Abstract:  The quantification of uncertainties inherent to parameters, initial and boundary conditions, measured data, and models themselves is necessary to make predictions with reduced and quantified uncertainties.  This requires a synergy between the underlying science, numerical and functional analysis, probability, and statistics.  In this presentation, we will discuss basic issues that must be addressed when quantifying input and output uncertainties in physical and biological models.  This will be motivated by discussion regarding the role of uncertainty quantification for weather and climate models, subsurface hydrology and geology, nuclear power plant design, and biology.  We will then discuss global sensitivity techniques for parameter selection, Bayesian model calibration, sampling and spectral methods for uncertainty propagation, and issues pertaining to surrogate model construction.   Open questions and future research directions will be noted throughout the presentation and graduate students are encouraged to attend.  Biosketch:  Ralph Smith is a Professor of Mathematics at North Carolina State University.  He is Editor-in-Chief of the SIAM book series on Advances in Design and Control and is on the editorial boards of the SIAM/ASA Journal on Uncertainty Quantification, the Journal of Intelligent Material Systems and Structures, and Dynamics of Continuous, Discrete and Impulsive Systems B.  His research areas include mathematical modeling of smart material systems, numerical analysis and numerical methods for physical systems, Bayesian model calibration, sensitivity analysis, control, and uncertainty quantification.  Host:  Prof. Igor Mezic