Research Interests

• Uncertainty quantification and stochastic modeling
• Numerical analysis and high-performance scientific computing
• Data-driven and reduced-order modeling
• Mori-Zwanzig formulation
• Approximation of functional-differential equations
• Theoretical and computational fluid dynamics

My research activity has been recently focused on developing new theoretical and computational methods for uncertainty quantification and dimensional reduction in large scale stochastic dynamical systems. In particular, I have been working on the Mori-Zwanzig formulation, data-driven modeling, hierarchical tensor methods for the numerical solution to high-dimensional PDEs, and the approximation of functional differential equations (e.g., Hopf characteristic functional equations).

My research featured in the UCSC magazine Inquiry :  https://inquiry.ucsc.edu/2020-21/superior-simulations/

Approximation of Functional Differential Equations:  https://www.soe.ucsc.edu/news/prof-venturi-addresses-long-standing-open-problem-computational-mathematics (PAPERS: Research in the Mathematical Sciences, Physics Reports)

Appointments

• 2021 - present, Professor of Applied Mathematics, UC Santa Cruz.
• 2019 - 2021, Associate Professor of Applied Mathematics, UC Santa Cruz.
• 2015 - 2019, Assistant Professor of Applied Mathematics, UC Santa Cruz.
• 2010 - 2015, Research Assistant Professor of Applied Mathematics, Brown University.
• 2006 - 2010, Postdoctoral Research Associate at the Department of Energy, Nuclear and Environmental Engineering, University of Bologna.