Department of Mathematics, University of Notre Dame

Office: B20 Hayes-Healy Center

Email: mperlman@nd.edu

I am a fifth-year Ph.D. student and NSF Graduate Fellow in the Department of Mathematics at the University of Notre Dame. My advisor is Claudiu Raicu.

Previously, I was an undergraduate at the University of Illinois at Chicago.

During academic year 2020-2021 I will be Coleman Postdoctoral Fellow at Queen's University, and starting Fall 2021 I will be Dunham Jackson Assistant Professor (postdoc) at University of Minnesota.

Here is my CV (last updated 2/19/2020).

My interests are in algebraic geometry, commutative algebra, D-modules, and their interactions with representation theory.

I like to study homological invariants of algebraic varieties, including local cohomology, syzygies, and mixed Hodge structure.

More recently, I have been thinking about singularities and invariants arising from birational geometry and the theory of D-modules (e.g. multiplier ideals, Hodge ideals, Bernstein-Sato polynomials).

**Publications and Preprints**

**Hodge ideals for the determinant hypersurface**

(with Mircea Mustaţă and Claudiu Raicu)

In preparation**Relations between the 2 x 2 minors of a generic matrix**

(with Hang Huang, Claudia Polini, Claudiu Raicu, and Alessio Sammartano)

Submitted

[arXiv]**Equivariant D-modules on alternating senary 3-tensors**

(with András C. Lőrincz)

Nagoya Mathematical Journal, DOI:10.1017/nmj.2019.33 (2020)

[arXiv, poster]**Lyubeznik numbers for Pfaffian rings**

Journal of Pure and Applied Algebra 224, no. 5 (2020)

[arXiv]**Computing Schur complexes**

(with Michael K. Brown, Hang Huang, Robert P. Laudone, Claudiu Raicu, Steven V Sam, and João Pedro Santos)

Journal of Software for Algebra and Geometry 9, no. 2: 111-119 (2019)

[arXiv]**Equivariant D-modules on 2 x 2 x 2 hypermatrices**

Journal of Algebra 544: 391-416 (2020)

[arXiv]**Regularity and cohomology of Pfaffian thickenings**

Journal of Commutative Algebra, to appear

[arXiv, poster]

- SchurComplexes.m2

(with Michael K. Brown, Hang Huang, Robert P. Laudone, Claudiu Raicu, Steven V Sam, and João Pedro Santos)

This package computes the Schur complex associated to a partition and a bounded complex of finitely-generated free modules over a commutative ring.

An introduction to the package may be found here. -
PossibleBettiTables.m2

(with Juliette Bruce and Mike Loper)

This package computes all possible Betti tables for zero-dimensional graded modules with a prescribed Hilbert function. - GLmnReps.m2

(with Claudiu Raicu)

This package is for computations with finite-dimensional representations of the general linear Lie superalgebra and syzygies of determinantal thickenings.

- During the Spring 2020 semester, I am teaching assistant for Linear Algebra and Differential Equations. My office hours are held in the Math Help Room (Hurley 153), Wednesday 4-6.
- During the Fall 2019 semester, I am teaching assistant for Linear Algebra and Differential Equations.
- During the Spring 2018 semester, I was teaching assistant for Calculus III.
- During the Fall 2017 semester, I was teaching assistant for Linear Algebra and Differential Equations.

**Upcoming:**

- AMS Sectional Meeting, Commutative Algebra and Connections with Algebraic Geometry, Purdue University, April 2020

**Recent Past**:

- Commutative Algebra Seminar, University of Michigan, November 2019
- AMS Sectional Meeting, Homological and Characteristic p>0 Methods in Commutative Algebra, University of Wisconsin - Madison, September 2019
- Length 3 Resolutions Workshop, UC San Diego, August 2019

**Reading Seminars**:

- Perverse Sheaves (Fall 2019), co-organized with Kostya Timchenko.
- Linkage Theory (Fall 2018, Spring 2019).

I grew up in the suburbs of Chicago (Bartlett, Schaumburg, Buffalo Grove).

Outside of mathematics, I am interested in listening to music (Rock, Hip hop, Techno) and film - I love to talk about movies.

In my free time I enjoy cooking, bicycling, and gardening - before pursuing math, I studied plant biology.

We have a Commutative Algebra and Algebraic Geometry Seminar at Notre Dame.

AMS Notices: What is a Syzygy? - This is a nice essay introducing syzygies.

Commalg.org - Here is a website dedicated to commutative algebra.

Macaulay2 - This is a program for computations in commutative algebra and algebraic geometry.