About me
I am currently a Lecturer in Pure Mathematics at the University of Reading, UK.
My current research has two broad themes: (1) structure of level sets of Laplace eigenfunctions on domains and manifolds
governed by various conjectures e.g. hot spots conjecture, Payne's nodal domain conjecture and Schiffer's conjecture, and
(2) small eigenvalues of Riemannian manfolds.
Other than this, I am also interested in various questions related to the length and angle spectrum of hyperbolic surfaces.
Please feel free to browse my papers below, and do not hesitate to get in touch if you have any question or suggestion.
Here is the link to the analysis seminar at University of Reading.
My CV.
My Phd thesis
Small eigenvalues of hyperbolic surfaces.
- A short note on the Schiffer's conjecture for centrally symmetric convex domains in the plane.
Pre-print.
- Spectral stability of coverings.
with Werner Ballmann.
In preparation.
- A note on the Hot spots property for a class of domains with mixed boundary conditions.
with Chris Judge.
In preparation.
- Small cuspidal eigenvalues of Riemannian surfaces.
with Werner Ballmann.
In preparation.
- Critical hypersurface of Neumann eigenfunctions
with C. Judge.
Submitted.
- Critical points of Laplace eigenfunctions on polygons
with C. Judge.
Published in Comm. in PDE. PDF
- Erratum: Euclidean Triangles have no hot spots.
with C. Judge.
Published in Ann. of Math. PDF
- Euclidean triangles have no hot spots.
with C. Judge.
Published in Ann. of Math. PDF
- Topological properties of eigenfunctions of Riemannian surfaces, Dedicated to Jean-Pierre Otal on his 60th birthday.
Published in Annales de la Facult\'{e} des Sciences de Toulouse.
- Small eigenvalues of Riemannian surfaces- old and new
with Werner Ballmann and Henrik Matthiesen.
Published in ICCM Not.
- An arithmetic property of the set of angles between closed geodesics on hyperbolic surfaces of finite type.
Published in Geometriae Dedicata. PDF
- Rigidity of the length-angle spectrum for closed hyperbolic surfaces.
Submitted. PDF
- On the analytic systole of complete Riemannian surfaces of finite type.
with Werner Ballmann and Henrik Matthiesen.
Published in Geom. and Func. Analysis. PDF
- Small eigenvalues of surfaces of finite typ.
with Werner Ballmann and Henrik Matthiesen.
Published in Comp. Math. PDF
- Geodesics and Nodal sets of eigenfunctions on Hyperbolic manifold.
with C. Judge.
Published in Proc. of AMS. PDF
- Small eigenvalues of closed surface.
with Werner Ballmann and Henrik Matthiesen.
Published in Jour. of Diff. Geom. PDF
- On largeness and multiplicity of the first eigenvalue of finite area hyperbolic surfaces.
Published in Math. Z. PDF
- On topological upper-bounds on the number of small cuspidal eigenvalues of finite area hyperbolic surfaces.
Published in IMRN. PDF
- Systole and $\lambda_{2g-2}$ of closed hyperbolic surfaces of genus g.
Published in Enseign. Math. PDF
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