Postdoctoral fellow, Mathematical Institute – Georg-August-Universität Göttingen (Germany).

Visiting researcher, Centre for Quantum Mathematics, University of Southern Denmark (Denmark).

Postdoctoral fellow, Aarhus University (Denmark).

Marie Curie Postdoctoral fellow, Center for Quantum Geometry of Moduli Spaces, Aarhus University (Denmark).

Postdoctoral fellow, Department of Mathematics, University of Toronto, (Canada).

Postdoctoral fellow, Max Planck Institute for Mathematics, Bonn (Germany).

University: Radboud Universiteit Nijmegen;

Date and place of doctoral degree: October, 19th 2015, Nijmegen (the Netherlands);

Title of thesis: “The BV formalism for matrix models: a noncommutative geometric approach”;

Supervisors: W. D. van Suijlekom and K. Landsman, Department of Mathematical Physics, Radboud Universiteit Nijmegen;

Doctoral thesis committee:

• G.J. Heckman, Radboud Universiteit Nijmegen (the Netherlands);
• G. Cornelissen, Universiteit Utrecht, (the Netherlands);
• G. Felder, Eidgenössische Technische Hochschule, Zürich (Switzerland);
• M. Marcolli, California Institute of Technology, Pasadena (United States);
• S. Shadrin, Universiteit van Amsterdam (the Netherlands).
  Main Subject: Mathematical Physics.

Topic:
Analysis of gauge theories and mathematical aspects of quantum field theory (more precisely, Batalin-Vilkovisky construction and BRST-quantization procedure), using techniques coming from noncommutative geometry and algebraic geometry. In my thesis, I focused on a family of gauge theories induced by finite spectral triples. For these theories I have first of all computed the BV-extended theory associated, by determining the associated ghost sector and a family of solution to the classical master equation. Then I have computed and determined the associated BV and BRST cohomology complex, the last one obtained from the first by gauge fixing procedure. Finally, I constructed two new spectral triples, one encoding the BV extended theory associated to the gauge theories under analysis and the second accounting for the associated fields required for the performing of a gauge fixing procedure. Finally, an explicit relation between the BRST complex and a new, generalized notion of graded Lie algebra cohomology has been determined and analysed in details. My thesis aimed to settle the basis for the construction of a BV formalism in the context of spectral triples, within the framework of noncommutative geometry.

University: University of Milan (Universitá degli Studi di Milano), Italy;

Date and place of the certificate: July, 20th 2010, Milan (Italy);

Grade: 110/110 summa cum laude;

Title: “F-theory and elliptic fibrations ”;

Supervisors:

• B. van Geemen, Department of Mathematics, University of Milan (Italy);
• S. Cacciatori, Department of Theoretic Physics, Insubria University (Italy).

Main Subject: Mathematics.

Topic:
The use of techniques of complex algebraic geometry to analyse elliptic fibrations as models of Calabi-Yau manifolds, suitable to describe the six compact extra spatial dimensions conjectured in string theory.

University: University of Milan (Universitá degli Studi di Milano), Italy;

Date and place of the certificate: October 2008, Milan (Italy);

Grade: 110/110;

Title: “Cremona transformations ”;

Supervisor: C. Turrini, Department of Mathematics, University of Milan (Italy);

Main Subject: Mathematics.