Dr Claudia Garetto

  • Senior Lecturer
  • E&D coordinator for the Department of Mathematics
  • Personal website
  • I received a PhD in Mathematics from University of Torino (Italy) in 2005. My PhD-studies as well as my thesis has been completed at Institut fur Technische Mathematik, Geometrie und Bauinformatik, University of Innsbruck (Austria). In 2009 I received the Habilitation (venia docendi) at the University of Innsbruck. My research has been funded by FWF (Austrian Science Fund), Imperial College London and EPSRC via two fellowships and one research grant.

    Academic career:

    • 2005-2009: Research fellow at Innsbruck University
    • 2010-2012: Junior Research Fellow at Imperial College London
    • 09/2012-07/2018: Lecturer at Loughborough University
    • Since 08/2018: Senior Lecturer at Loughborough University

    Member of the London Mathematical Society.

    My research focuses on hyperbolic equations and systems with singularities an multiplicities. I use energy estimates or Fourier integral operator techniques to prove well-posedness for the corresponding Cauchy problem in Gevrey classes and spaces of ultradistributions. I am also interested in propagation of singularities and microlocal analysis, i.e, how the singularities of the initial data are related to the singularities of the solution. A part of my work has been devoted to the problem of multiplying distributions by immersion in a differential algebra. In the recent past I have developed new analytic and functional analytic methods in the context of Colombeau algebras: generalised Fourier and pseudodifferential operator theory, microlocal analysis for generalised functions, foundations of topology and functional analysis for Colombeau algebras.

    Research Grants:

    • EP/V005529/1: Hyperbolic problems with discontinuous coefficients (2021-2025)

    • Hertha Firnberg Fellowship (FWF): Methods of functional analysis for operators on spaces of Colombeau type (36 months)
    • Schrödinger Fellowship (FWF) to visit Imperial College London (24 months, declined) 
    • Junior Research Fellowship (ICL): Generalised Fourier integral operator methods and systems with multiple characteristics (36 months)
    • First Grant (EPSRC): Hyperbolic systems with multiplicities (2014-2016)