A Rameswar Patro
Integrated M.Sc. Student in Mathematics
National Institute of Science Education and Research (NISER)
Education
Integrated M.Sc. in Mathematics
- Minor: Computer Science
- CGPA: 9.46/10.00
- M.Sc. Thesis: Groups of Lie Type | Advisor: Dr. Tushar Kanta Naik
Previous Education
- AISSCE (Class XII), CBSE - DAV Public School, Bhubaneswar (96.2%)
- AISSE (Class X), CBSE - Sankalp Senior Secondary School, Ralaba, Berhampur (94.6%)
Research Interests
Algebra
Core Focus: Algebraic Groups, Coxeter groups
Selected Advanced Coursework
- Advanced Linear Algebra
- Lie Algebras
- Commutative Algebra
- Algebraic Geometry
- Introduction to Manifolds
- Representation Theory
- Algorithmic Coding Theory
- Parametrized Algorithms
Preprints & Publications
Symmetry and Rigidity of Star-Shaped Coxeter Systems
with Arijit Mahato and Dr. Tushar Kanta Naik.
Research Projects
Geometric Invariant Theory
- Studied Hilbert's Finiteness Theorem, Matsushima's Criterion, Hilbert-Mumford Theorem, and Kempf-Ness Theorem.
Word Maps on Groups
- Investigated word maps across finite, profinite, and algebraic groups.
- Examined Waring-type problems, power maps (x ↦ x^M), and probabilistic aspects related to character theory.
Groups and Geometry
Supported by IAS Summer Research Fellowship
- Studied isometries of the Euclidean plane, Frieze and Discontinuous groups, and the structure of triangle groups.
- Explored regular tilings and introductory hyperbolic geometry.
Combinatorial Aspects of Coxeter Groups
- Explored reduced expressions, length functions, the strong exchange condition, and Bruhat order.
- Constructed geometric realizations of Coxeter groups using root systems.
Awards & Honors
- GATE Mathematics: AIR 37 (2026)
- CSIR-NET JRF: AIR JRF-34 (2025)
- NBHM Master's and Doctoral Scholarship: Selected (2025)
- Mimamsa Competition: Zonal Topper (2024)
- Abhiprajna Competition: Second Place (2025)
- Academic Excellence Award: Highest SGPA (2023, 2024, 2025)
- DAE DISHA Fellowship (2021-2026)
Contact
Email: arameswar.patro.math@gmail.com | Phone: +91 76840 83583
Room 301, Bhagirathi Hostel, NISER, Jatni, Odisha