K. S. Senthil Raani

Senthil Raani K. S.
Associate Professor (Mathematical Sciences), IISER Berhampur, Odisha – India.
Research Areas: Fourier Analysis, Geometric Measure Theory

PhD Thesis:
“ $L^p$ -Asymptotics of Fourier transform of fractal measures”
under Prof. E.K. Narayanan at Indian Institute of Science, Bengaluru.
I scribble a lot here a.e. ‘about me‘.
Links: MATHSCINET, GENEALOGY, GOOGLE SCHOLAR, CV(June2025)
Upcoming Harmonic analysis Event(s) in India:
19th DMHA 2025 along with workshop, “Geometry of Sparse Sets” at ICTS Bengaluru (December 2026)

Contact

IISER Berhampur

At/Po: -Laudigam, Dist.

Brahmapur

Ganjam, Odisha 760010

India

raani-at-iiserbpr.ac.in

Research Interests

My research interests : Fourier asymptotics of fractal sets with applications to distance set conjectures and other configurations like k-chains, k-necklaces, pinned distance set problems in null-measure sets.

Ongoing Research: Distance set problems in Heisenberg group; Interval distances in thin sets in Euclidean line; Descriptive structure of k-chains, k-necklaces, 2-point patterns in thin sets of large Hausdorff dimension.

Research Publications

Distances in sets of positive Koranyi upper density in Heisenberg group (joint with Rajesh K. Singh) -preprint(2025)
Distances in sparse sets of large Hausdorff dimension (joint with Malabika Pramanik)-preprint(2023)
$L^p-L^q$ estimates for generalized spherical averages (joint with Sayan Bagchi, Sourav Hait) Proceedings-Mathematical Sciences 132 (1), 35, 2022
Self-dual representations of SL(2,F)-an approach using the Iwahori-Hecke algebra (joint with Brahadeesh Sankarnarayanan, Kumar Balasubramanian) Communications in Algebra, 2019
$L^p$ Fourier asymptotics, Hardy-type inequality and fractal measures Monatshefte für Mathematik 184 (3), 459-487, 2017
$L^p$ -Integrability, Dimensions of Supports of Fourier Transforms and Applications , Journal of Fourier Analysis and Applications 20 (4), 801-815, 2014 (This paper was done for sets with pre-packing measure)

Mentoring

Please email me if you would like to work with me for internship or MS thesis. (aspiring PhD students, please see the updates here.)
Some of the keywords that would help find my interests:

Distance set of sets in Euclidean Space, p-adic field, manifolds; Heisenberg group

pinned Distance sets; Configurations (n-point pattern, k-chain, k-necklaces, trees);

$L^p-L^q$ inequalities of integral operators;

convolution operators;
Maximal functions on fractal set-ups;

construction of fractals with specific Fourier asymptotics;

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to be updated

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Post Doctoral Fellows

PhD Students

Dr. Rajesh Kumar Singh (September 2023 – June 2024)
- (Work done: Distances in sets of positive Koranyi upper density in Heisenberg group)
Dr. Aswin Govindan (September 2024 – September 2025)
- Ongoing work: Distance set problems, quantifying k-chains in thin sets

(Prerequisites for potential PhD students: Preferable knowledge in Measure theory/Functional Analysis. Yet if the candidate is interested in Real analysis, the candidate will achieve the prerequisite during their first year of Course work at IISER Berhampur in order to work in Harmonic Analysis & Geometric Measure theory. The selection is based on the departmental committee constituted by the HoD, Mathematical Sciences. Please click here for further details.)

Dr. Manish Chaurasia (September 2024 – August 2025)
- Proposed work: Quantifying two point patterns in thin sets

Mr. Meenakshi Sundaram (UGC JRF since January 2025)

Mentored MS Thesis

Co-Mentored MS Thesis (only administrative role)

Ms. Sruthi Ramkumar (2025-26)
- Topic: TBD (Keywords: Distances, graph, programming)
Mr. Prateek (2025-2026)
- Topic: TBD (keywords: Brownian motion, financial mathematics)
Mr. Md Fasil Imam (2025-2026)
- Topic: TBD (keywords: uniformly distributed sequences)
Mr. Saptarsi Ghosh (2024-2025)
- Topic: Sum Sets
Mr. Animesh Nayak (2022-2023)
- Topic: Fractal Dimensions
Mr. Pratik Sinha (2020-2021)
- Topic: Steiner formula for convex bodies

Mr. Mayank Agarwal (2024-2025)
- Topic: Algorithmic Graph Theory
Mr. S. Santosh (2023-2024)
- Topic: Independence of Continuum hypothesis and some applications of Martin’s axiom
Mr. Milap Kumar Rajgor (2023-2024)
- Topic: The Bergman Spaces and the Bergman Kernels
Mr. Neehar Verma (2022-2023)
- Topic: Error distance distribution of projective Reed – Solomon Codes from the perspective of Finite Geometry

Mentored JRF

Mentored Interns (only from outside IISER Berhampur)

Mr. Ankan Gosh (UGC-2024)
Ms. Aratrika Pandey (CSIR 2020-23)
Mr. Masud Haasan (CSIR 2018-20)

Mr. Sushoban Das (July-Dec 2025)
- Topic: TBD
Mr. Sarbartha Sarkar (June-July 2025)
- Topic: Introduction to Geometric measure theory
Mr. Rakesh Rath (May – June 2019)
- Topic: Measure theory

Miscellaneous

Selective Administrative responsibilities at IISER Berhampur: Associate Dean of Students Affairs (since January 31, 2025), Hostel Warden (since June 24, 2025; Past wardenship: July 2018-August 2022; September 2023 – November 2024); Departmental Responsibilities including DPGC Convener; Member in charge for BsMs-syllabus
Past responsibilities: Question paper setting (IISER, ANJAC), NBHM MS-PhD Interview panel
Membership: AMS, CMS
Reviewer: JFA