# Seminars & Events for PACM/Applied Mathematics Colloquium

##### Nonlinear Expectation, Nonlinear PDE and Stochastic Calculus under Knightian Uncertainty

JOINT PACM COLLOQUIUM & ANALYSIS SEMINAR: A. N. Kolmogorov's "Foundations of the Theory of Probability" published in 1933, has established the modern axiomatic foundations of probability theory. Since then this theory has been profoundly developed and widely applied to situations where uncertainty cannot be neglected. But in 1921 Frank Knight has been already clearly classified two types of uncertainties: the first one is for which the probability is known; the second one, now called Knightian uncertainty, is for cases where the probability itself is also uncertain. The situation with Knightian uncertainty has become one of main concerns in the domain of data processing, economics, statistics, and specially in measuring and controlling financial risks.

##### The 2D Boussinesq equations with partial dissipation

*JOINT PACM COLLOQUIUM & ANALYSIS SEMINAR*: The Boussinesq equations concerned here model geophysical flows such as atmospheric fronts and ocean circulations. Mathematically the 2D Boussinesq equations serve as a lower-dimensional model of the 3D hydrodynamics equations. In fact, the 2D Boussinesq equations retain some key features of the 3D Euler and the Navier-Stokes equations such as the vortex stretching mechanism. The global regularity problem on the 2D Boussinesq equations with partial dissipation has attracted considerable attention in the last few years.