Brad Dirks

Contact Info

  • Office: East Hall 4080
  • Email: bdirks @ umich dot edu
Biography

I am a fifth year PhD candidate at University of Michigan. My advisor is 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. I am always interested to learn more about the above topics. Some other topics which I would like to learn more about include perverse sheaves, singularities in the minimal model program, and singularities in positive characteristic. Please contact me if you would like to chat.

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, though the project was interrupted due to COVID.

Teaching
  • 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 locally complete intersection singularities (with Qianyu Chen, Sebastián Olano and Mircea Mustaţǎ). Submitted
arXiv
Minimal exponents of hyperplane sections: a conjecture of Teissier (with Mircea Mustaţǎ). To appear in J. Eur. Math. Soc.
arXiv
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). To appear in Publ. Res. Inst. Math. Sci.
arXiv
On Hodge Filtration, V-filtration and Fourier Transform (with Qianyu Chen).
Submitted. arXiv