Rudradip Biswas

I am a postdoctoral researcher in pure mathematics at the University of Warwick with research interests at the intersection of homological algebra, representation theory, category theory (triangulated categories), and group theory. Below are the details of my education, research work, selected research talks, and seminars organized by me. 

*News: we have recently obtained funding from the London Math Society for 2 events that we will organize next year at the University of Warwick: 

a) ‘Recent Developments in Algebraic K-theory’ - (the website is linked with the title) scheduled for 7-11 April, 2025. This will be a normal research conference with invited talks by several top experts like Tom Bachmann, Baptiste Calmes, Jean Fasel, Jens Hornbostel, Irakli Patchkoria, Sabrina Pauli, Vladimir Sosnilo, etc. This event is being co-organized with Marco Schlichting. Other than the LMS, we have also received some funding from the Heilbronn Institute for this meeting.

b) ‘Motives, equivariant topology, and tt-geometry’ - tentatively scheduled for 1-5 Sep, 2025. This will be an LMS Research School with three minicourses: noncommutative motives (by Goncalo Tabuada), tt geometry (by Greg Stevenson), and equivariant topology (by Dan Dugger and Christy Hazel). There will also be several plenary talks. This event will be co-organized with John Greenlees and Clover May. 

More information about the Research School will follow shortly. If you are interested in either of these events or have any questions, please feel free to get in touch.

Education and Degrees:

1. Ph.D. in Pure Mathematics, University of Manchester, UK (2016-2020). Thesis submitted in September 2020 and successfully defended in January 2021. Supervisor: Peter Symonds. A copy of my thesis is available here. 

2. M.Res in Mathematics, University of Leicester, UK (2015-2016). Thesis supervisor: Frank Neumann. (Frank has since moved to Pavia, his current webpage is here)

3. B.Sc in Mathematics and Physics, Chennai Mathematical Institute, India (2012-2015).

Email: rudradipbiswas@gmail.com

Seminars  organized:

1. New Directions in Group Theory and Triangulated Categories - This is an online seminar series that I started in the autumn of 2020. Until now, this series has featured talks by many young researchers as well as many leading experts in research areas within group theory and triangulated categories like Amnon Neeman, Srikanth Iyengar, Henning Krause, Paul Balmer, Akhil Mathew, John Greenlees, Jon Carlson, Doug Ravenel, etc. In the coming weeks, we will have many other experts speak in this series. If you are interested to know more about this series and also if you are interested in speaking, please feel free to send me an email.

2. Seminar by Harald Helfgott at Bonn (July 29, 2021) - This talk was originally planned to be a part of the abovementioned seminar series. In the end, it was organized as a lone seminar while I was a postdoctoral fellow at MPI Bonn, and the department there kindly agreed to let me host the talk on their website, hence the phrase "at Bonn" in the description of this talk. The research presented in this talk is very unique and insightful, and Prof Helfgott is one of the world's leading experts in the area of the talk. His presentation was recorded and the video can be accessed here. 

3. Triangulated Categories in Representation Theory - This was a one-day conference that took place on November 11, 2021. I gave one of the talks myself and the other two talks were by Sergio Estrada from the University of Murcia and Tsutomu Nakamura from the University of Tokyo. More details about this meeting, including video recordings of all the talks,  are available on its website.  

Physical meetings/conferences  where I've been a part of the organizing committee:

1.  Master Class on New Developments in Finite Generation of Cohomology. Universität Bielefeld, 25-27 September, 2023.

2.  BIREP Summer School on persistence modules—The Interplay of Representation Theory and Topological Data Analysis. Hotel Waldcafé Jäger, Bad Driburg, 31 July - 4 August, 2023.

