Brad Dirks

Contact Info

  • Office: Simonyi Hall S-211
  • Email: bradley.dirks@stonybrook.edu
Biography

I am an NSF post-doc/Simons Instructor at Stony Brook University, mentored by Christian Schnell. For the 2024-2025 academic year, I am a Postdoctoral Member at the Institute for Advanced Study. 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. You can find my CV here.

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 J. Reine Angew. Math.
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 J. Singul.
Upper bounds for roots of B-functions, following Kashiwara and Lichtin (with Mircea Mustaţǎ).
arXiv Publ. Res. Inst. Math. Sci.
On V-filtration, Hodge 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).
arXiv J. Ec. polytech. Math.
Verdier specialization and restrictions of Hodge modules (with Qianyu Chen and Morihiko Saito).
arXiv Math. Z.
Some applications of microlocalization for local complete intersection subvarieties.
Accepted arXiv
An introduction to V-filtrations (with Qianyu Chen and Mircea Mustaţǎ).
arXiv Springer
The minimal exponent of cones over smooth complete intersection projective varieties (with Qianyu Chen and Mircea Mustaţǎ).
arXiv Rev. Roumaine Math. Pures Appl.
Fourier transform and Radon transform for mixed Hodge modules.
Submitted arXiv
Restrictions of Hodge modules using generalized V -filtrations (with Qianyu Chen and Sebastián Olano).
Accepted arXiv
A Hodge theoretic generalization of Q-homology manifolds (with Sebastián Olano and Debaditya Raychaudhury).
Submitted arXiv
Hirzebruch-Milnor classes of local complete intersections, minimal exponent, and applications to higher singularities (with Laurenţiu Maxim and Sebastián Olano).
Submitted arXiv