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Research Interests:

CV and Research Statement


  1. Efficient algorithms for t-distributed Stochastic Neighborhood Embedding , G. Linderman, M. Rachh, J. Hoskins, S. Steinerberger, and Y. Kluger, arxiv.
  2. On the solution of Stokes equation on regions with corners , M. Rachh, and K. Serkh, Techincal report, YALEU/DCS/TR-1536 (Yale University, New Haven, CT).
  3. A fluctuating boundary integral method for Brownian suspensions, Y. Bao, M. Rachh, E. Keaveny, L. Greengard, and A. Donev, arxiv, submitted.
  4. Integral equation formulation of the biharmonic Dirichlet problem , M. Rachh, and T. Askham, arxiv, Journal of Scientific Computing (2017). doi.
  5. 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.
  6. On the diffusion geometry of Graph Laplacians and applications, X. Cheng, M. Rachh, and S. Steinerberger, arxiv, submitted.
  7. On the location of maxima of solutions of Schrödinger's equation, M. Rachh, S. Steinerberger, arxiv, (to appear in) CPAM.
  8. 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): 235-253.
  9. 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):504-519.
  10. A coarse-grained computational model of the nuclear pore complex predicts Phe-Gly nucleoporin dynamics, J. Pulupa, M. Rachh, M. Tomasini, J. Mincer, and S. Simon, Journal of General Physiology (2017).
  11. 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): 706-731.
  12. Accurate derivative evaluation for any Grad-Shafranov solver, L. Ricketson, A. Cerfon, M. Rachh, and J. Freidberg, arxiv, Journal of Computational Physics 305 (2016): 744-757.
  13. 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): 2889-2909.


  1. Spring 2018: Functional Analysis
  2. Fall 2017: Numerical methods for ordinary and partial differential equations
  3. Spring 2017: Partial differential equations
  4. Fall 2016: Ordinary differential equations
  5. Spring 2016: Integral equations and fast algorithms
  6. Fall 2015: Linear Algebra and its applications