Rishabh Gvalani's Home Page

I obtained my PhD in Mathematics in 2020 from Imperial College London, under the supervision of Greg Pavliotis and José A. Carrillo. From autumn 2020, I will be a post-doctoral research associate at the Max Planck Institute in Leipzig.
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 Matias G. Delgadino and Grigorios A. Pavliotis. On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions [arXiv]
  2. with José A. Carrillo. Phase transitions in nonlinear nonlocal aggregation-diffusion equations [arXiv]
  3. with André Schlichting. Barriers of the McKean-Vlasov energy via a mountain pass theorem in the space of probability measures, Journal of Functional Analysis, 2020. [ arXiv | doi ]
  4. 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, 2020. [ arXiv | doi ]
  5. 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, 2019. [ arXiv | doi ]