## Upcoming Events

## April 2018

## John Harlim, Penn State University, Data-driven methods for estimating operator and parameters of dynamical systems

I will discuss a nonparametric modeling approach for forecasting stochastic dynamical systems on smooth manifolds embedded in Euclidean space. This approach allows one to evolve the probability distribution of non-trivial dynamical systems with an equation-free modeling. In the second part of this…

Find out more## Daphne Klotsa, University of North Carolina at Chapel Hill, A touch of non-linearity at intermediate Reynolds numbers: where spheres “think” collectively and swim together

From crawling cells to orca whales, swimming in nature occurs at different scales. The study of swimming across length scales can shed light onto the biological functions of natural swimmers or inspire the design of artificial swimmers with applications ranging from…

Find out more## September 2018

## Roman Shvydkoy, University of Illinois at Chicago, Topological models of singular Cucker-Smale dynamics

In this talk we will discuss new classes of models that seek to describe evolution of a congregation of agents based on laws of self-organization. These models appear in a broad range of applications -- from biological sciences to social behavior. We…

Find out more## February 2019

## Rossana Capuani, NC State, Mean field games with state constraints

This talk will address deterministic mean field games for which agents are restricted in a closed domain of R^n with smooth boundary. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space…

Find out more## March 2019

## Pedro Aceves Sanchez, NC State, Fractional diffusion limit of a linear kinetic transport equation in a bounded domain

In recent years, the study of evolution equations featuring a fractional Laplacian has received much attention due to the fact that they have been successfully applied into the modelling of a wide variety of phenomena, ranging from biology, physics to…

Find out more## Charis Tsikkou, West Virginia University, Radial solutions to the Cauchy problem for the wave equation and compressible Euler system

In the first part of this work, we consider the strategy of realizing the solution of the three-dimensional linear wave equation with radial Cauchy data as a limit of radial exterior solutions satisfying vanishing Neumann and Dirichlet conditions, on the exterior of vanishing balls centered at the origin. We insist…

Find out more## H.T. Banks, North Carolina State University, Population Models-The Prohorov Metric Framework and Aggregate Data Inverse Problems

We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades. Theoretical results…

Find out more## April 2019

## Alexander Kiselev, Duke University, Small scale formation in ideal fluids

The incompressible Euler equation of fluid mechanics describes motion of ideal fluid, and was derived in 1755. In two dimensions, global regularity of solutions is known, and double exponential in time upper bound on growth of the derivatives of solution…

Find out more## Wen Shen, Penn State University, Scalar Conservation Laws with Discontinuous and Regulated Flux

Conservation laws with discontinuous flux functions arise in various models. In this talk we consider solutions to a class of conservation laws with discontinuous flux, where the flux function is discontinuous in both time and space, but regulated in the…

Find out more## Peter Wolenski, Louisiana State University, Fully convex Bolza problems with state constraints and impulses

In this talk, we shall review the Hamilton-Jacobi theory for A Fully Convex Bolza (FCB) problems when the data has no implicit state constraints and is coercive, in which case the minimizing class of arcs are Absolutely Continuous (AC).

Find out more## Boris Mordukhovich, Wayne State University, Criticality of Lagrange Multipliers in Conic Programming with Applications to Superlinear Convergence of SQP

His talk concerns the study of criticality of Lagrange multipliers in variational systems that have been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments dealing with polyhedral KKT systems and…

Find out more## Oleksandr Misiats, Virginia Commonwealth University, Patterns around us: a calculus of variations prospective

Crumples in a sheet of paper, wrinkles on curtains, cracks in metallic alloys, and defects in superconductors are examples of patterns in materials. A thorough understanding of the underlying phenomenon behind the pattern formation provides a different prospective on the properties…

Find out more## August 2019

## Angot Philippe, Aix-Marseille Université, Mathematical modeling and analysis towards the open problem of flow at a fluid-porous interface

We discuss mathematical modeling and analysis of the incompressible viscous flow at the interface of permeable media. Very recently, a simplified theory with asymptotic modeling and related approximations was extensively developed by to provide physically relevant jump interface conditions for…

Find out more## Michele Palladino, GSSI, Italy, Modeling the root growth: an optimal control approach

In this talk we will propose a new framework to model control systems in which a dynamic friction occurs. In particular, such a framework is motivated by the study of the movement of a robotic root tip in the soil.…

Find out more## September 2019

## Kazufumi Ito, NC State, Optimal control of sate constrained PDEs system with Spars controls

In this talk we discuss a point-wise state constraint problem for a general class of PDEs optimal control problems and sparsity optimization. We use the penalty formulation and derive the necessary optimality condition based on the Lagrange multiplier theory.The existence of…

Find out more## Yulong Lu, Duke University, Understanding and accelerating statistical sampling algorithms: a PDE perspective

A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from probability distributions. Standard Markov chain Monte Carlo methods could be prohibitively expensive due to various complexities of the target distribution, such as multimodality, high dimensionality, large datesets, etc.…

Find out more## October 2019

## Mikhail Klibanov, UNC Charlotte, Carleman Estimates for Globally Convergent Numerical Methods for Coefficient Inverse Problems

The ill-posedness and nonlinearity are two factors causing the phenomenon of multiple local minima and ravines of conventional least squares cost functionals for Coefficient Inverse Problems. Since any minimization method can stop at any point of a local minimum, then…

Find out more## Piermarco Cannarsa, University of Rome “Tor Vergata”, Bilinear control for evolution equations of parabolic type

Recently, in a series of joint papers with F. Alabau-Boussouira and C. Urbani, I have studied the response of an evolution equation on a Hilbert space to the action of a bilinear control. As is well-known, a bilinear control is…

Find out more## Cass Miller, UNC, Toward a New Generation of Models to Simulate Two-Fluid Flow in Porous Media

Two fluid flow in porous medium systems is an important application in many different areas of science and engineering. Overwhelmingly, it is necessary to mathematically model the behavior of applications of concern at an averaged scale where the juxtaposed position…

Find out more## November 2019

## Shan Gao, Beijing Institute of Technology, Discrete Geometrically-Exact Beams

A geometrically-exact beam is a nonlinear field-theoretic model for elongated elastic objects. It utilizes moving frames to reduce the number of system’s independent spatial variables, which is a further development of Euler’s approach to the rotational dynamics of rigid bodies.…

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