Hall algebras and their refined versions (cohomological, K-theoretical, etc), moduli spaces of sheaves, quiver varieties, geometric representation theory, mathematical physics, gauge theory

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]****- 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. [journal], [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. [journal], [arXiv] - Framed sheaves on projective stacks. (with U. Bruzzo.)
*Advances in Mathematics*, volume no. 272, pages 20–95, 2015. [journal], [arXiv] - 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. [journal], [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. [journal], [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. [journal], [arXiv] - Instantons and framed sheaves on Kähler Deligne-Mumford stacks. (with P. Eyssidieux.)
*Annales de la Faculté des Sciences de Toulouse*, to appear. [arXiv] - Hall algebra of the infinite root stack of a curve and a geometric model for \(\mathbf{U}_q\big(\widehat{\mathfrak{sl}}(\mathbb{Q}/\mathbb{Z})\big)\). (with O. Schiffmann.) [arXiv]
- Cohomological Hall algebra of Higgs sheaves on a curve. (with O. Schiffmann.) [arXiv] --- submitted

- Hall algebra of the infinite root stack of a curve and geometric Langlands duality. (with M. Porta and O. Schiffmann.)

- 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]

Updated on February 12th, 2018

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