My work deals with the applications of triangulated categories to algebraic geometry, including the theories of singularities, algebraic stacks, noncommutative algebras, integral transforms, and (recently) mixed Hodge modules. Please feel free to reach out if you are interested in chatting.

See below for preprints and publications.

Compact approximation and descent for algebraic stacks
Jack Hall, Fei Peng, Alicia Lamarche
arXiv

Vanishing of higher cohomology and cohomological rationality
arXiv

Regularity and bounded t-structures for algebraic stacks
Timothy De Deyn, Kabeer Manali Rahul, Fei Peng
arXiv

Descending strong generation in algebraic geometry
Timothy De Deyn, Kabeer Manali Rahul
arXiv

Integral transforms on singularity categories for Noetherian schemes
Uttaran Dutta, Kabeer Manali Rahul
arXiv

Derived characterizations for rational pairs à la Schwede–Takagi and Kollár–Kovács
Peter McDonald, Sridhar Venkatesh
arXiv

Descent and generation for noncommutative coherent algebras over schemes
Timothy De Deyn, Kabeer Manali Rahul
arXiv

Approximability and Rouquier dimension for noncommuative algebras over schemes
Timothy De Deyn, Kabeer Manali Rahul
arXiv

Triangulated characterizations of singularities
Sridhar Venkatesh
arXiv | Nagoya Math. J.

Classification and nonexistence for t-structures on derived categories of schemes
Alexander Clark, Kabeer Manali Rahul, Chris J. Parker
arXiv

Closedness of the singular locus and generation for derived categories
Souvik Dey
arXiv

Dévissage for generation in derived categories
Souvik Dey
arXiv

Approximation by perfect complexes detects Rouquier dimension
Noah Olander
arXiv | Mosc. Math. J.

Preservation for generation along the structure morphism of coherent algebras over a scheme
Anirban Bhaduri, Souvik Dey
arXiv | Bull. Lond. Math. Soc.

Descent conditions for generation in derived categories
arXiv | J.Pure Appl. Algebra

Strong generation for module categories
Souvik Dey, Ryo Takahashi
arXiv

High Frobenius Pushforwards generate the bounded derived category
Matthew Ballard, Srikanth B. Iyengar, Alapan Mukhopadhyay, Josh Pollitz
arXiv

Generation and dimension for derived categories
PhD thesis, 2024

---

Regular locus and singularity categories for noncommutative algebras over schemes
Timothy De Deyn, Kabeer Manali Rahul
in preparation