[Invited talk] Uncertainty quantification for partial differential equations and their optimal control problems

There will be an invited talk.

Title: Uncertainty quantification for partial differential equations and their optimal control problems
Speaker: Prof. Hyungcheon Lee (Ajou University)
Time: 2018 April 26th, 2:00pm~3:00pm
Place: 27-220
Abstract:
We consider the determination of statistical information about outputs of interest that depend on the solution of a partial differential equation and optimal control problems having random inputs, e.g. coefficients, boundary data, source term, etc. Monte Carlo methods are the most used approach used for this purpose. We discuss other approaches that, in some settings, incur far less computational costs. These include quasi-Monte Carlo, polynomial chaos, stochastic collocation, compressed sensing, reduced-order modelling.

[Invited talk]Fixed Point Method for Backward Stochastic Differential Equations

There will be an invited talk.

Title: Fixed Point Method for Backward Stochastic Differential Equations
Speaker: Prof. Ki-Hoon Nam (Monash Univ. of Melbourne, Australia)
Time: 2017 September 1st 11:00 – 11:50
Place: 129-301
Abstract:
Backward stochastic differential equation (BSDE) is a generalization of martingale representation theorem and it has been widely used for financial derivative pricing and stochastic optimization. Traditionally, most of well-posedness result of BSDE were based on contraction mapping theorem on the space of stochastic processes. In our work, we were able to transform BSDEs into fixed point problems in the space of Lp random variables. The simplicity of our framework enables us to apply various kind of fixed point theorems which have not been tried in previous literature. In particular, this enables to remove infinite dimensionality arise from time and we were able to use white noise analysis to use topological fixed point theorems. As a result, we were able to generalize previous well-posedness results: e.g. time-delayed type, mean-field type, multidimensional super-linear type. The talk is aimed for those who are not familiar with BSDE and it is based on BSE’s, BSDE’s and fixed point theorem (Annals of Probability, 2017, joint work with Patrick Cheridito).

[Invited talk] Some algebraic aspects of overdetermined PDE systems

There will be an invited talk

Title: Some algebraic aspects of overdetermined PDE systems
Speaker: Prof. Chong Kyu Han (한종규)
Time: 2016 September 30th, October 7th and November 4th 10:00am~11:30am
Place: 27-116
Abstract:
I will survey the subject starting with examples and the notion of involutivity.
Then we review related topics in generalized Frobenius theorems and the Cartan-Kaehler theory,
Finally, we discuss open problems in the following areas:
1) Conservation laws for boundaries and for submanifolds of higher codimensions,
2) Existence of complex varieties (with singularities) in a real hypersurface of a complex space
3) Applications to control theory.

[Invited talk]Uncertainty quantification for kinetic equations

There will be an invited talk

Title: Uncertainty quantification for kinetic equations
Speaker: Shi Jin (University of Wisconsin-Madison, USA and Shanghai Jiao Tong University, China)
Time: 2016 July 25th 14:00 – 15:00
Place: 129-406
Abstract:
Kinetic equations have uncertain inputs, such as the scattering kernels, initial or boundary data.
In this talk we will study the generalized polynomial chaos (gPC) approach to such kinetic equations with multiple time or space scales,
and show that they can be made asymptotic-preserving, in the sense that the gPC scheme preserves various asymptotic limits in the discrete space.
This allows the implemention of the gPC methods for these problems without numerically resolving (by space, time, and gPC modes) the small scales. We also give a fast gPC algorithm for the Boltzmann equation with uncertainties in its collision kernel, initial or boundary data.