Research Interests
I use tools from partial differential equations and probability to study a variety of problems. A few topics of current interest are the interaction between mixing and diffusion, and high dimensional sampling problems. Other topics I've worked on recently include anomalous diffusion, anomalous dissipation, BoseβEinstein condensation, coagulation, fluid mechanics, homogenization, the Kompaneets equation, mixing, Q-tensors, and residual diffusion.
Awards, and Support Acknowledgement
- Individual NSF grants: 2024β27, 2021β25, 2018β22, CAREER 2013β18, 2010β14, 2009β11, 2007β09.
- Collaborative NSF grants: RTG 2024β29, HCC Medium 2022β26.
- Simons Fellow (2016-17)
- Alfred P. Sloan research fellowship (2013-15).
- The Center for Nonlinear Analysis
All findings my own and do not necessarily reflect the views of respective funding agencies.
Publications
β’ MathSciNet Profile β’ Arxiv Publications
Recent Publications
- R. Han, G. Iyer, D. SlepΔev, Polynomial complexity sampling from multimodal distributions using Sequential Monte Carlo. (2025).
- W. Cooperman, G. Iyer, K. Rowan, S. Son, Exponentially mixing flows with slow enhanced dissipation. (2025).
- W. Cooperman, G. Iyer, J. Nolen, Residual Diffusivity for Expanding Bernoulli Maps. (2025).
- G. Iyer, J. Nolen, Residual diffusivity for noisy Bernoulli maps. (2024).
- W. Cooperman, G. Iyer, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert, Nonlinearity (2024).
- M. Coti Zelati, G. Crippa, G. Iyer, A. Mazzucato, Mixing in Incompressible Flows: Transport, dissipation and their interplay, AMS Notices (2024).
- A. Christie, Y. Feng, G. Iyer, A. Novikov, Speeding up Langevin Dynamics by Mixing. (2023).
- G. Iyer, E. Lu, J. Nolen, Using Bernoulli maps to accelerate mixing of a random walk on the torus, Quarterly of Applied Mathematics (2024).
- G. Iyer, H. Zhou, Quantifying the dissipation enhancement of cellular flows, SIAM J. Math. Anal. (2023).
- J. Ballew, G. Iyer, C. D. Levermore, H. Liu, R. Pego, Global Dynamics and Photon Loss in the Kompaneets Equation, SIAM J. Math Anal (2023).
All Publications
- R. Han, G. Iyer, D. SlepΔev, Polynomial complexity sampling from multimodal distributions using Sequential Monte Carlo. (2025).
- W. Cooperman, G. Iyer, K. Rowan, S. Son, Exponentially mixing flows with slow enhanced dissipation. (2025).
- W. Cooperman, G. Iyer, J. Nolen, Residual Diffusivity for Expanding Bernoulli Maps. (2025).
- G. Iyer, J. Nolen, Residual diffusivity for noisy Bernoulli maps. (2024).
- W. Cooperman, G. Iyer, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert, Nonlinearity (2024).
- M. Coti Zelati, G. Crippa, G. Iyer, A. Mazzucato, Mixing in Incompressible Flows: Transport, dissipation and their interplay, AMS Notices (2024).
- A. Christie, Y. Feng, G. Iyer, A. Novikov, Speeding up Langevin Dynamics by Mixing. (2023).
- G. Iyer, E. Lu, J. Nolen, Using Bernoulli maps to accelerate mixing of a random walk on the torus, Quarterly of Applied Mathematics (2024).
- G. Iyer, H. Zhou, Quantifying the dissipation enhancement of cellular flows, SIAM J. Math. Anal. (2023).
- J. Ballew, G. Iyer, C. D. Levermore, H. Liu, R. Pego, Global Dynamics and Photon Loss in the Kompaneets Equation, SIAM J. Math Anal (2023).
- G. Crippa, T. Elgindi, G. Iyer, A. Mazzucato, Growth of Sobolev norms and loss of regularity in transport equations, Philosophical Transactions of the Royal Society A (2021).
- C. Gomez, G. Iyer, H. Le, A. Novikov, An oscillator driven by algebraically decorrelating noise, Commun. Math. Phys. (2023).
- G. Iyer, S. Van, Bounds on the heat transfer rate via passive advection, SIAM J. Math. Anal. (2021).
