• Ph.D- Insitute of Mathematical Sciences, Chennai, India, 2008-2013, Advisor: Prof. V. S. Sunder
• B.Sc, M.Sc- Ramakrishna Mission Vidyamandira, Belur (Calcutta University), 2003-2008
My Primary research areas are functional analysis and Ergodic Theory. My central research area is operator algebra and it evolves around operator algebra. I study one parameter family of endomorphisms on von Neumann algebras.
I also study structure theory of von Neumann algebras, Connes's classifications theory of type III factors and various others property of type III factors and verious dynamical system on von Neumann algebras.
• Post Doctorate Fellowship 2013-2015, Ben-Gurion University of the Negev
• Integrated Ph.D Fellowship, TIFR, 2006
• CSIR (NET) Fellowship 2008, Junior Research Fellowship 2008, ISI Kolkata, NBHM Ph.D Scholarship, 2008,
• Ranked 4rth in IIT JAM,
• NBHM Master Scholarship, 2006-2008
16. P. Bikram, R. Kumar and K. Mukherjee, On factoriality of mixed q-deformed Araki-Woods von Neumann algebras, to appear in Infin. Dimens. Anal. Quantum Probab. Relat. Top , 2023.
15. P. Bikram, Rahul K and K. Mukherjee, On non-injectivity of mixed q-deformed Araki-Woods von Neumann algebras, to appear in Kyoto J. Math., 2023.
14. P. Bikram and K. Mukherjee, E. Ricard and S. Wang ” On the factoriality of q-deformed Araki-Woods von Neumann algebras” , to appear in Comm. Math. Phys., 2023 , arXiv:2203.06366,
13. Mixed q-deformed Araki-Woods von Neumann algebras with Rahul K and K. Mukherjee, to appear in J. Noncommut. Geom., 2023.
12. P. Bikram and D. Saha, "On the non-commuttative Neveu decomposition and stochastic ergodic theorems" J. Funct. Anal., 284 (2023), no 1, Paper No. 109706, 45 pp.
11. ”On the commutants of generaors of q-deformed Araki-Woods von Neumann algebras” with K. Mukherjee, Publ. RIMS Kyoto Univ, 58(2022), 1-21.
10. ”Poisson boundary on full Fock space” with B. V. R. Bhat, S. De and N. Rakshit, Trans. Amer. Math. Soc., Volume 375, Number 8, 2022, Pages 5645-5668.
9. ”Contractivity properties of OrnsteinUhlenbeck semigroup for mixed q-ArakiWoods von Neumann algebras with R. Mohanta, J. Math. Phys. 62, 113502 (2021)
8. ”On the von Neumann algebras associated to Yang-Baxter operators” with Rahul K, R. Mohanta, ; K. Mukherjee and D.. Saha, Proc. Roy. Soc. Edinburgh Sect. A 151 (2021), no. 4, 1331-1354.
7. ”On the classification and modular extend- ability of E0-semigroups on factors’ with D. Markiewicz, Math. Nachr., 293 (2020), no. 7, 1228-1250.
6. A Note on Coarse Bimodules with J. Bannon, and K. Mukherjee, Journal of Mathematical Analysis and Applications Vol. 475, Issue 2, 2019, 1404-1415.
5. On the E0-semigroups of free Araki- Woods factors, with Kunal Mukherjee, Internat. J. Math., Vol. 28, No. 10 (2017).
4. Generator masas in q-deformed Araki-Woods von Neumann algebras and factoriality, with Kunal Mukherjee, J. Func. Anal. 273(2017) 1443-1478.
3. CAR flows on type III factors and their extendability, Infinite Dimentional Analysis and Quantum Probability and Related Topics, Vol. 17, No. 4(2014) 1450026.
2. On the Extendability of endomorphisms and E0-semigroups on factors, with Masaki Izumi, R. srinivasan and V. S. Sunder, Kyushu J. Math. 68 (2014), 165–179.
1. Hilbert von Neumann modules, with Kunal Mukherjee, R. Srinivasan and V. S. Sunder, (special issue of) Communications in Stochastic Analysis (in honour of Professor K. R. Parthasarathy), vol. 6, no. 1, (March 2012).
8. P. Bikram and K. Mukherjee, Split property, preprint.
7. P. Bikram, K. Mukherjee, On the factoriality and Haagerup Property of the von Neumann algebra associated with a Yang-Bxter Operator, 2022.
6. P. Bikram, Free Monotone transport of the von Neumann algebra associated with a Yang-Bxter Operator, 2022.
5. P. Bikram, R. Kumar and K. Mukherjee, On factoriality of mixed q-deformed Araki-Woods von Neumann algebras, submitted, 2023.
4. P. Bikram and D. Saha, Weighted subsequential ergodic theorems on Orlicz spaces, Submitted, 2023.
3. P. Bikram and D. Saha, On noncommutative ergodic theorems for semigroup and free group actions, submitted, 2023.
2. P. Bikram and R. Mohanto, and K. Mukherjee, Complete metric approximation property for mixed q-Araki-Wood von Neumann algebras, submitted, 2022.
1. P. Bikram, R. Kumar and K. Mukherjee, Yang Baxter deformation of mixed q-deformed Araki-Woods von Neumann algebras, submitted, 2022.
Measure Theory, Topology, Complex analysis, Metric Space, Calculas, Functional Analysis, Ergodic Theory
Post-Docs
1. Debabrata De
Ph.D. students
1. Diptesh Kumar Saha
2. Rajeeb Ranjan Mohanta
• Early Career Research Awards, SERB, DST, from 2019 to 2021 (Rs. 6L).
• CEFIPRA, The Indo-French Centre for the Promotion of Advanced Research, Co- Pi, from 2019 to 2021 (Rs. 41L+ 60L).