### Julia Elisenda (Eli) Grigsby

Professor

I believe that you (yes you) are a mathematician.

Boston College Math Department

Boston College Math&ML Seminar

### research

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

During Fall 2024, I am teaching a graduate topics course on geometric deep learning theory, focusing on representing computational structures with neural network architectures. A significant portion of the course will focus on mechanistic interpretability of transformers, the architecture underlying large language models. During the period September 3-November 1, my lectures will be held at the Harvard CMSA as part of the Mathematics and Machine Learning program. The webpage for the course, with reading links, is here.

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

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

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.

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 2024

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 URF. Here 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:

So Eun Park, The group of symmetries of the Tower of Hanoi graph, to appear in the American Mathematical Monthly.

Michael Rand, On the Frame-Stewart Algorithm for the Tower of Hanoi

Ian Spafford, Tower of Hanoi research project

Andy Zhang, Properties of the Tower of Hanoi graph for 4 pegs

### 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.

### contact

Eli Grigsby

Boston College Department of Mathematics

5th floor, Maloney

Chestnut Hill, MA 02467-3806

office: 522 Maloney

email: grigsbyjjjjjjjj(at)bc(dot)edu (Ummm...no. 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.)