Nick Switala

Research Assistant Professor and NSF Postdoctoral Fellow
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

Contact

Address: UIC MSCS Department, 322 SEO (M/C 249), 851 S Morgan Street, Chicago, IL 60607
Telephone: 312-996-5924
Email: nswitala [at] uic [dot] edu
Office: SEO 630

Curriculum Vitae (as of August 2017)

Research

I work in commutative algebra and algebraic geometry. My NSF sponsor is Wenliang Zhang. I received my Ph.D. from the University of Minnesota in 2015. My adviser was Gennady Lyubeznik.

The title of my NSF project is "Local cohomology and D-modules". Here are the project summary and project description with references. My tenure as an NSF postdoctoral fellow began on September 1, 2016.

Here is a list of my papers (see this link for the arXiv preprints):

Lyubeznik numbers for nonsingular varieties,
Bull. London Math. Soc. 47 (1) 1--6, 2015.

Van den Essen's theorem on the de Rham cohomology of a holonomic D-module over a formal power series ring,
Expo. Math. 35 (2) 149--165, 2017.

On the de Rham homology and cohomology of a complete local ring in equicharacteristic zero,
Compos. Math. 153 (10) 2075--2146, 2017.

Duality and de Rham cohomology for graded D-modules (with Wenliang Zhang),
arXiv:1705.00788, submitted, 2017.

A dichotomy for the injective dimension of F-finite F-modules and holonomic D-modules (with Wenliang Zhang),
arXiv:1708.06481, submitted, 2017.

Teaching at UIC

In fall 2016, I taught a 12-lecture mini-course on algebraic D-modules, following the first part of the book by Hotta, Takeuchi, and Tanisaki. Here are the notes from the mini-course.

In spring 2018, I taught Math 310 (Applied Linear Algebra). Here is the final exam from Math 310.

In fall 2018, I will teach Math 520 (Commutative and Homological Algebra). More information will be available here in July or August.

Disclaimer

My work is supported by the National Science Foundation under award number 1604503. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.