Welcome!

I am a Senior Lecturer (this is equivalent to Associate Professor) at the School of Mathematics at Cardiff University. I am a member of the Mathematical Analysis group. My research is supported by an EPSRC Early Career Fellowship (EP/N020154/1).

Broadly speaking, I am interested in analysis and partial differential equations. Primarily, I study problems with a strong physical motivation. These include problems in kinetic theory and multiscale problems. I also have a particular interest in the spectral theory associated to these problems, and in particular its applications in ergodic theory and computational complexity.

*NEW* Workshop: Together with Baptiste Morisse we are organizing a workshop planned for 25-29 June 2018, entitled "An Analyst, a Geometer and a Probabilist Walk Into a Bar".

 

EPSRC project website: QUEST: Quantitative Estimates in Spectral Theory and Their Complexity

Conference: In September 2015 I organized a conference entitled "The Cauchy Problem in Kinetic Theory: Recent Progress in Collisionless Models".

Students: I am happy to supervise students in any of the above topics (also see my Research page for more details). Please contact me if you are interested. Click here for a brief description of projects.

 

 


Publications

This is a concise list of my publications and work-in-progress that is near completion. For further details go to Research.
  1. The density of states of fibered self-adjoint operators
    In preparation

  2. A characterisation of operators that can be obtained from finite-dimensional approximations
    In preparation

  3. Uniform convergence in von Neumann's ergodic theorem
    In preparation with C. Mouhot

  4. Arbitrarily large solutions of the Vlasov-Poisson system
    Submitted, 19 pages, 2017 | preprint | arXiv with S. Calogero and S. Pankavich

  5. The density of states of Markov semigroups satisfying a weak Poincaré inequality
    In preparation with A. Einav

  6. The Solvability Complexity Index - Computer Science and Logic Meet Scientific Computing
    Submitted, 15 pages, 2015 | preprint with A. Hansen, O. Nevanlinna and M. Seidel

  7. Instabilities of the relativistic Vlasov-Maxwell system on unbounded domains
    SIAM J. Math. Anal., 49, 4024-4063, 2017 | preprint | postprint | arXiv | journal | doi with T. Holding

  8. Moment bounds on the corrector of stochastic homogenization of non-symmetric elliptic finite difference equations
    Commun. PDE, 42, 179-234, 2017 | preprint | arXiv | journal | doi with D. Marahrens and S. Neukamm

  9. Can everything be computed? - On the Solvability Complexity Index and Towers of Algorithms
    Submitted, 79 pages, 2015 | preprint | arXiv with A. Hansen, O. Nevanlinna and M. Seidel

  10. Approximations of strongly continuous families of unbounded self-adjoint operators
    Commun. Math. Phys., 345, 615-630, 2016 | preprint | arXiv | journal | doi | erratum with T. Holding

  11. New barriers in complexity theory: On The Solvability Complexity Index and Towers of Algorithms
    C. R. Acad. Sci., 353, 931-936, 2015 | preprint | journal | doi with A. Hansen, O. Nevanlinna and M. Seidel

  12. Instabilities in kinetic theory and their relationship to the ergodic theorem
    Contemp. Math., 653, 25-40, 2015 | preprint | arXiv | journal | doi

  13. On the spectrum of shear flows and uniform ergodic theorems
    J. Funct. Anal., 267, 299-322, 2014 | preprint | arXiv | journal | doi

  14. Instability of nonsymmetric nonmonotone equilibria of the Vlasov-Maxwell system
    J. Math. Phys., 52, 123703, 21 pages, 2011 | preprint | arXiv | journal | doi

  15. Instability of nonmonotone magnetic equilibria of the relativistic Vlasov-Maxwell system
    Nonlinearity, 24, 3353-3389, 2011 | preprint | arXiv | journal | doi