Papers and preprints:

1. "Bounded t-structures, finitistic dimensions, and singularity categories of triangulated categories." Joint with Hongxing Chen, Kabeer Manali Rahul, Chris Parker, and Junhua Zheng. [42 pages], v1 arXived on 30 Dec 2023. arXiv:2401.00130  

2. "Injective generation of derived categories and other applications of cohomological invariants of infinite groups." Comm. Algebra 50 (2022), no. 10, 4460-4480. [journal version]

3. "Benson's cofibrants, Gorenstein projectives, and a related conjecture." Proc. Edinb. Math. Soc. (2) 64 (2021), no. 4, 779-799. [journal version]

4. "Generating derived categories of groups in Kropholler's hierarchy." Munster J. Math. (2021) no. 1, 191-221. [journal version]

5. "On some cohomological invariants for large families of infinite groups." New York J. Math. 27 (2021), 818-839. [journal version]

6. "On generation operators in the module category and their applications." Currently a preprint. [my current version]

Other Mathematical Writing:

1. Oberwolfach extended abstract - Cohomological finiteness conditions and stable categories on rational discrete modules over TDLC (totally disconnected locally compact) groups. From "Homological aspects for TDLC groups" Oberwolfach meeting, 26 Nov - 1 Dec, 2023.  

Research Visits (recent):

1.  Wayne State University, Detroit, Michigan, 12-16 August, 2024. 

2.  University of Copenhagen, 15-19 April, 2024

3.  École Polytechnique Fédérale de Lausanne, 24-28 March, 2024

4.  IMPAN Warsaw, 4-8 March, 2024

5.  University of Stuttgart, 26 Feb - 1 March, 2024

6.  University of Seville, 4-5 Dec, 2023

7.  NTNU Trondheim, 20-23 Nov, 2023

8.  University of Santiago de Compostela, 13-17 Nov, 2023

Selected Research Talks:

2024

1. "An Antieau-Gepner-Heller conjecture and generalizations." Topology Seminar, Johns Hopkins University, 24 October, 2024.

2. "An Antieau-Gepner-Heller conjecture and generalizations." Topology Seminar, University of Illinois Urbana-Champaign, 22 October, 2024.

3. "Bounded t-structures with completion theory." Topology Seminar, Wayne State University, Detroit. 13 August, 2024.

4. "Bounded t-structures, finitistic dimensions, and singularity categories of triangulated categories." Plenary talk at ICRA (International Conference on Representations of Algebras), Shanghai Jiaotong University, China. 7 August 2024. 

5. "Bounded t-structures, finitistic dimensions, and singularity categories of triangulated categories." Approximation theory & its Applications. Zhejiang University of Technology, Hangzhou, China. 16-20 July, 2024. 

6.  "Bounded t-structures on derived categories of schemes - new results and generalizations." Algebraic Geometry Seminar, Cardiff University. 12 June, 2024

7. "Completion of perfect modules over ring spectra, and a new general obstruction to bounded t-structures." Algebraic Topology Seminar at Universität Hamburg. 4 April, 2024.

8. "Regularity for E1 rings, schemes, and abstract triangulated categories, with new general results on bounded t-structures." Topology Seminar at École Polytechnique Fédérale de Lausanne (EPFL). 26 March, 2024.

9. "Some Hopf algebra invariants and new results on their relations with each other." North Atlantic Noncommutative Geometry Seminar, IMPAN Warsaw. 6 March, 2024.

10. "Applications of a new findim concept to derived categories arising in representation theory." Algebra - Darstellungstheorie - Homologische Methoden (Algebra - Representation Theory - Homological Methods) Seminar, Universität Stuttgart. 27 February, 2024.

11. "Algebraic conditions for discrete groups to admit finite-dimensional models for their classifying space of proper actions." Algebra Seminar, University of Warwick. 12 February, 2024.

12. "Bounded t-structures and singularity categories of triangulated categories." 118th meeting of Transalpine Topology Tetrahedron (TTT), University of Sheffield. 1 February, 2024.

2023

13. "There is only one equivalence class of bounded t-structures in the derived bounded category of coherent sheaves on a noetherian finite dimensional scheme." Algebraic Geometry Seminar, University of Warwick. December 6, 2023.