- Y. Feng, G. Iyer, L. Li, Scheduling fixed length quarantines to minimize the total number of fatalities during an epidemic, Journal of Mathematical Biology (2020).
- Y. Feng, Y. Feng, G. Iyer, J.-L. Thiffeault, Phase separation in the advective Cahn--Hilliard equation, Journal of Nonlinear Science (2019).
- T. Drivas, T. M. Elgindi, G. Iyer, I.-J. Jeong, Anomalous Dissipation in Passive Scalar Transport, Archive for Rational Mechanics and Analysis (2019).
- G. Iyer, X. Xu, A. ZlatoΕ‘, Convection-Induced Singularity Suppression in the Keller-Segel and Other Non-linear PDEs, Transactions of the American Mathematical Society (2019).
- Y. Feng, G. Iyer, Dissipation Enhancement by Mixing, Nonlinearity (2019).
- S. Cohn, G. Iyer, J. Nolen, R. L. Pego, Anomalous diffusion in one and two dimensional combs, Commun. Math. Sci. (2018).
- X. Geng, G. Iyer, Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary, ALEA (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).
- J. Ballew, G. Iyer, R. L. Pego, Bose-Einstein condensation in a Hyperbolic model for the Kompaneets Equation, SIAM J. Math. Anal. (2016).
- G. Gie, C. Henderson, G. Iyer, L. Kavalie, J. P. Whitehead, Stability of vortex solutions to an extended Navier-Stokes system, Commun. Math. Sci. (2016).
- G. Iyer, A. Novikov, Anomalous diffusion in fast cellular flows at intermediate time scales, Probab. Theory Related Fields (2015).
- G. Iyer, X. Xu, A. D. Zarnescu, Dynamic Cubic Instability in a 2D Q-tensor Model for Liquid Crystals, Math. Models Methods Appl. Sci (2015).
- G. Iyer, A. Kiselev, X. Xu, Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows, Nonlinearity (2014).
- M. Ignatova, G. Iyer, J. P. Kelliher, R. L. Pego, A. D. Zarnescu, Global existence for two extended Navier-Stokes systems, Commun. Math. Sci. (2015).
- G. Iyer, N. Leger, R. L. Pego, Limit theorems for Smoluchowski dynamics associated with critical continuous-state branching processes, Ann. Appl. Probab. (2015).
- G. Iyer, R. L. Pego, A. D. Zarnescu, Coercivity and stability results for an extended Navier-Stokes system, J. Math Physics (2012).
- G. Iyer, K. C. Zygalakis, Numerical studies of homogenization under a fast cellular flow, SIAM Multiscale Model. Simul. (2012).
- G. Iyer, T. Komorowski, A. Novikov, L. Ryzhik, From homogenization to averaging in cellular flows, Ann. Inst. H. PoincarΓ© Anal. Non LinΓ©aire (2014).
- 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, L. Ryzhik, A. ZlatoΕ‘, Exit times for diffusions with incompressible drift, SIAM J. Math. Anal. (2010).
- G. Iyer, A. Novikov, The regularizing effects of resetting in a particle system for the Burgers' equation, Ann. Probab. (2011).
- P. Constantin, G. Iyer, J. Wu, Global regularity for a modified critical dissipative quasi-geostrophic equation, Indiana Univ. Math. J. (2008).
- 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. PoincarΓ© Anal. Non LinΓ©aire (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, Commun. Math. Phys. (2006).
- G. Iyer, Transport in viscous rotating fluids, Commun. Math. Sci. (2004).
Partial Differential Equations
- R. Han, G. Iyer, D. SlepΔev, Polynomial complexity sampling from multimodal distributions using Sequential Monte Carlo. (2025).
- W. Cooperman, G. Iyer, K. Rowan, S. Son, Exponentially mixing flows with slow enhanced dissipation. (2025).
- W. Cooperman, G. Iyer, J. Nolen, Residual Diffusivity for Expanding Bernoulli Maps. (2025).
- G. Iyer, J. Nolen, Residual diffusivity for noisy Bernoulli maps. (2024).
- W. Cooperman, G. Iyer, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert, Nonlinearity (2024).
- M. Coti Zelati, G. Crippa, G. Iyer, A. Mazzucato, Mixing in Incompressible Flows: Transport, dissipation and their interplay, AMS Notices (2024).
