Research Interests
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, anomalous dissipation, coagulation, fluid mechanics, homogenization, Q-tensors and mixing.
Awards, and Support Acknowledgement
- NSF (various standard grants since 2006, CAREER 2013-18)
- 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
Recent Publications
- W. Cooperman, G. Iyer, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert. (2024).
- M. Coti Zelati, G. Crippa, G. Iyer, A. Mazzucato, Mixing in Incompressible Flows: Transport, dissipation and their interplay. (2023).
- 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. (2023).
- G. Iyer, H. Zhou, Quantifying the dissipation enhancement of cellular flows. (2022).
All Publications
- W. Cooperman, G. Iyer, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert. (2024).
- M. Coti Zelati, G. Crippa, G. Iyer, A. Mazzucato, Mixing in Incompressible Flows: Transport, dissipation and their interplay. (2023).
- 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. (2023).
- G. Iyer, H. Zhou, Quantifying the dissipation enhancement of cellular flows. (2022).
- J. Ballew, G. Iyer, C. D. Levermore, H. Liu, R. Pego, Global Dynamics and Photon Loss in the Kompaneets Equation. (2022).
- 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. (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).
Partial Differential Equations
- W. Cooperman, G. Iyer, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert. (2024).
- M. Coti Zelati, G. Crippa, G. Iyer, A. Mazzucato, Mixing in Incompressible Flows: Transport, dissipation and their interplay. (2023).
- 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. (2022).
- J. Ballew, G. Iyer, C. D. Levermore, H. Liu, R. Pego, Global Dynamics and Photon Loss in the Kompaneets Equation. (2022).
- 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
- W. Cooperman, G. Iyer, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert. (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. (2023).
- C. Gomez, G. Iyer, H. Le, A. Novikov, An oscillator driven by algebraically decorrelating noise. (2021).
- 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, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert. (2024).
- M. Coti Zelati, G. Crippa, G. Iyer, A. Mazzucato, Mixing in Incompressible Flows: Transport, dissipation and their interplay. (2023).
- G. Iyer, H. Zhou, Quantifying the dissipation enhancement of cellular flows. (2022).
- 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
- C. Gomez, G. Iyer, H. Le, A. Novikov, An oscillator driven by algebraically decorrelating noise. (2021).
- 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, S. Son, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert. (2024).
- M. Coti Zelati, G. Crippa, G. Iyer, A. Mazzucato, Mixing in Incompressible Flows: Transport, dissipation and their interplay. (2023).
- 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. (2023).
- G. Iyer, H. Zhou, Quantifying the dissipation enhancement of cellular flows. (2022).
- 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
- 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 joint paper.
- Hongyi Zhou, The mixing time of cellular flows with small molecular diffusivity (2022) which led to this joint paper.
- James T. Murphy III, Resolving the one-dimensional autonomous flow-free explosion problem (2014) which was published in SIURO.
Misc.
- Open Source Code
- Linux/LaTeX tips "blog"