Pat Lank

I am a postdoctoral research fellow for the Department of Mathematics at Università degli Studi di Milano under the supervision of Amnon Neeman. During April 2024, I was a research associate at the Simons-Laufer Mathematical Sciences Institute. Prior to this, I was a PhD student at the University of South Carolina under the supervision of Matthew Ballard, as well as an M.Sc. student at the University of New Mexico under the supervision of Alexandru Buium.

My work is on algebraic geometry, especially towards singularity theory, using methods from derived categories and homological algebra. See below for details.

A copy of my CV may be found here. See arXiv for a complete list of preprints.

Publications and selected preprints
Germwise singular Fourier--Mukai partnerships
arXiv

Gluing weak approximability along recollements
arXiv

A blowup criterion for regularity
arXiv

Fourier--Mukai loci are open and base change
Elías Guisado Villalgordo
arXiv

Fppf descent and localizing subcategories for algebraic spaces
arXiv

Proxy smallness meets t-structures
Michal Hrbek, Giovanna Le Gros, Sergio Pavon
arXiv

Remarks on diagonal dimension for algebraic stacks
Fei Peng
arXiv

Dualizing complexes and t-structures for algebraic spaces
arXiv

Fiberwise criteria for Fourier--Mukai equivalences
Elías Guisado Villalgordo, Kabeer Manali Rahul, Nebojsa Pavic
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 | Bull. Lond. Math. Soc.

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 spaces
Michal Hrbek, Simone Pizzirani
arXiv

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

Measuring rationality of Schwede--Takagi pairs
Peter McDonald, Sridhar Venkatesh
arXiv | J. Pure Appl. Algebra

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

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

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
Notes
Full faithful loci for integral transforms on algebraic stacks
PDF

Gorensteinness is Fourier--Mukai invariant: A classical approach
PDF

Teaching
University of South Carolina University of New Mexico
A real slice of the quintic Calabi–Yau threefold