A Rameswar Patro
PhD Researcher in Mathematics
Indian Institute of Science (IISc), Bengaluru
Welcome to my personal website. I am a mathematician primarily focusing on the beautiful and intricate structures found within Coxeter groups, Groups of Lie type, and Algebraic Groups.
My academic journey started with an Integrated M.Sc. at NISER Bhubaneswar, leading to my current doctoral research at IISc. Beyond mathematics, this space serves as a collection of my professional history, personal galleries, and resources I find valuable.
Email: arameswar.patro.math@gmail.com | Phone: +91 76840 83583
Room 002 C, KRVH, IISc, Bengaluru, Karnataka
Education
PhD in Mathematics
Integrated M.Sc. in Mathematics
- Minor: Computer Science
- CGPA: 9.46/10.00 (up to 9th semester)
- 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%)
Selected Advanced Coursework
- Advanced Linear Algebra
- Lie Algebras
- Commutative Algebra
- Algebraic Geometry
- Introduction to Manifolds
- Representation Theory
- Algorithmic Coding Theory
- Parametrized Algorithms
Publications
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 ($x \mapsto x^{M}$), and probabilistic aspects related to character theory.
Groups and Geometry
- 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.
Conferences and Workshops
- Rigidity of Discrete Groups | IISER Mohali 2025
- Recent Developments in Group Theory | IIT Bhubaneswar 2025
- The Singapore-Bangalore "What is ...?" Workshop on Mathematics | IISc Bangalore 2025
- Seminar Series on Algebraic Graph Theory | NISER 2025
Awards & Honors
- GATE Mathematics: AIR 37 (2026)
- NBHM Master's and Doctoral Scholarship: Selected (2025)
- CSIR-NET JRF: AIR JRF-34 (2025 December)
- Mimamsa Competition: Zonal Topper (2024)
- Abhiprajna Competition: Second Place (2025)
- Academic Excellence Award: Highest SGPA (2023, 2024, 2025)
- DAE DISHA Fellowship (2021-2026)
Activities & Service
- Active member of Mathematix Club, NISER: Organized events and mathematical outreach programs.
- Coordinated Pi-Day Celebrations at NISER (2024, 2025).
- Volunteered at Open Day and Science Camp demonstrations for school students (2023, 2024).
Gallery
A collection of moments from conferences, campus life, and beyond.
Miscellaneous
Links to the personal pages of my friends and colleagues.
Mathematical Resources
A curated list of websites, databases, and blogs that are invaluable.
An incredible, open-source repository of algebraic geometry. It rigorously builds up the foundations of scheme theory, algebraic spaces, and stacks.
A wiki-driven project focused on mathematics, physics, and philosophy from the perspective of higher category theory and homotopy theory.
A question-and-answer site specifically dedicated to research-level mathematics. The discussions here often provide insights you won't find in textbooks.
The standard repository for electronic preprints (e-prints) of research papers in mathematics. Essential for keeping up with the absolute latest developments in the field.
Updates on Terence Tao's research, as well as brilliant, accessible expositions of deep mathematical concepts and advice for young researchers.
Excellent high-level journalism that covers breakthroughs in mathematics. It's a great way to stay informed about what's happening outside your specific subfield.