- CV
## Videos

- Here is a video of myself talking about the flops paper below during the Workshop on Homological Mirror Symmetry: Methods and Structures at the IAS. [video]
- Here is a video of Jørgen Rennemo talking about our work on the Crepant Resolution Conjecture in Donaldson-Thomas theory (joint with Sjoerd Beentjes) during the Structures in Enumerative Geometry workshop at MSRI. [video]
- Here are two videos of Jim Bryan providing background and motivation for his Crepant Resolution Conjecture during the Introductory Workshop: Enumerative Geometry Beyond Numbers at MSRI. [video 1, video 2]
## Papers

- A proof of the Donaldson-Thomas crepant resolution conjecture.
*with Sjoerd Beentjes, Jørgen Rennemo. [pdf]* - Gabriel's theorem and birational geometry.
*with Roberto Pirisi. [pdf]* - Relative Singular Twisted Bondal-Orlov.
*Math. Res. Lett.*(to appear) [pdf] - A note on derived equivalences and birational geometry.
*Bull. Lond. Math. Soc.*[pdf] - Chopping up derived categories.
*[pdf]* - A remark on generators of D(X) and flags.
*Manuscripta Math.*154 (2017), no. 1-2, 275--278. [pdf] -
Derived equivalent Calabi-Yau 3-folds from cubic 4-folds.
*Math. Ann.*365 (2016), no. 1-2, 155-172, with Richard Thomas. [pdf] -
On the Crepant Resolution Conjecture for Donaldson--Thomas invariants.
*J. Algebraic Geom.*25 (2016), no. 1, 1-18. [pdf] -
Donaldson-Thomas invariants and flops.
*J. Reine Angew. Math.*716 (2016), 103-145. [pdf] [erratum] -
Moduli problems in abelian categories and the reconstruction theorem.
*Algebr. Geom.*2 (2015), no. 1, 1-18, with Michael Groechenig. [pdf]

## Teaching

- Fall 17

MATH 465/565 Lie Theory.

MATH 355 Linear Algebra. - Spring 17

MATH 466/566 Introduction to Derived Categories.

MATH 212 Multivariable Calculus. - Fall 14

MATH 465/565 Introduction to Algebraic Geometry.

MATH 354 Honors Linear Algebra. - Spring 14

MATH 390 Undergraduate Colloquium.

MATH 382 Complex Analysis.

## Theses

- In the Hall of the Flop King,
DPhil thesis.

[pdf] This contains some serious mistakes which are addressed in the published papers above. - On a Theorem of Beilinson,
tesi specialistica.

[pdf] An exposition of basics of derived categories and Beilinson's celebrated theorem on D(P^n). - Rivoltare la Sfera,
tesi triennale.

[pdf] A summary of Smale's infamous paper on turning the sphere inside out (in italian).

## Not intended to be published

- whatsaVermaModule.
- Compact groups also have representations.
- Sheaves4Knots.
- The fourth homotopy group of the sphere.
- Sheaves, covering spaces, monodromy and an application.
- Points and reconstructions.
- Flops and DT invariants.
- Introduction to derived categories.
- The Atiyah-Guillemin-Sternberg theorem.