Brad Dirks

Contact Info

  • Office: Math Tower 4-101B
  • Email: bradley.dirks@stonybrook.edu
Biography

I am an NSF post-doc/Simons Instructor at Stony Brook University, mentored by Christian Schnell. In Spring 2023, I graduated with a PhD in Mathematics from University of Michigan. My advisor was Mircea Mustaţǎ. Before that, I was an undergraduate student at UCLA. I am interested in algebraic geometry. Specifically, I like to think about Hodge modules and their applications to the study of singularities. Some of the topics I have found most interesting are Hodge Ideals, (generalized) V-filtrations and their interaction with the Hodge filtration of Hodge modules, and Bernstein-Sato polynomials.

At UCLA, I was a mentor in the LA Math Circle (now the ORMC). I have also acted as a mentor in the Michigan Mathematics DRP.

Teaching (at Michigan)
  • Winter 2022: Math 116 (Calc 2)
  • Fall 2021: Math 115 (Calc 1)
  • Fall 2020: Math 115 (Calc 1)
  • Fall 2019: Math 116 (Calc 2)
  • Winter 2019: Math 115 (Calc 1)
  • Fall 2018: Math 105 (Pre-Calc)

Papers
V-filtrations and minimal exponents for local complete intersection singularities (with Qianyu Chen, Sebastián Olano and Mircea Mustaţǎ).
arXiv Crelle's Journal
Minimal exponents of hyperplane sections: a conjecture of Teissier (with Mircea Mustaţǎ).
arXiv J. Eur. Math Soc.
The Hilbert series of Hodge ideals of hyperplane arrangements (with Mircea Mustaţǎ).
arXiv Journal of Singularities
Upper bounds for roots of B-functions, following Kashiwara and Lichtin (with Mircea Mustaţǎ).
arXiv Publ. Res. Inst. Math. Sci.
On Hodge Filtration, V-filtration and Fourier Transform (with Qianyu Chen).
arXiv Selecta Math.
The minimal exponent and k-rationality for local complete intersections (with Qianyu Chen and Mircea Mustaţǎ).
Submitted. arXiv
Verdier specialization and restrictions of Hodge modules (with Qianyu Chen and Morihiko Saito).
Submitted. arXiv
Some applications of microlocalization for local complete intersection subvarieties.
Submitted. arXiv
An introduction to V-filtrations (with Qianyu Chen and Mircea Mustaţǎ).
To appear in Handbook of Geometry and Topology of Singularities, Volume VII arXiv
The minimal exponent of cones over smooth complete intersection projective varieties (with Qianyu Chen and Mircea Mustaţǎ).
arXiv
Fourier transform and Radon transform for mixed Hodge modules.
Submitted arXiv