14. "Bounded t-structures and singularity categories of triangulated categories." Seminario del Departamento de Álgebra, Universidad de Sevilla. December 4, 2023.

15. "Cohomological finiteness in rational discrete modules over tdlc groups." Oberwolfach - Homological aspects for TDLC groups. November 27, 2023.

16. "Generalizing Neeman's work on bounded t-structures on derived perfect categories and derived bounded categories." Algebra Seminar, NTNU Trondheim. November 21, 2023.

17. "Generalizing Neeman's work on bounded t-structures on derived perfect categories and derived bounded categories." Seminario García Rodeja - Instituto de Matemáticas, University of Santiago de Compostela. November 14, 2023.

18. "Progress on two general projectivity questions for infinite groups." Algebra Seminar at the University of Birmingham. October 12, 2023.

19. "New generation results for stable module categories of large classes of infinite groups (and their consequences for Balmer spectra)." Homological Algebra and Representation Theory, University of the Aegean, Karlovasi, Samos, Greece. July 10-14, 2023.

20. "Bounded t-structures and the finitistic dimension conjecture." Workshop on Finitistic Dimensions, Universität Bielefeld. June 15-16, 2023.

21. "Two new generation results on stable module categories of infinite groups." Algebra Seminar at West Virginia University. Feb 15, 2023.

2022

22. "Stable categories and complete cohomology for various classes of topological groups". "Geometry & Topology" satellite of the International Congress of Mathematicians, University of Copenhagen. July 6-14, 2022.

23. "Stable categories of rational discrete modules over large classes of topological groups". Groups & Algebras in Bicocca for Young algebraists (GABY), Milan. June 13-17, 2022.

24. "Well-behaved stable categories of discrete modules over large classes of topological groups under cohomological finiteness hypotheses." Al@Bicocca Seminar, Università degli Studi di Milano Bicocca. May 6, 2022.

25. "Generation properties of triangulated categories using cohomological/homotopical invariants." Seminar at Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México (UNAM), Morelia, Michoacán, México. April 29, 2022.

26. "Stable categories of rational discrete modules over large classes of topological groups." Representation Theory and Geometry, Queen's University (Kingston, Ontario) and Royal Military College of Canada. Feb 14-16, 2022.

27. "Cofibrant objects in representation theory - new results and applications." Algebra Seminar, Rutgers University. Feb 2, 2022.

28. "Derived and stable categories of modules over infinite groups." Algebra Seminar, University of Aberdeen. Jan 26, 2022.

29. "Generation results for Gorenstein derived categories." Yau MSC Events Hub, Tsinghua University, Beijing. Jan 19, 2022.

30. "Cofibrant objects in representation theory - new results and applications." MALGA Seminar, Universities of Padova and Verona. Jan 18, 2022.

2021

31. "On the Noetherian-ness (and connectedness) of the Balmer spectra of stable module categories of infinite groups." Lunchtime seminar, University of Southampton. Nov 22, 2021. 

32. "New results on Cofibrants and Gorenstein projectives and applications." Thursday Colloquium, Tata Institute of Fundamental Research, Mumbai. Nov 18, 2021.

33. "Injective generation of the derived category for group algebras." Triangulated Categories in Representation Theory. Nov 11, 2021.

34. "Cohomological Invariants for Infinite Groups and Discrete + TDLC Applications." University of Lincoln. Oct 29, 2021.

35. "New results on the behaviour of a wide range of cohomological (and homotopical) invariants for infinite groups." Algebra Seminar at the University of the Basque Country, Bilbao. Sep 15, 2021. 

36. "Some sufficient algebraic conditions from representation theory for the compactness of the sphere spectrum." Workshop on Homotopy Theory and Group Theory, Centre de Recerca Matematica, Barcelona. July 7, 2021.

