Francesco Sala

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I am an Associate Professor at the Department of Mathematics of the University of Pisa and a Visiting Scientist at Kavli IPMU (Kavli Institute for the Physics and Mathematics of the Universe), the University of Tokyo, Japan.
I am a member of the Italian interuniversity research group GRT: Geometry and Representation Theory.


I received my Ph.D. in October 2011 from SISSA, Trieste, and the Université Lille (formerly, Université de Lille 1) under the supervision of Ugo Bruzzo and Dimitri Markushevich, respectively. I have held several postdoctoral positions abroad: at the Heriot-Watt University in Edinburgh, UK (2012 - 2014), at the University of Western Ontario in London, Canada (2014 - 2016), and at Kavli IPMU (Kavli Institute for the Physics and Mathematics of the Universe), the University of Tokyo, Japan (2016 - 2019). I was an Assistant Professor (RTDb) at the University of Pisa from 2019 to 2022.


My research interests originate from the interplay between representation theory, algebraic geometry, and mathematical physics. In recent years, I have been focusing on the study of Hall algebras and their refined versions (cohomological, K-theoretical, categorified), and their relation to the theory of quantum groups. For more details, you can check out my publications page or see my full CV here.


My research is partially supported by JSPS KAKENHI Grant-in-Aid for Scientific Research C no. 21K03197. Before, it was partially supported by PRA (Progetti di Ricerca di Ateneo) no. 2020_40 funded by the University of Pisa, JSPS KAKENHI Grant-in-Aid for Young Scientists no. 18K13402, and by JSPS KAKENHI Grant-in-Aid for Research Activity Start-up no. 17H06598.

news

Apr 19, 2024 I will participate in the Workshop on “Ricercatori in Algebra e Geometria 2024” at the Università degli Studi di Milano La Statale, from September 25 to September 27, 2024.
Apr 18, 2024 I will participate in the Workshop on “Hopf algebras and monoidal categories” at the University of Ferrara, from September 3 to September 6, 2024.
Dec 2, 2023 I will participate in the Workshop on “Quantization in Representation Theory, Derived Algebraic Geometry, and Gauge Theory” at the SwissMAP Research Station in Les Diablerets, Switzerland, from September 15 to September 20, 2024.
Dec 2, 2023 I will participate in the Workshop on “Enumerative Invariants, Quantum Fields and String Theory Correspondences” at Institut Mittag-Leffler, Sweden, from July 22 to July 26, 2024.
Dec 1, 2023 I will participate in the Workshop on “Algebraic structures in gauge theory and geometry” at the Lorentz Center, Leiden, The Netherlands, from July 1 to July 5, 2024.

selected publications

  1. JEMS
    Two-dimensional categorified Hall algebras
    Sala, Francesco, and Porta, Mauro
    Journal of the European Mathematical Society  (2023), no. 3, pages 1113–1205
  2. Algebr. Geom.
    Cohomological Hall algebra of Higgs sheaves on a curve
    Sala, Francesco, and Schiffmann, Olivier
    Algebraic Geometry  (2020), no. 3, pages 346–376
  3. Selecta Math. (N.S.)
    The circle quantum group and the infinite root stack of a curve
    Sala, Francesco, and Schiffmann, Olivier
    Selecta Mathematica. New Series  (2019), no. 5, pages Paper No. 77, 86
  4. Adv. Math.
    Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces
    Bruzzo, Ugo, Pedrini, Mattia,  Sala, Francesco, and Szabo, Richard J.
    Advances in Mathematics  (2016), pages 1175–1308
  5. Adv. Math.
    Framed sheaves on projective stacks
    Bruzzo, Ugo, and Sala, Francesco
    Advances in Mathematics  (2015), pages 20–95