# Dr Suresh Eswarathasan

Lecturer

*Email:*- eswarathasans@cardiff.ac.uk
*Telephone:*- +44 (0)29 2087 0935
*Fax:*- 029 2087 4199
*Location:*- M/2.53, 2nd Floor, Mathematics Institute, Senghennydd Road, Cardiff, CF24 4AG

### Research Group

### Research Interests

- Microlocal analysis
- differential geometry
- dynamical systems
- geometric measure theory
- partial differential equations

### Personal Website

### Education

Ph.D. under Allan Greenleaf, Mathematics, May 2011

M.A., Mathematics, December 2007

University of Rochester, Rochester, NY.

B.S. Mathematics with Honors and Phi Beta Kappa, Minors in Computer Science and Economics, May 2006

Syracuse University, Syracuse, NY.

**Appointments**

Lecturer (assistant professor with tenure), Cardiff University

Cardiff, Wales, United Kingdom Fall 2015 -

Postdoctoral Fellow, McGill University

Montreal, QC Canada Fall 2014 - Summer 2015

Postdoctoral Fellow/Research member, Institut des Hautes Études Scientiques

Paris, France Fall 2013 - Summer 2014

CRM-ISM Fellowship (joint with Centre de Recherches Mathématiques), McGill University

Montreal, QC Canada Fall 2011 - Summer 2013

### 2018

- Eswarathasan, S. and Silberman, L. 2018. Scarring of quasimodes on hyperbolic manifolds. Nonlinearity 31(1), pp. 1-29. (10.1088/1361-6544/aa92e3)
- Eswarathasan, S. 2018. Tangent nodal sets for random spherical harmonics. arXiv

### 2017

- Eswarathasan, S. and Nonnenmacher, S. 2017. Strong scarring of logarithmic quasimodes. Annales de l'Institut Fourier 67(6), pp. 2307-2347. (10.5802/aif.3137)

### 2016

- Eswarathasan, S., Iosevich, A. and Taylor, K. 2016. Intersections of sets and Fourier analysis. Journal d'Analyse Mathématique 128(1), pp. 159-178. (10.1007/s11854-016-0004-1)
- Eswarathasan, S. 2016. Expected values of eigenfunction periods. Journal of Geometric Analysis 26(1), pp. 360-377. (10.1007/s12220-014-9554-6)

### 2015

- Eswarathasan, S., Polterovich, I. and Toth, J. 2015. Smooth billiards with a large Weyl remainder. Internation Mathematics Research Notices 12, pp. 3639-3677. (10.1093/imrn/rnv256)
- Eswarathasan, S. and Riviere, G. 2015. Perturbations of the Schrodinger equation on negatively curved surfaces. Journal of the Mathematical Institute of Jussieu (10.1017/S1474748015000262)

### 2013

- Eswarathasan, S. and Toth, J. A. 2013. Averaged pointwise bounds for deformations of Schrödinger Eigenfunctions. Annales Henri Poincaré 14(3), pp. 611-637. (10.1007/s00023-012-0198-4)

### 2012

- Eswarathasan, S. 2012. Microlocal analysis of scattering data for nested conormal potentials. Journal of Functional Analysis 262(5), pp. 2100-2141. (10.1016/j.jfa.2011.12.013)

### 2011

- Eswarathasan, S., Iosevich, A. and Taylor, K. 2011. Fourier integral operators, fractal sets, and the regular value theorem. Advances in Mathematics 228(4), pp. 2385-2402.

Fall 2015: MA2002 – Matrix Algebra

Fall 2016: MA2002 - Matrix Algebra, MA3009 - Differential Geometry

**Question: What is “microlocal analysis”?**

Microlocal analysis originated in the study of partial differential equations through the lens of phase space methods, that is, by combining ideas from symplectic geometry and Fourier analysis to investigate qualitative and quantitative properties of PDEs. In particular, the philosophy has lead to major advances in the understanding of linear PDEs in the last 50 years (as can be seen from the now classical four volume treatise The Analysis of Linear Partial Differential Operators I-IV by Lars Hörmander).

`Microlocalisation’ is a process which combines the standard techniques of localisation and Fourier transforms: one localises not only in the space variable x, but as well in the Fourier transform variable p. The resulting space of the variables (x,p) is called the phase space and enjoys the structure of a symplectic manifold. The symplectic geometry of this space and the corresponding Hamiltonian dynamical system are then used to study the original PDE problems. The beauty of the field lies in this interaction between analysis and geometry, hence why I find the adjacent fields of differential geometry, dynamical systems, and geometric measure theory equally as fascinating!

The subject continues to develop to this day and is constantly finding new applications in diverse areas of mathematics, such as the spectral theory of self and non-self adjoint operators, scattering theory, inverse problems in medical imaging, mixing in dynamical systems, and so forth.

For more information on my travel, research lectures/visits, etc. please see my detailed CV on my personal webpage.