CV
Grants
My research was partially supported by JSPS KAKENHI Grant-in-Aid for Young Scientists no. 18K13402 and by JSPS KAKENHI Grant-in-Aid for Research Activity Start-up no. 17H06598.
Research Interests
Representation theory, algebraic geometry, and mathematical physics. At the moment I am dealing with
- 2-dimensional categorified Hall algebras of quivers, curves, and surfaces, and their representation theories (see, e.g., a talk on February 2019 at the Perimeter Institute for Theoretical Physics);
- cohomological Hall algebra of Higgs sheaves on a curve \(X\) and its geometric actions on moduli spaces of sheaves on \(T^\ast X\) (see, e.g., an older talk on February 2017 at the Perimeter Institute for Theoretical Physics);
- continuum Kac-Moody Lie algebras and their quantization; and
- moduli spaces of (either framed or semistable) sheaves on surfaces, and four-dimensional supersymmetric gauge theories.
Submitted Preprints
Publications
- Quantization of continuum Kac-Moody algebras (with A. Appel), to appear in Pure and Applied Mathematics Quarterly. [arXiv]
- Cohomological Hall algebra of Higgs sheaves on a curve (with O. Schiffmann), to appear in Algebraic Geometry (Foundation Compositio Mathematica). [arXiv]
- Fock space representation of the circle quantum group (with O. Schiffmann), International Mathematics Research Notices, IMRN, 2019. [IMRN], [arXiv]
- The circle quantum group and the infinite root stack of a curve (with O. Schiffmann and with an appendix by T. Kuwagaki), Selecta Mathematica, 2019. [Selecta], [arXiv]
- Instantons and framed sheaves on Kähler Deligne-Mumford stacks (with P. Eyssidieux), Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série 6, volume no. 27, issue no. 3, pages 599-628, 2018. [Ann.Toulouse], [arXiv]
- AGT relations for abelian quiver gauge theories on ALE spaces (with M. Pedrini and R. J. Szabo), Journal of Geometry and Physics, volume no. 103, pages 43-89, 2016. [J.Geom.Phys.], [arXiv]
- Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces (with U. Bruzzo, M. Pedrini and R. J. Szabo), Advances in Mathematics, volume no. 288, pages 1175-1308, 2016. [Advances], [arXiv]
- \(\mathcal{N}=2\) quiver gauge theories on A-type ALE spaces (with U. Bruzzo and R. J. Szabo), Letters in Mathematical Physics, volume no. 105, issue no. 3, pages 401-445, 2015. [Lett.Math.Phys.], [arXiv]
- Framed sheaves on projective stacks (with U. Bruzzo and with an appendix by M. Pedrini), Advances in Mathematics, volume no. 272, pages 20–95, 2015. [Advances], [arXiv]
- Restriction theorems for \(\mu\)-(semi)stable framed sheaves. Journal of Pure and Applied Algebra, volume no. 217, issue no. 12, pages 2320-2344, 2013. [J.Pure.Appl.Algebra], [arXiv]
- Symplectic structures on moduli spaces of framed sheaves on surfaces. Central European Journal of Mathematics, volume no. 10, issue no. 4, pages 1455-1471, 2012. [Cent.Eur.J.], [arXiv]
Thesis
- Some topics in the geometry of framed sheaves and their moduli spaces. Ph.D. Dissertation. SISSA (Trieste, Italy) and Université Lille 1 (France), 2011. [pdf]
Editorial Work
- Editor (with U. Bruzzo and A. Grassi). Geometric Representation Theory and Gauge Theory. Cetraro, Italy 2018. Lecture Notes in Mathematics. C.I.M.E. Foundation Subseries. Springer, 2019. [journal]
- Special Issue Managing Editor. Interactions between Geometry and Physics: A special issue in honor of Ugo Bruzzo’s 60th birthday. Journal of Geometry and Physics. [journal]
- Guest Editor (with U. Bruzzo). Special issue Instanton Counting: Moduli Spaces, Representation Theory and Integrable Systems. Journal of Geometry and Physics. [journal]
Collaborators
- Andrea Appel (Università di Parma, Italy)
- Ugo Bruzzo (SISSA, Trieste, Italy)
- Philippe Eyssidieux (Institut Fourier, Grenoble, France)
- Tatsuki Kuwagaki (Kavli IPMU, Tokyo, Japan)
- Mattia Pedrini (Milan, Italy)
- Mauro Porta (Université de Strasbourg, France)
- Olivier Schiffmann (CNRS and Université de Paris-Sud, France)
- Richard J. Szabo (Heriot-Watt University, Edinburgh, UK)
Visitors
2019: Andrea Appel (University of Edinburgh, UK), Sjoerd Beentjes (University of Edinburgh, UK), Ben Davison (University of Edinburgh, UK), Andrea d'Agnolo (University of Padova, Italy), Tudor Dimofte (UC Davis, USA), Iordan Ganev (IST, Austria), Sam Gunningham (University of Edinburgh, UK), Anton Mellit (University of Vienna, Austria), Andrei Negut (MIT, USA), Mauro Porta (Université de Strasbourg, France), Alexander Schmitt (Freie Universität Berlin, Germany), Valerio Toledano Laredo (Northeastern University, USA).
2018: Andrea Appel (University of Edinburgh, UK), Ugo Bruzzo (SISSA, Trieste, Italy), Pedram Hekmati (University of Auckland, New Zealand), Victoria Hoskins (Freie Universität Berlin, Germany), Mauro Porta (Université de Strasbourg, France), Olivier Schiffmann (Université de Paris-Sud Orsay, France), Mattia Talpo (Simon Fraser University, Canada), Fabio Tanturri (Université de Lille, France).
2017: Ben Davison (University of Glasgow, UK), Antonio Lerario (SISSA, Trieste, Italy), Sven Meinhardt (University of Sheffield, UK), Andrei Negut (MIT, USA).
2018: Andrea Appel (University of Edinburgh, UK), Ugo Bruzzo (SISSA, Trieste, Italy), Pedram Hekmati (University of Auckland, New Zealand), Victoria Hoskins (Freie Universität Berlin, Germany), Mauro Porta (Université de Strasbourg, France), Olivier Schiffmann (Université de Paris-Sud Orsay, France), Mattia Talpo (Simon Fraser University, Canada), Fabio Tanturri (Université de Lille, France).
2017: Ben Davison (University of Glasgow, UK), Antonio Lerario (SISSA, Trieste, Italy), Sven Meinhardt (University of Sheffield, UK), Andrei Negut (MIT, USA).
Other Links
Updated on February 9th, 2020
