Brad Dirks

Contact Info

  • Office: Math Tower 4-105
  • Email: bradley.dirks@stonybrook.edu
Biography

I am a Simons Instructor at Stony Brook University, mentored by Christian Schnell, and previously sponsored by the NSF MSPRF. For the 2024-2025 academic year, I was 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 Hodge theory, D-modules and singularities in algebraic geometry.

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
Characterization and finite descent of local cohomological invariants (with Sebastián Olano and Debaditya Raychaudhury).
Submitted arXiv
Partial Cohomologically Complete Intersections via Hodge Theory (with Qianyu Chen and Sebastián Olano).
Submitted arXiv
Hodge theory of secant varieties (with Qianyu Chen, Sebastián Olano and Debaditya Raychaudhury).
Submitted arXiv
Multiplier modules, V-filtrations and Bernstein-Sato polynomials on singular ambient varieties
Submitted arXiv
Hirzebruch-Milnor classes of local complete intersections, minimal exponent, and applications to higher singularities (with Laurenţiu Maxim and Sebastián Olano).
Submitted arXiv
A Hodge theoretic generalization of Q-homology manifolds (with Sebastián Olano and Debaditya Raychaudhury).
Submitted arXiv
Restrictions of Hodge modules using generalized V -filtrations (with Qianyu Chen and Sebastián Olano).
Accepted arXiv
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.
Math. Ann. 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.
Accepted arXiv
The minimal exponent and k-rationality for local complete intersections (with Qianyu Chen and Mircea Mustaţǎ).
arXiv J. Ec. polytech. Math.
V-filtrations and minimal exponents for local complete intersection singularities (with Qianyu Chen, Sebastián Olano and Mircea Mustaţǎ).
arXiv J. Reine Angew. Math.
On V-filtration, Hodge filtration and Fourier Transform (with Qianyu Chen).
arXiv Selecta 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.