Research

My area of research encompasses mathematical quantum field theory, microlocal analysis and stochastic partial differential equations. I study how these topics talk to each other at the interface of analysis, probability and algebra.

Research interests

• Singular stochastic PDEs
• Algebraic quantum field theory
• Algebraic and analytic aspects of renormalization
• Microlocal analysis
• path integral formulation of SDEs

Publications and preprints

• On the stochastic Sine-Gordon model: an interacting field theory approach
  A.B., Claudio Dappiaggi, Paolo Rinaldi
  Communications in Mathematical Physics 405, 288 (2024) DOI

• A microlocal investigation of stochastic partial differential equations for spinors with an application to the Thirring model
  A.B., Beatrice Costeri, Claudio Dappiaggi, Paolo Rinaldi
  Mathematical Physics, Analysis and Geometry 27 (3), 1-52 DOI

• An algebraic correspondence between stochastic differential equations and the Martin-Siggia-Rose formalism
  A.B., Claudio Dappiaggi, Nicolò Drago
  arXiv:2302.10579 [math-ph]

• An Algebraic and Microlocal Approach to the Stochastic Nonlinear Schrödinger Equation
  A.B., Claudio Dappiaggi, Paolo Rinaldi
  Annales Henri Poincaré 24, 2443–2482 (2023) DOI

Other writings

• "Holder-Besov spaces and space-time white noise
  with Fabrizio Zanella. Oberwolfach Reports. Arbeitsgemeinschaft: QFT and Stochastic PDEs (2023) DOI

• Algebraic methods for the perturbative analysis of stochastic equations
  PhD Thesis DOI

Collaborators

• Claudio Dappiaggi, University of Pavia
  
• Nicolò Drago, University of Genova
  
• Paolo Rinaldi, University of Pavia
  
• Lorenzo Zambotti, Sorbonne Université, LPSM
  
• Beatrice Costeri, University of Pavia