Research

I study random graphs and interacting stochastic processes (such as probabilistic cellular automata, interacting particle systems), in particular processes whose interaction structure can be represented by a heterogenous network. I'm interested in applications in epidemiology, neuroscience, opinion dynamics.

My research combines methods from probability theory (including stochastic analysis, filtering, Markov chains, control theory), dynamical systems, statistical physics, graphical models, network science, and modeling. My goal is to gain mathematically rigorous understanding of how global behaviors emerge from the structure of local interactions in realistic networks.

My advisor is Professor Kavita Ramanan.

Publications

J. Cocomello and K. Ramanan. Exact description of limiting SIR and SEIR dynamics on locally tree-like graphs. Preprint, arXiv:2309.08829 (2023)
J. Cocomello, M. Davydov, K. Ramanan. Tractable characterization of time marginals of a class of interacting jump processes on sparse graphs. In preparation (2024).

Talks and presentations

Exact description of limiting SEIR dynamics on locally tree-like graphs. Poster. Stochastic Networks Conference. KTH Royal Institute of Technology. Stockholm, Sweden. July 2024.
Exact description of limiting SEIR dynamics on locally-tree like graphs. Queer in Computational and Applied Mathematics (QCAM). ICERM. Providence, RI. June 2024.
Exact description of limiting SIR and SEIR dynamics on locally-tree like graphs. Spectra Mathematics Conference. September 2023.
Using Math to Understand Network Dynamics. Research Matters. Brown University. April 19, 2023. Watch a recording here.
Analyzing SIR epidemics on large sparse networks. Trans Day of Math. Dec 13 2022.
Predicting SIR epidemics on large random networks. Social Media and QSR Flash Session INFORMS Annual Meeting. Indianapolis, IN. Oct 16-19 2022.
Dynamics on Sparse and Heterogeneous Networks - Tutorial session. Led three 1-hour long tutorial sessions as part of Prof. Kavita Ramanan’s lecture series. Summer School: Mathematics of Large Networks. Erdős Center. Budapest, Hungary. May 30 - June 3, 2022.

Other Projects

Probabilistic Cellular Automata on a Heterogenous Graph

Independent Study Project - Summer 2020

Under the mentorship of Professor Kavita Ramanan, I learned about interacting stochastic processes - from classical mean-field techniques to modern local convergence approaches. I surveyed literature on the role of heterogeneous networks structure in a number of applications fields (material science, neuroscience, systemic risk, epidemics, neural networks ). Inspired by some of this literature, I formulated an heterogenous graph model and studied its asymptotic behavior, deriving results on weak convergence of empirical measure and propagation of chaos.

Social Equity & Applied Math (SEAM) Seminar

Working Group Member

Social Equity and Applied Mathematics (SEAM) at Brown University is a seminar series and working group organized by Professor Kavita Ramanan and Darryl Xie. We discuss mathematical models, and theoretical and computational aspects of problems that are of relevance to social equity in the world. Past invited speakers include Timnit Gebru, ("Computer vision: who is harmed and who benefits?"), Sharad Goel ("Quantifying Bias in Human and Machine Decisions"). You can find the full list and recordings of most talks here.