About
I am a postdoctoral researcher at the Faculty of Mathematics and Physics, University of Ljubljana, working with Igor Klep. Since November 2026 I lead the ARIS research project Mathematical Foundation of Bilinear Matrix Inequalities. I received my PhD from the Indian Institute of Science in 2024, advised by Tirthankar Bhattacharyya.
My research interests are operator theory, free analysis, noncommutative polynomial positivity and factorization, operator-valued Positivstellensätze, matrix convexity, operator algebras, and complete Nevanlinna–Pick spaces.
News
- Nov 2026 · Two new preprints on arXiv: Operator Fejér–Riesz theorems with gaps and degree bounds with A. Zalar, and Fejér–Riesz factorization for free products with I. Klep, J. Levenson, and S. McCullough.
- Nov 2026 · Our paper with R. Duhan, UCP maps on finite Toeplitz systems, is now published (open access) in International Mathematics Research Notices.
- Nov 2026 · Started as head of the ARIS research project N1-0536, Mathematical Foundation of Bilinear Matrix Inequalities.
- Aug 2026 · Talks at the 37th International Workshop on Operator Theory and its Applications (IWOTA), Université Laval, Québec, and at IISER Pune.
- Jul 2026 · Awarded the Martin Forster Medal for the best doctoral thesis in Mathematics at the Indian Institute of Science.
- Jun 2026 · Two new preprints on arXiv: Spectra of 1/k-contractions via characteristic functions with P. Kumar, and UCP maps on finite Toeplitz systems with R. Duhan.
- Apr 2026 · New preprint on arXiv: Operator-valued Positivstellensätze on matrix convex sets and free products of finite abelian groups with I. Klep and S. McCullough.
- Feb 2026 · My Marie Skłodowska-Curie fellowship proposal was awarded the Seal of Excellence by the European Commission.
- Apr 2025 · Joined the University of Ljubljana as a postdoctoral researcher.
- Oct 2024 · Defended my PhD thesis at the Indian Institute of Science.
Positions
- Apr 2025–now Postdoctoral Researcher Faculty of Mathematics and Physics, University of Ljubljana · Mentor: Igor Klep
- Aug 2024–Feb 2025 Research Associate Indian Institute of Science, Bengaluru · Mentor: Tirthankar Bhattacharyya
- Aug 2019–Jul 2024 Doctoral Researcher Indian Institute of Science, Bengaluru · Supervisor: Tirthankar Bhattacharyya
Education
- 2019–2024 PhD in Mathematics Indian Institute of Science, Bengaluru · Thesis: Invariants Associated with Complete Nevanlinna–Pick Spaces · Defended 1 October 2024
- 2017–2019 M.Sc. in Mathematics Indian Institute of Science, Bengaluru · Project: Existence of Unitary Dilation of Commuting Contractions and von Neumann Inequality
Honours and awards
- Feb 2026 Seal of Excellence Marie Skłodowska-Curie Actions, European Commission
- Jul 2026 Martin Forster Medal Indian Institute of Science, best doctoral thesis (2024–25)
- 2023 Dr. K. V. Rao Scientific Society Research Award Mathematics
- 2018 All India Rank 10 Joint CSIR–UGC National Eligibility Test (JRF)
- 2017 All India Rank 3 Joint Admission Test for M.Sc. (JAM)
Grants and fellowships
- Nov 2026–2028 Project Head, ARIS project N1-0536 Mathematical Foundation of Bilinear Matrix Inequalities, University of Ljubljana
- 2020–2024 Prime Minister's Research Fellowship Government of India
- 2019–2020 Junior Research Fellowship Indian Institute of Science, Bengaluru
- 2017–2019 M.Sc. Fellowship Indian Institute of Science, Bengaluru
Collaborators
- Daniel Alpay, Chapman University, California, USA
- Tirthankar Bhattacharyya, Indian Institute of Science, Bangalore, India
- Ritul Duhan, Indian Institute of Science, Bangalore, India
- Igor Klep, University of Ljubljana, Slovenia
- Poornendu Kumar, University of Ljubljana, Slovenia
- Jacob Levenson, University of Florida, USA
- Scott McCullough, University of Florida, USA
- Aljaž Zalar, University of Ljubljana, Slovenia
Complex Analysis Seminar Series
Since 2024 I co-organise COMPASS, an online seminar series on complex analysis, function spaces, and complex geometry. To contact the organisers, write to compass.talks.updates@gmail.com.
Department of Mathematics
Faculty of Mathematics and Physics
University of Ljubljana, Slovenia