My work deals with the applications of triangulated categories to algebraic geometry. See below for details.

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Publications, preprints, and in preparation:

Compact approximation implies compactly generated aisles for algebraic stacks
Michal Hrbek
In preparation

Comparing Grothendieck groups of mixed Hodge modules and coherent sheaves
Sridhar Venkatesh
In preparation

Numerics and product-compatibility for algebraic stacks
Fei Peng
In preparation

Semistable proxy smallness for schemes
Michal Hrbek, Giovanna Le Gros, Sergio Pavon
In preparation

Thomason condition for regular algebraic stacks
arXiv

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

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

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

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 | J. of Algebra

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

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 | J. Pure Appl. Algebra

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

Generation and dimension for derived categories
PhD thesis, 2024

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Expository:

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

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Lecture notes:
Basque Center for Applied Mathematics, PDF