, 12 March 2025
  • “Knots, Links and the Harer–Zagier factorisability”, The 20th East Asian Conference on Geometric Topology, University of Tokyo, 4 Feb. 2025
  • “Knot Polynomials and the Harer–Zagier Transform”, winter school at skcm2, Hiroshima University, 12 Dec. 2024
  • “Towards Knot Matrix Models via the Harer-Zagier transform”, ICGTMP Group33/35, Palais des Congres in Cotonou,  18 July 2024
  • “The Harer–Zagier transform of the HOMFLY–PT polynomial”, Knot Theory: LMO invariants and related topics, OIST, 11 March 2024
  • “The Harer–Zagier transform of the HOMFLY–PT polynomial”, The 19th East Asian Conference on Geometric Topology, RIMS (University of Kyoto), 20 Feb. 2024
  • “Harer-Zagier formulas for families of twisted hyperbolic knots”, University of Tokyo and OIST Joint Symposium of Knot theory, University of Tokyo, 11 Sept. 2023
  • “Harer-Zagier formulas for families of twisted hyperbolic knots”, Silver Workshop VI, OIST, 8 Aug. 2023
  • “Knot Matrix models for families of twisted hyperbolic knots”, Women at the intersection of Mathematics and Theoretical physics, OIST, 20 April 2023 
  • “Knot Matrix models for families of twisted hyperbolic knots”, Silver Workshop V, OIST, 10 Nov. 2022
Outreach Presentation
  • “Knots: What can they tell us”, Okiden Science Festival, 15 February 2025
 

Past degrees

2019, University of Edinburgh, MSc in Mathematical Physics

2017, Leiden University, BA in Physics