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• 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
I work in operator algebra and Ergodic Theory. I study one parameter family of endomorphisms on von Neumann algebras and 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. I also study various ergodic properties of dynamical systems.
• 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
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32. P. Bikram and D. Saha, Weighted subsequential ergodic theorems on Orlicz spaces, to appear in Operators and Matrices, 2024.
31. P. Bikram, R. Kumar and K. Mukherjee, Yang Baxter deformation of mixed q-deformed Araki-Woods von Neumann algebras, to appear in Kyushu J. Math, 2024.
30. 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, 2024.
29. P. Bikram, Rahul K and K. Mukherjee, On non-injectivity of mixed q-deformed Araki-Woods von Neumann algebras, Kyoto J. Math. 64 (2024), no. 2, 501–518.
28. P. Bikram and K. Mukherjee, E. Ricard and S. Wang ” On the factoriality of q-deformed Araki-Woods von Neumann algebras”, Comm. Math. Phys. 398 (2023), no. 2, 797–821
27. Mixed q-deformed Araki-Woods von Neumann algebras with Rahul K and K. Mukherjee, J. Noncommut. Geom. 17 (2023), no. 4, 1231–1297.
26. 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.
25. ”On the commutants of generaors of q-deformed Araki-Woods von Neumann algebras” with K. Mukherjee, Publ. Res. Inst. Math. Sci. 58(2022), 1-21.
24. ”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.
23. ”Contractivity properties of OrnsteinUhlenbeck semigroup for mixed q-ArakiWoods von Neumann algebras with R. Mohanta, J. Math. Phys., 62, 113502 (2021)
22. ”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.
21. ”On the classification and modular extend- ability of E0-semigroups on factors’ with D. Markiewicz, Math. Nachr., 293 (2020), no. 7, 1228-1250.
20. A Note on Coarse Bimodules with J. Bannon, and K. Mukherjee, J. Math. Anal. Appl. Vol. 475, Issue 2, 2019, 1404-1415.
19. On the E0-semigroups of free Araki- Woods factors, with Kunal Mukherjee, Internat. J. Math., Vol. 28, No. 10 (2017).
18. Generator masas in q-deformed Araki-Woods von Neumann algebras and factoriality, with Kunal Mukherjee, J. Funct. Anal. 273(2017) 1443-1478.
17. CAR flows on type III factors and their extendability, Infin. Dimens. Anal. Quantum Probab. Relat. Top Vol. 17, No. 4(2014) 1450026.
16. 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.
15. Hilbert von Neumann modules, with Kunal Mukherjee, R. Srinivasan and V. S. Sunder, (special issue of) Commun. Stoch. Anal. (in honour of Professor K. R. Parthasarathy), vol. 6, no. 1, (March 2012).
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Submitted
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8. P. Bikram, Ergodic theorem for the action of a non-amenable group on non-commutative L^p-spaces, submitted, 2023.
7,.P. Bikram, On the stochastic ergodic theorems for free group actions, submitted, 2024.
6. P. Bikram and K. Mukherjee, Yang Baxter deformation of mixed q-deformed Araki-Woods von Neumann algebras, submitted, 2024.
5. P. Bikram and R. Mohanto, and K. Mukherjee, Complete metric approximation property for mixed q-Araki-Wood von Neumann algebras, submitted, 2023.
4. P. Bikram and D. Saha, Note on noncommutative ergodic theorems associated to vector-valued Besicovitch weights, Submitted 2024.
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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, 2019 to 2021 ( 1 crore).