Rishabh Gvalani's Home Page


I am a post-doctoral research associate at the Max Planck Institute in Leipzig in the groups of Benjamin Gess and Felix Otto. I obtained my PhD in Mathematics in June, 2020 from Imperial College London, under the supervision of Greg Pavliotis and José Antonio Carrillo.

I work mainly at the intersection of the analysis and probability. Topics I am interested in include interacting particle systems and their scaling limits, large deviations and macroscopic fluctuations, gradient flows and optimal transport, singular SPDEs, and passive scalar mixing in incompresible fluid flows.

Together with Francesco Mattesini, Felix Otto, and Markus Tempelmayr, I am co-organising a summer school on "PDEs and Randomness" at the MPI this May.
You can find more information about the school here.

Publications

  1. with Benjamin Gess and Vitalii Konarovskyi. Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent. [ arXiv ]
  2. with Benjamin Ferhman and Benjamin Gess. Ergodicity and random dynamical systems for conservative SPDEs. [ arXiv ]
  3. with Alex Blumenthal and Michele Coti Zelati. Exponential mixing for random dynamical systems and an example of Pierrehumbert. [ arXiv ]
  4. with Antonio Esposito, André Schlichting, and Markus Schmidtchen. On a novel gradient flow structure for the aggregation equation. [ arXiv ]
  5. with Matías G. Delgadino, Grigorios A. Pavliotis, and Scott A. Smith. Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time propagation of chaos for weakly interacting diffusions. to appear, Comm. Math. Phys. [ arXiv ]
  6. with Benjamin Gess, Florian Kunick, and Felix Otto. Thermodynamically consistent and positivity preserving discretization of the thin-film equation with thermal noise. to appear, Math. Comp. [ arXiv ]
  7. with José A. Carrillo and Jeremy Wu. An invariance principle for gradient flows in the space of probability measues. J. Differential Equations, 2022 [ arXiv | doi ]
  8. with Matías G. Delgadino and Grigorios A. Pavliotis. On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions. Arch. Ration. Mech. Anal., 2021 [ arXiv | doi ]
  9. with José A. Carrillo. Phase transitions in nonlinear nonlocal aggregation-diffusion equations. Comm. Math. Phys., 2021. [ arXiv | doi ]
  10. with André Schlichting. Barriers of the McKean-Vlasov energy via a mountain pass theorem in the space of probability measures. J. Funct. Anal., 2020. [ arXiv | doi ]
  11. with José A. Carrillo, Grigorios A. Pavliotis, and André Schlichting. Long-time behaviour and phase transitions for the McKean–Vlasov equation on the torus. Arch. Ration. Mech. Anal., 2020. [ arXiv | doi ]
  12. with Miguel A. Durán-Olivenca, Serafim Kalliadasis, and Grigorios A. Pavliotis. Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations. J. Stat. Phys., 2018. [ arXiv | doi ]