Mathematical Sciences

Department staff

Dr Claudia Garetto

Photo of Dr Claudia Garetto

Senior Lecturer

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.

Academic career:

  • 2005-2009: Research assistant at Innsbruck University
  • 2010-2012: Junior Research Fellow at Imperial College London
  • Since September 2012: Lecturer at Loughborough University

My research focuses on hyperbolic equations with singularities and/or 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, i.e, how the singularities of the initial data are related to the singularities of the solution. A part of my work is devoted to the problem of multiplying distributions by immersion in a differential algebra (Colombeau algebra). In the recent past I have developed new analytic and functional analytic methods in the Colombeau context: generalised Fourier and pseudodifferential operator theory, microlocal analysis for generalised functions, foundations of topology and functional analysis for Colombeau algebras

  • Member of the London Mathematical Society

Research Grants:

  • Hertha Firnberg Fellowship (FWF): Methods of functional analysis for operators on spaces of Colombeau type (36 months)
  • Junior Research Fellowship (ICL): Generalised Fourier integral operator methods and systems with multiple characteristics (36 months)
  • LMS Scheme 1 grant: Hyperbolic equations: solvability and asymptotic properties.