My work deals with the applications of triangulated categories to algebraic geometry. This includes interactions with the theories of singularities, algebraic stacks, integral transforms, and noncommutative algebras. See below for details.

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Published:

High Frobenius Pushforwards generate the bounded derived category
Matthew Ballard, Srikanth B. Iyengar, Alapan Mukhopadhyay, Josh Pollitz
arXiv | accepted to Forum Math. Sigma

Integral transforms on singularity categories for Noetherian schemes
Uttaran Dutta, Kabeer Manali-Rahul
arXiv | accepted to Michigan Math. J.

Dévissage for generation in derived categories
Souvik Dey
arXiv | accepted to Proc. Amer. Math. Soc.

Strong generation for module categories
Souvik Dey, Ryo Takahashi
arXiv | J. Pure Appl. Algebra

Closedness of the singular locus and generation for derived categories
Souvik Dey
arXiv | J. of Algebra

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

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

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

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

Generation and dimension for derived categories
PhD thesis, 2024

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In preparation:
Revisiting perfect complexes on algebraic stacks, PDF

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Preprints:

Yoga for Fourier–Mukai partnership
Kabeer Manali-Rahul, Nebojsa Pavic
arXiv

Frobenius generation for algebraic stacks
Fei Peng
arXiv

Nonexistence of singly compactly generated t-structures for schemes
Anirban Bhaduri, Timothy De Deyn, Michal Hrbek, Kabeer Manali-Rahul
arXiv

Measuring (birational) derived splinters
Timothy De Deyn, Kabeer Manali-Rahul, Sridhar Venkatesh
arXiv

A note on quasi-perfect morphisms
Timothy De Deyn, Kabeer Manali-Rahul
arXiv

Simple criteria for higher rational singularities
Sándor Kovács, Sridhar Venkatesh
arXiv

Perfectly generated t-structures for algebraic stacks
arXiv

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

A short note on Du Bois singularities
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

Measuring rationality of Schwede–Takagi pairs
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

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

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Expository:

Chatzistamatiou–Rülling higher vanishing in the non-excellent case, PDF