- A. Christie, Y. Feng, G. Iyer, A. Novikov, Speeding up Langevin Dynamics by Mixing. (2023).
- G. Iyer, H. Zhou, Quantifying the dissipation enhancement of cellular flows, SIAM J. Math. Anal. (2023).
- J. Ballew, G. Iyer, C. D. Levermore, H. Liu, R. Pego, Global Dynamics and Photon Loss in the Kompaneets Equation, SIAM J. Math Anal (2023).
- G. Crippa, T. Elgindi, G. Iyer, A. Mazzucato, Growth of Sobolev norms and loss of regularity in transport equations, Philosophical Transactions of the Royal Society A (2021).
- G. Iyer, S. Van, Bounds on the heat transfer rate via passive advection, SIAM J. Math. Anal. (2021).
- Y. Feng, G. Iyer, L. Li, Scheduling fixed length quarantines to minimize the total number of fatalities during an epidemic, Journal of Mathematical Biology (2020).
- Y. Feng, Y. Feng, G. Iyer, J.-L. Thiffeault, Phase separation in the advective Cahn--Hilliard equation, Journal of Nonlinear Science (2019).
- T. Drivas, T. M. Elgindi, G. Iyer, I.-J. Jeong, Anomalous Dissipation in Passive Scalar Transport, Archive for Rational Mechanics and Analysis (2019).
- G. Iyer, X. Xu, A. ZlatoΕ‘, Convection-Induced Singularity Suppression in the Keller-Segel and Other Non-linear PDEs, Transactions of the American Mathematical Society (2019).
- Y. Feng, G. Iyer, Dissipation Enhancement by Mixing, Nonlinearity (2019).
- S. Cohn, G. Iyer, J. Nolen, R. L. Pego, Anomalous diffusion in one and two dimensional combs, Commun. Math. Sci. (2018).
- X. Geng, G. Iyer, Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary, ALEA (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).
- J. Ballew, G. Iyer, R. L. Pego, Bose-Einstein condensation in a Hyperbolic model for the Kompaneets Equation, SIAM J. Math. Anal. (2016).
- G. Gie, C. Henderson, G. Iyer, L. Kavalie, J. P. Whitehead, Stability of vortex solutions to an extended Navier-Stokes system, Commun. Math. Sci. (2016).
- G. Iyer, A. Novikov, Anomalous diffusion in fast cellular flows at intermediate time scales, Probab. Theory Related Fields (2015).
- G. Iyer, X. Xu, A. D. Zarnescu, Dynamic Cubic Instability in a 2D Q-tensor Model for Liquid Crystals, Math. Models Methods Appl. Sci (2015).
- G. Iyer, A. Kiselev, X. Xu, Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows, Nonlinearity (2014).
- M. Ignatova, G. Iyer, J. P. Kelliher, R. L. Pego, A. D. Zarnescu, Global existence for two extended Navier-Stokes systems, Commun. Math. Sci. (2015).
- G. Iyer, N. Leger, R. L. Pego, Limit theorems for Smoluchowski dynamics associated with critical continuous-state branching processes, Ann. Appl. Probab. (2015).
- G. Iyer, R. L. Pego, A. D. Zarnescu, Coercivity and stability results for an extended Navier-Stokes system, J. Math Physics (2012).
- G. Iyer, K. C. Zygalakis, Numerical studies of homogenization under a fast cellular flow, SIAM Multiscale Model. Simul. (2012).
- G. Iyer, T. Komorowski, A. Novikov, L. Ryzhik, From homogenization to averaging in cellular flows, Ann. Inst. H. PoincarΓ© Anal. Non LinΓ©aire (2014).
- 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, L. Ryzhik, A. ZlatoΕ‘, Exit times for diffusions with incompressible drift, SIAM J. Math. Anal. (2010).
- G. Iyer, A. Novikov, The regularizing effects of resetting in a particle system for the Burgers' equation, Ann. Probab. (2011).
- P. Constantin, G. Iyer, J. Wu, Global regularity for a modified critical dissipative quasi-geostrophic equation, Indiana Univ. Math. J. (2008).
- 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. PoincarΓ© Anal. Non LinΓ©aire (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, Commun. Math. Phys. (2006).
- G. Iyer, Transport in viscous rotating fluids, Commun. Math. Sci. (2004).
