I am a postdoc in the Simons Collaboration on Global Categorical Symmetries supervised by Dan Freed at CMSA. Previously I was a graduate student at Notre Dame working with Chris Schommer-Pries.
📬︎ lorenzo (at) cmsa (dot) fas (dot) harvard (dot) edu
🧮 This year I'm organizing the GCS Student and Postdoc Colloquium with Pranay Gorantla and Zhengdi Sun.
When I'm not doing math I enjoy cooking, reading mystery novels, and solving the New York Times Crossword with my partner Emma Dooley.
I do research in higher categories and topological field theories, and I try to maintain a healthy interest in a variety of other subjects (mainly logic, manifold topology, and some parts of mathematical physics). Here are some questions I have thought about recently:
Is there a simplicial space model for (∞,n)-categories that resembles n-complicial sets? The combinatorics of orientals, which dictates the lifting properties of complicial sets, is pretty complicated; can it be simplified so as to have one "Segal style" condition in every dimension?
How do we freely add adjoints to k-morphisms in an n-category? The cobordism & tangle hypotheses provide an answer for very simple n-categories as long as we add all adjoints at once. What if we only want to add some adjoints? Do we still get cobordisms?
Given a (complete) Segal space, its colimit computes the completion of the associated (∞,1)-category, i.e. the space obtained by inverting all of its morphisms. This space is initial with respect to maps out of the (∞,1)-category that land into the invertible part of the target. Since adjoints can be thought of as lax inverses, is there a context in which the process of freely adding adjoints to an (∞,1)-category can be expressed in terms of a (possibly lax) colimit?
Zigzags and free adjunctions
with Martina Rovelli
arXiv:2510.05371
Higher categories of push-pull spans, II: Matrix factorizations
To appear in Homology, Homotopy and Applications.
arXiv:2409.00219
Higher categories of push-pull spans, I: Construction and applications
Math. Z. 309, 28 (2025).
arXiv:2404.14597, doi:10.1007/s00209-024-03623-4
Low regularity of non-L^2(R^n) local solutions to gMHD-alpha systems
with Nathan Pennington
Electron. J. Differential Equations, Vol. 2020 (2020), No. 54.
arXiv:2005.14130, doi:10.58997/ejde.2020.54
About freely adding adjoints and connections to the cobordism category:
Zigzags and free adjunctions - on some work done with Martina Rovelli, prepared for a seminar at Texas Tech University, November 2025
About the Rozansky-Witten 3-category:
A step towards the Rozansky-Witten TFT - brief overview of my thesis project, prepared for "(∞,n)-Categories and Applications" in Utrecht, April 2024
Longer overviews of my thesis project: an expository version (Rhind seminar, November 2024), a longer expository version (Vienna seminar, May-June 2024), a more categorical version (TUM seminar, September 2024)
Some useful or otherwise interesting links:
Twoples, an online directed reading program for undergraduates ran by Stephen McKean
Harvard's math seminars and events, Notre Dame's math seminars and events, and more
Kerodon, the Clowder Project, and the Stacks project, three online subject-specific encyclopedias