37. "New results on the behaviour of a wide range of cohomological (and homotopical) invariants for infinite groups." Oberseminar, Max Planck Institute for Mathematics, Bonn. May 27, 2021. 

38. "Generation of derived and stable categories for groups in Kropholler's hierarchy." Pure Maths Colloquium at Royal Holloway, University of London. Feb 3, 2021.

2020

39.  "Generation of derived and stable categories for groups in Kropholler's hierarchy." Seminar at BIREP (Representations of finite-dimensional algebras at Bielefeld), University of Bielefeld. Dec 11, 2020.

40. "Generation of derived and stable categories for groups in Kropholler's hierarchy." 1st Meeting of "New Directions in Group Theory and Triangulated Categories". Nov 10, 2020.

41. "Cohomological Invariants for Infinite Groups and their Applications." Algebra Seminar, University of Manchester. Nov 3, 2020.

42.  "Cohomological Invariants for a large class of Infinite Groups and their Applications."  Lunchtime Seminar, University of Southampton. Oct 19, 2020.

43. "Generation of unbounded derived categories of modules over groups in Kropholler's hierarchy." Geometry and Topology Online, Warwick Mathematics Institute, University of Warwick. Oct 15, 2020.

44. "Generation of Derived Categories for Groups Lying in Kropholler's Hierarchy." Junior Algebra/Logic/Number Theory Seminar, University of Cambridge. May 15, 2020.

45. "Generating Derived and Stable Categories for families of Infinite Groups." Pure Maths Colloquium, University of Southampton. Feb 21, 2020.

2019

46. "Generation results in algebraic characterisations of Kropholler’s hierarchy and a path to stable module categories." Seminar at Tata Institute of Fundamental Research (TIFR), Mumbai. Dec 23, 2019.

47.  "Generation results in algebraic characterisations of Kropholler’s hierarchy and a path to stable module categories." Seminar at Harish Chandra Research Institute (HRI), Allahabad. Dec 16, 2019.

48.  "Generation results in algebraic characterisations of Kropholler’s hierarchy and a path to stable module categories." Seminar at the Indian Institute of Science Education and Research (IISER), Mohali. Dec 9, 2019.

49.  "Towards an algebraic characterisation of Kropholler’s Hierarchy through some generation results." Algebra Seminar at the University of Lincoln. Sep 17, 2019.

50.  "Generation of modules in Kropholler’s hierarchy." Algebra Seminar, University of Kent. May 17, 2019.

51.  "Towards an algebraic characterisation of Kropholler’s Hierarchy through some generation results." Algebra Seminar, Newcastle University. April 30, 2019.

52.  "Some Results on Generation and Hierarchies of Groups." British Young Mathematicians Colloquium, University of Birmingham. April 17, 2019.

2018

53.  "On Don Zagier’s famous 1-sentence proof." Graduate Student Meeting of the London Mathematical Society, held at BMA House, Tavistock Square, London. June 29, 2018.  

2017

54.  "Settling the differences between different class systems of groups." London Mathematical Society South West and South Wales Regional Meeting, Cardiff University. Dec 13, 2017.

55.  "Relations between certain cohomological invariants of groups and their consequences." British Topology Meeting, University of Leicester. Sep 6-8, 2017.

56.  "Complete Resolutions and Gorenstein Projectives." Groups St. Andrews 2017, University of Birmingham. Aug 5-13, 2017.

57.  "Discussion of open problems on complete resolutions and Gorenstein projectives." Homological Algebra and Topological Groups, University of Southampton. July 10-14. 2017.

58.  "Complete Resolutions and the long road ahead." Graduate Student Meeting of the London Mathematical Society, held at BMA House, Tavistock Square, London. June 29, 2017.

2016

59.  "A theorem of Gauss and a curious classification of primes into classes using a mechanism from its proof." Graduate Student Meeting of the London Mathematical Society, held at UCL, Gower Street, London. July 8, 2016.