Dr. Sagar B. Kalane

Publications :

1. With John R. Parker, “Free Groups Generated by Two Parabolic Maps”, Mathematische Zeitschrift (2023). Link

2. With Devendra Tiwari, “On Free Groups Generated by Two Heisenberg Translations”, Proceedings of the Indian Academy of Sciences – Mathematical Sciences (2022). Link

3. With Krishnendu Gongopadhyay, “Local Coordinates for Complex and Quaternionic Hyperbolic Pairs”, Journal of the Australian Mathematical Society (2021). Link

4. With Krishnendu Gongopadhyay, “On Conjugation Orbits of Semisimple Pairs in Rank One”, Forum Mathematicum, (2019). Link

5. With Krishnendu Gongopadhyay, “Quaternionic Hyperbolic Fenchel–Nielsen Coordinates”, Geometriae Dedicata, (2019). Link

6. With I. D. Platis, “Free and Discrete Groups Generated by Two Parabolic Maps of Quaternionic Hyperbolic Isometries” (submitted, 2025). Link .

7. With Krishnendu Gongopadhyay, “Strongly Doubly Reversible Pairs in the Quaternionic Unitary Group of Signature (n, 1)” (submitted, 2025). Link

Preprints :

With Krishnendu Gongopadhyay, “Decomposition of Quaternionic Hyperbolic Isometries” (submitted, 2025).
With John Parker, Krishnendu Gongopadhyay, and Abhishek Mukherjee, “Surface Group Representations to Quaternionic Möbius Transformations” (in preparation, 2025).
“Geometric Interpretation of the Trace of a Regular Elliptic Element in PU(3,1) (in preparation, 2025).

Talks :

Invited speaker at International conference: World of Group Craft V (Online), 1st September, 2025. Talk: "Discrete subgroups generated by two parabolic maps from rank one isometry groups", Video link
Invited talk on “Free and discrete groups generated by two parabolic maps ” , at NISER Bhubaneswar, India, 17th March, 2025.
Invited talk on “Free and discrete groups generated by two parabolic maps ” , at HRI Allahabad, India, 13th February, 2023
Gave a talk on “Free and discrete groups generated by two parabolic maps ” , in workshop on Group theory, at IISER Pune, India, 13th January, 2023.
Gave a talk on “Free and discrete groups generated by two parabolic maps ” , at IISER Mohali, India, 21st April, 2022.
Gave a talk on “Free and discrete groups generated by two parabolic maps ” in the, In-house Mathematics Symposium, at IISER Pune, India, 17th March, 2022.
Gave a talk on “Free groups generated by two parabolic maps in PU(2,1)” in the, Postdoc Seminar, at IISER Pune, India, 17th March, 2021.
Gave a talk on “Classification of pairs of quaternionic and complex hyperbolic isometries", at IIT Bombay, India, 17th Feb, 2021.
Gave a talk on “Local coordinates of loxodromic pairs in rank one” in the, Postdoc Seminar, at IISER Pune, India, 13th March, 2020.
Gave a talk on “Classification of Pairs of Quaternionic Hyperbolic Isometries” in the, Math in House Symposium, at IISER Pune, India, 31st August, 2019.
Gave a talk on “Classification of Pairs of Quaternionic Hyperbolic Isometries” at IISER Mohali, India, June 19, 2019.
Gave a talk on “Classification of Pairs of Quaternionic Hyperbolic Isometries” at IISER Mohali, India, April 01, 2019.
Gave a talk on “Quaternionic Hyperbolic Fenchel-Nielsen Coordinates” in the Inter IISER Maths meet (IINMM 2018), at IISER Bhopal, India, August 07, 2018.
Gave a talk on “Invitation to hyperbolic geometry” in the Graduate Student Group seminar (GSG), at IISER Mohali, India, April 11, 2018.