## 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.
- The density of states of fibered self-adjoint operators
*In preparation*

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

- Uniform
convergence in von Neumann's ergodic
theorem

*In preparation*with C. Mouhot

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

- Weak PoincarĂ© and Nash-type inequalities via density of states estimates

*Submitted*, 12 pages, 2018 | preprint | arXivwith A. Einav

- Arbitrarily large solutions of the Vlasov-Poisson system
, accepted, 19 pages, 2017 | preprint | arXiv*SIAM J. Math. Anal.*with S. Calogero and S. Pankavich

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

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

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

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

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

- Instabilities in
kinetic theory and their relationship to the ergodic theorem

*Contemp. Math.*,**653**, 25-40, 2015 | preprint | arXiv | journal | doi

- On the spectrum
of shear flows and uniform ergodic theorems

*J. Funct. Anal.*,**267**, 299-322, 2014 | preprint | arXiv | journal | doi

- Instability
of
nonsymmetric nonmonotone
equilibria of the Vlasov-Maxwell system

*J. Math. Phys.*,**52**, 123703, 21 pages, 2011 | preprint | arXiv | journal | doi

- Instability of
nonmonotone magnetic
equilibria of the relativistic Vlasov-Maxwell system

*Nonlinearity*,**24**, 3353-3389, 2011 | preprint | arXiv | journal | doi