Probability
- R. Han, G. Iyer, D. SlepΔev, Polynomial complexity sampling from multimodal distributions using Sequential Monte Carlo. (2025).
- W. Cooperman, G. Iyer, K. Rowan, S. Son, Exponentially mixing flows with slow enhanced dissipation. (2025).
- W. Cooperman, G. Iyer, J. Nolen, Residual Diffusivity for Expanding Bernoulli Maps. (2025).
- G. Iyer, J. Nolen, Residual diffusivity for noisy Bernoulli maps. (2024).
- W. Cooperman, G. Iyer, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert, Nonlinearity (2024).
- A. Christie, Y. Feng, G. Iyer, A. Novikov, Speeding up Langevin Dynamics by Mixing. (2023).
- G. Iyer, E. Lu, J. Nolen, Using Bernoulli maps to accelerate mixing of a random walk on the torus, Quarterly of Applied Mathematics (2024).
- C. Gomez, G. Iyer, H. Le, A. Novikov, An oscillator driven by algebraically decorrelating noise, Commun. Math. Phys. (2023).
- G. Iyer, S. Van, Bounds on the heat transfer rate via passive advection, SIAM J. Math. Anal. (2021).
- S. Cohn, G. Iyer, J. Nolen, R. L. Pego, Anomalous diffusion in one and two dimensional combs, Commun. Math. Sci. (2018).
- X. Geng, G. Iyer, Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary, ALEA (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. PoincarΓ© Anal. Non LinΓ©aire (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, Commun. 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
- W. Cooperman, G. Iyer, K. Rowan, S. Son, Exponentially mixing flows with slow enhanced dissipation. (2025).
- W. Cooperman, G. Iyer, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert, Nonlinearity (2024).
- M. Coti Zelati, G. Crippa, G. Iyer, A. Mazzucato, Mixing in Incompressible Flows: Transport, dissipation and their interplay, AMS Notices (2024).
- G. Iyer, H. Zhou, Quantifying the dissipation enhancement of cellular flows, SIAM J. Math. Anal. (2023).
- Y. Feng, Y. Feng, G. Iyer, J.-L. Thiffeault, Phase separation in the advective Cahn--Hilliard equation, Journal of Nonlinear Science (2019).
- T. Drivas, T. M. Elgindi, G. Iyer, I.-J. Jeong, Anomalous Dissipation in Passive Scalar Transport, Archive for Rational Mechanics and Analysis (2019).
- G. Iyer, X. Xu, A. ZlatoΕ‘, Convection-Induced Singularity Suppression in the Keller-Segel and Other Non-linear PDEs, Transactions of the American Mathematical Society (2019).
- Y. Feng, G. Iyer, Dissipation Enhancement by Mixing, Nonlinearity (2019).
- G. Gie, C. Henderson, G. Iyer, L. Kavalie, J. P. Whitehead, Stability of vortex solutions to an extended Navier-Stokes system, Commun. Math. Sci. (2016).
- M. Ignatova, G. Iyer, J. P. Kelliher, R. L. Pego, A. D. Zarnescu, Global existence for two extended Navier-Stokes systems, Commun. Math. Sci. (2015).
- G. Iyer, R. L. Pego, A. D. Zarnescu, Coercivity and stability results for an extended Navier-Stokes system, J. Math Physics (2012).
- 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).
- P. Constantin, G. Iyer, J. Wu, Global regularity for a modified critical dissipative quasi-geostrophic equation, Indiana Univ. Math. J. (2008).
- 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. PoincarΓ© Anal. Non LinΓ©aire (2009).
- 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, Commun. Math. Phys. (2006).
- G. Iyer, Transport in viscous rotating fluids, Commun. Math. Sci. (2004).
Harmonic Analysis
- P. Constantin, G. Iyer, J. Wu, Global regularity for a modified critical dissipative quasi-geostrophic equation, Indiana Univ. Math. J. (2008).
Homogenization
- W. Cooperman, G. Iyer, J. Nolen, Residual Diffusivity for Expanding Bernoulli Maps. (2025).
- G. Iyer, J. Nolen, Residual diffusivity for noisy Bernoulli maps. (2024).
- C. Gomez, G. Iyer, H. Le, A. Novikov, An oscillator driven by algebraically decorrelating noise, Commun. Math. Phys. (2023).
