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 Christopher 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 Time Crossword with my partner Emma Dooley.
There used to be a little blurb here about my research, but lately I've been thinking about a lot of different things that are somewhat interconnected but that, together, do not really form a cohesive research plan. I spend a lot of time thinking about higher categories, both pluri-dimensional (like n-categories) and homotopical (like (∞,1)-categories): how to build them, their model-independent properties, what they tell us about low-dimensional phenomena, and so on. I am also motivated by manifold topology, logic (categorical and not), and combinatorics. Here are some questions I am pondering:
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?
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.
pdf, arXiv:2005.14130, doi:10.58997/ejde.2020.54
Higher categories of push-pull spans, I: Construction and applications
Math. Z. 309, 28 (2025).
pdf, arXiv:2404.14597, doi:10.1007/s00209-024-03623-4
Higher categories of push-pull spans, II: Matrix factorizations
To appear in Homology, Homotopy and Applications.
pdf, arXiv:2409.00219
Zigzags and free adjunctions
pdf, arXiv:2510.05371
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)
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