Lorenzo Riva

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.

My research at the moment is on a specific combinatorial model for the oriented cobordism higher category and infinity-categorical aspects of that construction. My thesis project concerned 3-dimensional TFTs arising from physics and algebraic geometry. I am also interested in (and motivated by) manifold topology, simplicial methods, and categorical logic. On the side, I enjoy reading mystery novels and cooking.

My email is lorenzo (at) cmsa (dot) fas (dot) harvard (dot) edu.

Papers and preprints

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

Slides

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)

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