- G. Iyer, S. Van, Bounds on the heat transfer rate via passive advection, SIAM J. Math. Anal. (2021).
- G. Iyer, X. Xu, A. ZlatoΕ‘, Convection-Induced Singularity Suppression in the Keller-Segel and Other Non-linear PDEs, Transactions of the American Mathematical Society (2019).
- S. Cohn, G. Iyer, J. Nolen, R. L. Pego, Anomalous diffusion in one and two dimensional combs, Commun. Math. Sci. (2018).
- 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, K. C. Zygalakis, Numerical studies of homogenization under a fast cellular flow, SIAM Multiscale Model. Simul. (2012).
- G. Iyer, T. Komorowski, A. Novikov, L. Ryzhik, From homogenization to averaging in cellular flows, Ann. Inst. H. PoincarΓ© Anal. Non LinΓ©aire (2014).
Liquid Crystals
- G. Iyer, X. Xu, A. D. Zarnescu, Dynamic Cubic Instability in a 2D Q-tensor Model for Liquid Crystals, Math. Models Methods Appl. Sci (2015).
Mixing
- W. Cooperman, G. Iyer, K. Rowan, S. Son, Exponentially mixing flows with slow enhanced dissipation. (2025).
- W. Cooperman, G. Iyer, J. Nolen, Residual Diffusivity for Expanding Bernoulli Maps. (2025).
- G. Iyer, J. Nolen, Residual diffusivity for noisy Bernoulli maps. (2024).
- W. Cooperman, G. Iyer, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert, Nonlinearity (2024).
- M. Coti Zelati, G. Crippa, G. Iyer, A. Mazzucato, Mixing in Incompressible Flows: Transport, dissipation and their interplay, AMS Notices (2024).
- A. Christie, Y. Feng, G. Iyer, A. Novikov, Speeding up Langevin Dynamics by Mixing. (2023).
- G. Iyer, E. Lu, J. Nolen, Using Bernoulli maps to accelerate mixing of a random walk on the torus, Quarterly of Applied Mathematics (2024).
- G. Iyer, H. Zhou, Quantifying the dissipation enhancement of cellular flows, SIAM J. Math. Anal. (2023).
- G. Crippa, T. Elgindi, G. Iyer, A. Mazzucato, Growth of Sobolev norms and loss of regularity in transport equations, Philosophical Transactions of the Royal Society A (2021).
- Y. Feng, Y. Feng, G. Iyer, J.-L. Thiffeault, Phase separation in the advective Cahn--Hilliard equation, Journal of Nonlinear Science (2019).
- T. Drivas, T. M. Elgindi, G. Iyer, I.-J. Jeong, Anomalous Dissipation in Passive Scalar Transport, Archive for Rational Mechanics and Analysis (2019).
- G. Iyer, X. Xu, A. ZlatoΕ‘, Convection-Induced Singularity Suppression in the Keller-Segel and Other Non-linear PDEs, Transactions of the American Mathematical Society (2019).
- G. Iyer, A. Kiselev, X. Xu, Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows, Nonlinearity (2014).
- G. Iyer, A. Novikov, L. Ryzhik, A. ZlatoΕ‘, Exit times for diffusions with incompressible drift, SIAM J. Math. Anal. (2010).
Ph.D. thesis's of former Students
- Son Van, Investigations of the Dynamics of Models of Heat Transfer and Clustering, 2021.
- Yuanyuan Feng, Dissipation Enhancement by Mixing, 2019.
- Samuel Cohn, On the Homogenization of Diffusions in Periodic Comb-like Structures, 2018.
Masters's thesis's / projects of former Students
- Alexander Wang, Discrete vs Continuous Cheeger Constants (2024).
- Erica Wang, Generating low discrepancy samples, and an application to image stippling (2024).
- Haveesh Viswanatha, Phase transitions in the Ising Model (2024).
- Ethan Lu, A probabilistic analysis of enhanced dissipation (2022), which led to this paper in the Quarterly of Applied Mathematics.
- Hongyi Zhou, The mixing time of cellular flows with small molecular diffusivity (2022) which led to this paper in SIAM J. Math. Anal.
- James T. Murphy III, Resolving the one-dimensional autonomous flow-free explosion problem (2014) which was published in SIURO.