Rishabh Gvalani's Home Page


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

I work mainly at the intersection of the analysis and probability with an interest towards applications to problems from mathematical physics. Specifically, I am interested in understanding the qualitative and quantitative properties of interacting particle systems using techniques from optimal transport, PDEs, and stochastic analysis. Other topics I am interested in include large deviations theory, mathematical fluid mechanics, and kinetic equations.

Publications

  1. with José A. Carrillo and Jeremy Wu. An invariance principle for gradient flows in the space of probability measures. [ arXiv ]
  2. with Matias G. Delgadino and Grigorios A. Pavliotis. On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions. [ arXiv ]
  3. with José A. Carrillo. Phase transitions in nonlinear nonlocal aggregation-diffusion equations. [ arXiv ]
  4. with André Schlichting. Barriers of the McKean-Vlasov energy via a mountain pass theorem in the space of probability measures. Journal of Functional Analysis [ arXiv | doi ]
  5. with José A. Carrillo, Grigorios A. Pavliotis, and André Schlichting. Long-time behaviour and phase transitions for the McKean–Vlasov equation on the torus. Archive for Rational Mechanics and Analysis [ arXiv | doi ]
  6. with Miguel A. Durán-Olivenca, Serafim Kalliadasis, and Grigorios A. Pavliotis .Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations. Journal of Statistical Physics [ arXiv | doi ]