Welcome to my homepage!
I am an assistant professor at the Indian Institute of Science Education and Research (IISER) Mohali, India.
Contact: 1F6, AB2, IISER Mohali, Knowledge City, Sector 81, Punjab 140306;
ratnapal`AT'iisermohali'DOT'ac'DOT'in; ratna'DOT'math'AT'gmail'DOT'com
Research Interest: Holomorphic Dynamics, Complex Geometric Analysis, Potential Theory.
Education:
Ph.D, 2016, Indian Institute of Science, Bangalore, India.
Thesis Advisor: Kaushal Verma.
M.Sc., 2010, Indian Institute of Technology Kanpur, India.
B.Sc. (Mathematics(Hons.)), 2008, Jadavpur University, Kolkata, India.
Employment:
Assistant Professor, Department of Mathematics, IISER Mohali, Punjab (10/05/2022-till date).
Assistant Professor, Department of Mathematics, IISER Berhampur, Odisha (08/12/20--09/05/2022).
NBHM Post-doctoral fellow, Department of Mathematics, TIFR Centre for Applicable Mathematics, Bangalore (01/08/19--07/12/20).
SERB National Post-doctoral fellow, Department of Mathematics, IISER Pune (15/05/17--14/05/19).
Institute Post-doctoral fellow, Department of Mathematics,IISER Pune (08/12/16--14/05/17).
Research Associate, Department of Mathematics, Indian Institute of Science, Bangalore (01/08/15-07/12/16).
Publications and preprints
Published/ Accepted
(With J. E. Fornaess) Increasing sequences of complex manifolds with uniform squeezing constants and their Bergman spaces, to appear in Mathematische Annalen, https://arxiv.org/pdf/2407.02130
Relation between Henon maps with biholomorphic escaping sets, Mathematische Annalen, https://doi.org/10.1007/s00208-023-02630-w
(With K. Verma and S. Bera) On the automorphism group of certain Short C2's, International Mathematics Research Notices (IMRN), rnac235, https://doi.org/10.1093/imrn/rnac235
(With J. E. Fornaess) Notes on Short C^k's, J. Geom. Anal. 32 (2022), no. 4, Paper No. 133, 22 pp.
(With S. Bera) Rigidity of Julia sets in higher dimensions, Comput. Methods Funct. Theory 22 (2022), no. 1, 55–93.
Further remarks on rigidity of Julia sets of Henon maps, Journal of Mathematical Analysis and Applications, 484 (2020), no 2, 123658, 15 pp.
Fatou-Julia dichotomy of matrix-valued maps, Journal of Mathematical Analysis and Applications 473 (2019), no 2, 918-933.
(With S. Bera and K. Verma) A rigidity property of Henon maps, Eur. J. Math. 6 (2020), no. 2, 508–532.
(With K. Verma) Ergodic properties of families of Henon maps, Annales Polonici Mathematici, 121 (2018), no. 1, 45-71.
(With S. Bera and K. Verma) Examples of non-autonomous basins of attraction, Illinois Journal of Math, 61 (2017), no. 3-4, 531-567.
(With S. Bera) Dynamics of semigroups of entire maps in C^k, Complex Anal. Synerg. 2(2016), no. 1, Paper No. 2, 22 pp.
(With K. Verma) Dynamical properties of families of holomorphic mappings, Conformal Geometry and Dynamics 19 (2015), 323-350.
Preprints
1. (With K. Ramachandran, S. Ravisankar) Conformal Rigidity of Polar Set Complements, https://arxiv.org/pdf/2201.05898.pdf.
Grants/ Awards:
INSA (Indian National Science Academy) Young Associates 2024.
2. MATRICS grant by Science and Engineering Research Board (SERB), India in 2023.
3. Start-up grant by Science and Engineering Research Board (SERB), India in 2023.
Teaching:
August-December, 2018: MTH 311(Real Analysis), IISER Pune
August-December, 2020: MTH 407 (Complex Analysis I), IISER Berhampur
January-April, 2021: MTH 504 (Complex Analysis II), IISER Berhampur
August-December, 2021: MTH 201 (Linear Algebra) & MTH 407 (Complex Analysis), IISER Berhampur
January-April, 2022: MTH 202 (Multi-variable calculus), IISER Berhampur
August-December, 2022: MTH 414 (Advanced Complex Analysis), IISER Mohali
January-April, 2023: MTH 605 (Topics in Analysis), IISER Mohali
August-December, 2023: MTH 414 (Advanced Complex Analysis), IISER Mohali