Gautam Iyer

Associate Professor, Dept. of Math. Sci., Carnegie Mellon University.

gautam@math.cmu.edu. WEH 6121. 412 268 8419.

Research Interests

Mixing image

My research concerns "Theoretical Applied Math" using tools from partial differential equations and probability. More specifically, I've worked on a variety of problems related to anomalous diffusion, coagulation, fluid mechanics, homogenization, Q-tensors and mixing.

Awards, and Support Acknowledgement

All findings my own and do not necessarily reflect the views of respective funding agencies.

Publications

Recent Publications

  • Y. Feng, G. Iyer, Dissipation Enhancement by Mixing. (2018).
  • S. Cohn, G. Iyer, J. Nolen, R. L. Pego, Anomalous diffusion in one and two dimensional combs. (2018).
  • X. Geng, G. Iyer, Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary. (2018).
  • G. Iyer, N. Leger, R. L. Pego, Coagulation and universal scaling limits for critical Galton-Watson processes, Advances in Applied Probability (2018).
  • G. Iyer, D. Spirn, A model for vortex nucleation in the Ginzburg-Landau equations, Journal of Nonlinear Science (2017).

All Publications

Partial Differential Equations

Probability

  • S. Cohn, G. Iyer, J. Nolen, R. L. Pego, Anomalous diffusion in one and two dimensional combs. (2018).
  • X. Geng, G. Iyer, Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary. (2018).
  • G. Iyer, N. Leger, R. L. Pego, Coagulation and universal scaling limits for critical Galton-Watson processes, Advances in Applied Probability (2018).
  • G. Iyer, D. Spirn, A model for vortex nucleation in the Ginzburg-Landau equations, Journal of Nonlinear Science (2017).
  • M. Hairer, G. Iyer, L. Koralov, A. Novikov, Z. Pajor-Gyulai, A fractional kinetic process describing the intermediate time behaviour of cellular flows, Ann. Probab. (2016).
  • G. Iyer, A. Novikov, Anomalous diffusion in fast cellular flows at intermediate time scales, Probab. Theory Related Fields (2015).
  • G. Iyer, N. Leger, R. L. Pego, Limit theorems for Smoluchowski dynamics associated with critical continuous-state branching processes, Ann. Appl. Probab. (2015).
  • P. Constantin, G. Iyer, A stochastic-Lagrangian approach to the Navier-Stokes equations in domains with boundary, Ann. Appl. Probab. (2011).
  • G. Iyer, A. Novikov, The regularizing effects of resetting in a particle system for the Burgers' equation, Ann. Probab. (2011).
  • G. Iyer, J. C. Mattingly, A stochastic-Lagrangian particle system for the Navier-Stokes equations, Nonlinearity (2008).
  • G. Iyer, A stochastic Lagrangian proof of global existence of the Navier-Stokes equations for flows with small Reynolds number, Ann. Inst. H. Poincaré Anal. Non Linéaire (2009).
  • P. Constantin, G. Iyer, Stochastic Lagrangian transport and generalized relative entropies, Commun. Math. Sci. (2006).
  • G. Iyer, A stochastic Lagrangian formulation of the incompressible Navier-Stokes and related transport equation, Ph.D. Thesis, University of Chicago (2006).
  • P. Constantin, G. Iyer, A stochastic Lagrangian representation of the $3$-dimensional incompressible Navier-Stokes equations, Comm. Pure Appl. Math. (2008).
  • G. Iyer, A Stochastic perturbation of inviscid flows, Comm. Math. Phys. (2006).

Coagulation

  • G. Iyer, N. Leger, R. L. Pego, Coagulation and universal scaling limits for critical Galton-Watson processes, Advances in Applied Probability (2018).
  • G. Iyer, N. Leger, R. L. Pego, Limit theorems for Smoluchowski dynamics associated with critical continuous-state branching processes, Ann. Appl. Probab. (2015).

Fluid Dynamics

Harmonic Analysis

Homogenization

Liquid Crystals

Mixing