I study the mathematical foundations of machine learning algorithms, particularly those involving neural networks. 

During Fall 2023, I am teaching a graduate topics course on geometric/topological aspects of deep learning theory.  Here is the webpage for that course.

In a former life, I studied the interactions between Heegaard Floer homology and Khovanov homology, and applications of both theories to questions about braids, Dehn surgery, and concordance. I still like hearing about what's new in low-dimensional topology and knot theory, but I'm not as up on recent developments as I once was.

In my early days of learning about learning, I blogged about it. You can find that blog here.


My Papers

Here is the poster for Hidden symmetries of ReLU networks (joint w/ K. Lindsey and D. Rolnick), which  appeared at ICML 2023.

Two 50-minute lectures entitled "Neural networks and Boolean functions" and "The topology, geometry, and combinatorics of feedforward neural networks" I gave as part of the Niven Lecture Series at the University of Oregon in May 2023.

A 30-minute general-audience talk on "Geometry and Neural Networks" I gave at the awards ceremony for Math Prize for Girls, October 2022.

I organized a mini-workshop on applications of ML to math as a part of the Braids semester program at ICERM, Spring 2022.

Here is an expository note I wrote for the Notices of the AMS (credit to Siddhi Krishna for the excellent figures).

I organized a mini-workshop on Mathematics & Machine Learning during Fall 2018.

I co-organized a triple-header birthday conference in Berkeley (June 25-29, 2018) starring Abby Thompson (60), with supporting cast members Marty Scharlemann (70) and Rob Kirby (80).

I co-organized the 2016 Hamilton Geometry and Topology Workshop, (August 22-26, 2016), partially supported by my NSF CAREER grant.

I co-organized this topical ICERM workshop (August 4-8, 2014), partially supported by my NSF CAREER grant. See videos of some of the (excellent) talks here! (Under "Programs and Workshops 2014/Summer 2014")

teaching + mentorship

Here is the webpage for MT875: Topics in deep learning theory, Fall 2023.

Here is the website for MT855: Surfaces, braids, and homology-type invariants, Spring 2016.

Here is the website for a graduate reading seminar on the Schoenflies conjecture and generalized property R, co-organized with John Baldwin, Peter Feller, and Josh Greene during spring 2015.

Here is the website for MT831: Algebraic topology and low-dimensional topology, Fall 2014.

Here is the website for MT855: Applications of homology-type invariants in low-dimensional topology, Spring 2014.

Here is the syllabus for MT808: Graduate Algebraic Topology, Fall 2011.

Here is the syllabus for the undergraduate knot theory course I taught at Columbia, Fall 2008.

I directed Lisa Piccirillo in a summer research project on Khovanov homology in the Summer of 2011, funded by a BC URFHere is the poster she created, summarizing her results.

I co-led a 10-week research program for undergraduates with Jason Behrstock at Columbia University in the Summer of 2008.

Some of the students' final papers:

odds + evens

I used to blog about the dangers of parenting while mathing. Nobody has time to read--let alone, compose--long blog posts anymore, so I stopped.

I served as a deputy director of ICERM at Brown from 2018-19.  The programs on Nonlinear Algebra, Illustrating Mathematics, and Braids are the ones I was most heavily involved with.

I have a large mathematical family. (A pic from Rob Kirby's 70th birthday conference at MSRI, August 2008, which I co-organized with Rob Schneiderman, Peter Teichner, and Kevin Walker.)

I am on the board of directors of Girls' Angle, a Cambridge, MA math club for girls that was founded by my undergraduate thesis advisor (and one of my first and most important mentors), Ken Fan.

KEXP is a Seattle-based radio station that everyone should know about.


Eli Grigsby

Boston College Department of Mathematics

5th floor, Maloney

Chestnut Hill, MA 02467-3806

office: 522 Maloney

email: grigsbyjjjjjjjj(at)bc(dot)edu ( Delete all but one of the j's and replace "at" and "dot" with their symbols. IMPORTANT: If you accidentally delete ALL the j's, your e-mail will accidentally go to someone that isn't me.)