Kabeer Manali Rahul

I am currently a postdoc at Bonn where my mentor is Daniel Huybrechts. Before that, I did my PhD at the Australian National University under the supervision of Amnon Neeman. Most of my research is on derived and triangulated categories in the context of algebraic geometry.

I am currently giving a mini-course on approximability and metric techniques for triangulated categories on Wedensdays at 2pm at the MPIM Seminar Hall. You can find the course outline here and the course notes here.

Research

Accepted/Published work

• Integral transforms on singularity categories for Noetherian schemes, with Uttaran Dutta and Pat Lank. Accepted at Mich. Math. J. Preprint avaliable at arXiv:2501.13834.
• Measuring birational derived splinters, with Timothy De Deyn, Pat Lank, and Sridhar Venkatesh. Accepted at Bull. Lon. Math. Soc. Preprint avaliable at arXiv:2510.26648.

Preprints

• Bounded t-structures, finitistic dimensions, and singularity categories of triangulated categories, with Rudradip Biswas, Hongxing Chen, Chris J. Parker, and Junhua Zheng. Preprint available at arXiv:2401.00130.
• Classification and nonexistence results for tensor t-structures on derived categories of schemes, with Alexander Clark, Pat Lank, and Chris J. Parker. Preprint avaliable at arXiv:2404.08578.
• Approximability and Rouquier dimension for noncommuative algebras over schemes, with Timothy De Deyn and Pat Lank. Preprint avaliable at arXiv:2408.04561.
• Descent and generation for noncommutative coherent algebras over schemes, with Timothy De Deyn and Pat Lank. Preprint avaliable at arXiv:2410.01785.
• Integral transforms on singularity categories for Noetherian schemes, with Uttaran Dutta and Pat Lank. Preprint avaliable at arXiv:2501.13834.
• Descending strong generation in algebraic geometry, with Timothy De Deyn and Pat Lank. Preprint avaliable at arXiv:2502.08629.
• Regularity and bounded t-structures for algebraic stacks, with Timothy De Deyn, Pat Lank, and Fei Peng. Preprint avaliable at arXiv:2504.02813.
• Representability theorems via metric techniques. Preprint avaliable at arXiv:2504.11768.
• Admissible subcategories and metric techniques. Available here. Outdated version at arXiv:2504.11772.
• Quasi-perfect blowups detect regularity, with Timothy De Deyn and Pat Lank. Preprint avaliable at arXiv:2508.10845.
• Nonexistence of singly compactly generated t-structures for schemes, with Anirban Bhaduri, Timothy De Deyn, Pat Lank, and Michal Hrbek. Preprint avaliable at arXiv:2511.01622.
• Coherent sheaves in logarithmic geometry, with Hannah Dell, Xianyu Hu, Patrick Kennedy-Hunt, and Maximilian Schimpf. Preprint available at arXiv:2604.05053.

Conferences/Summer schools/masterclasses attended

• Homological Algebra in Algebraic Geometry and Representation Theory, Salerno, 2-6 March 2026
• Tensor Triangular Geometry and Interactions, MFO Oberwolfach, 19-24 October 2025
• Geometric aspects of algebraic varieties, IISER Mohali, 17-19 March 2025
• Tale of Geometries, Université libre de Bruxelles, 28-30 October 2024
• Masterclass on Derived Category Methods in Ring Theory. Aarhus University, 13-16 August 2024.
• Summer School on Interactions between Algebra, Equivariance, and Homotopy Theory. Universität Regensburg, 24-28 June 2024.
• Purity, Approximation Theory and Spectra. Cetraro, 13-17 May 2024.
• Workshop on Finitistic Dimensions. Universität Bielefeld, 15-16 June 2023.
• Categories, clusters, and completions master class. Aarhus University, 22-24 March 2023.
• Tensor Categories in Sydney. University of Sydney, 28 Nov-2nd Dec 2022.

Email: kabeermr “dot” maths “at” gmail “dot” com

Photo by: Rudradip Biswas