Research Interests:
 Integral equation methods for the solution of PDEs of mathematical physics
 Analysis of corner singularities in integral equations
 Analysis and evaluation of eigenvalues and eigenfunctions of elliptic PDEs
 Fast algorithms for applications in electrostatics, acoustics, elasticity,
viscous flow, electromagnetics, computational biology, and biomedicine
CV and
Research Statement
Publications:
 Efficient algorithms for tdistributed Stochastic Neighborhood Embedding , G. Linderman,
M. Rachh, J. Hoskins, S. Steinerberger, and Y. Kluger,
arxiv.
 On the solution of Stokes equation on regions with corners ,
M. Rachh, and K. Serkh, Techincal report,
YALEU/DCS/TR1536 (Yale University, New Haven, CT).
 A fluctuating boundary integral method for Brownian suspensions,
Y. Bao,
M. Rachh,
E. Keaveny,
L. Greengard,
and
A. Donev,
arxiv, submitted.
 Integral equation formulation of the biharmonic Dirichlet problem ,
M. Rachh, and T. Askham, arxiv, Journal of Scientific Computing (2017).
doi.
 Optimal Jittered Sampling for two points in the unit square,
F. Pausinger,
M. Rachh, and
S. Steinerberger,
arxiv, (to appear in) Statistics and Probability Letters.
 On the diffusion geometry of Graph Laplacians and applications,
X. Cheng,
M. Rachh, and
S. Steinerberger,
arxiv, submitted.
 On the location of maxima of solutions of
Schrödinger's equation, M. Rachh,
S. Steinerberger,
arxiv, (to appear in) CPAM.
 An efficient high order method for dislocation climb
in two dimensions, S. Jiang, M. Rachh,
and
Y. Xiang, Multiscale Modeling and Simulation 15.1 (2017): 235253.
 An integral equation formulation for rigid bodies in
Stokes flow in three dimensions,
E. Corona,
L. Greengard, M.Rachh, and
S. Veerapaneni,
arxiv, Journal of Computational Physics 332 (2017):504519.

A coarsegrained computational model of the nuclear pore complex predicts PheGly nucleoporin dynamics,
J. Pulupa, M. Rachh, M. Tomasini,
J. Mincer,
and S. Simon,
Journal of General Physiology (2017).
 Fast algorithms for Quadrature by Expansion I:
Globally valid expansions, M. Rachh,
A. Klöckner,
and M. O'Neil,
arxiv, Journal of Computational Physics 345 (2017): 706731.
 Accurate derivative evaluation for any GradShafranov solver,
L. Ricketson,
A. Cerfon, M. Rachh, and
J. Freidberg,
arxiv,
Journal of Computational Physics 305 (2016): 744757.
 Integral equation methods for elastance and mobility
problems in two dimensions,
M. Rachh, and
L. Greengard,
arxiv, SIAM Journal on Numerical Analysis 54.5(2016): 28892909.