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Mathematics Colloquium

Thanh Dang, Anuj Kumar and Mohammad Nooranidoost

1. Non-convex optimization via Stein's method
2. On localized instability of shear flows of the 2D Euler equations
3. A multi-scale mathematical model for biofilm structure and viscoelasticity

Date: Friday, September 15, 2023
Place and Time: Room 101, Love Building, 3:05-4:55 pm

Abstracts. 1. In a convex/non-convex optimization problem, one may use an Euler discretization of a suitable Langevin diffusion equation to target the global minimizers. In this talk, we will show how Stein's method can be used to derive quantitative convergence result of these Euler discrete schemes. The main technical tool will be the classical Bismut formula for the semigroup associated with our Langevin diffusion.

2. In this work, we establish linear instability for the 2D Euler equation around a shear flow, and provide a simple proof for the result of Lin. For this, we employ the functional analytic framework developed recently by Vishik and prove existence of solutions of the Rayleigh equation that correspond to purely growing modes. Joint work with Wojciech Ozanski. .

3. Biofilms are initiated by individual polymer-producing bacteria in aqueous that undergo a phenotypic switch and produce various types of extracellular polymeric substances (EPS). The EPS form a polymeric network combined with fluid solvent creating a gel-like fluid that exhibits rheological behavior. In this talk, I will discuss how I use differential equations and Bayesian inference to model the viscoelasticity and spatiotemporal organization of biofilm structure across different scales. This model helps us understand the physics of the biofilm polymeric network that forms the backbone of the biofilm