Understanding the brain is one of greatest scientific challenges of our time. We still don't know how thoughts emerge from neural activity, how our memories are stored and retrieved, or how our brain so flexibly adapts to new situations.

Meanwhile, today, an equally profound challenge has arisen: understanding the artificial intelligence (AI) that emerges in machines of our own making.

My research shows that these challenges are linked. I show mathematically and empirically that natural and machine intelligence can be studied under a common framework: geometric intelligence.

I founded the Geometric Intelligence Lab where I lead a team of 16: 5 sole-advised Ph.D. students, 4 co-advised at UCSB and peer institutions, 2 visiting Ph.D. students, 3 postdoctoral fellows, and 2 staff. My three postdoctoral alumni hold faculty, research-faculty, and staff scientist positions. I was nominated by my Ph.D. students for UCSB’s Best Graduate Mentor award (2023).

Publications

Visit my lab’s website for an overview of our team, our research and the complete list of our publications.

Open-source Software

I’m dedicated to creating and maintaining open-source scientific infrastructure for the geometric and topological deep learning communities, with three flagship libraries (2,000+ combined GitHub stars) and peer-reviewed software papers in JMLR (2020, 2024) and DMLR (2025).

Geomstats  ·  GitHub  ·  1.5k stars  ·  286 forks

•     Creator and developer. Paper in JMLR (2020). Follow-ups in FTML (2023), TOMS (2023, 2025).

•     Organizer, ICLR Comp. Geometry & Topology Challenges (2021, 2022) — 2022 results in PMLR.

–    27 and 33 international contributors (organizers, reviewers and participants).

TopoX  ·  GitHub  ·  334 stars  ·  103 forks

•     Co-creator and developer (TopoNetX, TopoEmbedX, TopoModelX). Paper in JMLR (2024).

•     Senior co-organizer, ICML Topological Deep Learning Challenges (2023, 2024) — results in PMLR.

–    52 and 73 international contributors (organizers, reviewers and participants).

TopoBench  ·  GitHub  ·  235 stars  ·  77 forks

•     Developer and senior co-mentor. Paper in DMLR (2025).

•     Senior co-mentor, TAG Topological Deep Learning Challenges (2025, 2026) — 2025 results in PMLR.

–    66 international contributors (organizers, reviewers and participants).