Luca Casarin

I am currently working in representation theory at Unversity of Rome 1 "La Sapienza" as a post-doc.

e-mail: luca dot casarin at uniroma1.it

Some stuff I wrote

Here is some "serious" stuff that I wrote, not much at the moment.

My bachelor and Master Thesis

• Bachelor Thesis (only in italian): Connessioni Olomorfe su varietà
• Master Thesis: The center of the enveloping algebra of an affine Kac-Moody algebra

Papers

• A Feigin-Frenkel theorem with n singularities - Advances in Mathematics Vol. 434 - arXiv
• A note on the bundle underling Opers - arXiv 2501:08923
• Topological sheaves and spaces of distributions in the global case - Joint with Andrea Maffei - arXiv 2501:08925
• The factorizable Feigin-Frenkel center - Joint with Andera Maffei - arXiv 2501:09589

Talks & Lectures

This is a list of moments in which I talked about math

Research talks

• A Feigin-Frenkel theorem with n singularities. I held various seminars in different occasions where I explained the results of my article "A Feigin Frenkel theorem with n singularities". Respectively: at an international event on infinite dimensional Lie algebras held in Rome, during the conference "Interactions between Mathematics and Physics" in honor of Victor J. Kac and finally at the algebra and geometry seminar at the University of Bologna.

Introductory talks

• A tour of the representation theory of the affine algebra at the critical level, Winter meeting in Algebra and Geometry in Rome 2023.An occasion in which I told the story of the Feigin-Frenkel theorem about the center at the critical level and the Frenkel-Gaitsgory theorem about spherical representations of the affine algebra at the critical level.

Classes

• Cycle of seminars on Geometric representation theory Rome, Spring-Summer 2024. I was the main lecturer of a cycle of seminars on Geometric Representation theory. I introduced basic material with a view towards the Geomtric Langlands Conjectures. We treated mainly treated Geometric Function Theory and the Geometric Satake correspondence.

CV

Here you can find my CV

Extra

Notes

These are some hand-written notes I wrote on various topics on which I gave talks. There is no claim of originality since these are mostly taken from other people's work. They are not fully revised so please excuse me for any typos and mistakes.

• Notes on Local Systems and Connections
• Notes on Tannakian Duality
• Bits of Geometric Function Theory
• Topological algebras and their modules, notes on a seminar I gave at the University of Florence, based on Sam Raskin's work "Homological methods in semi-infinite contexts"