Seminar
Some algorithms and analysis for first order interacting particle systems
Two Conservative, High-Order Coupling Methods for Fluid-Fluid Interaction
The distribution of energy across space and time scales is quite different between the atmosphere and ocean. Therefore, codes for air-sea interaction are constructed by coupling together atmosphere and ocean components, each highly optimized internally using different numerical methods, by passing fluxes of conserved quantities between the components in the form of boundary conditions at the air-sea interface. For efficiency, the fluxes are usually asynchronous, meaning they are calculated using data extrapolated from previous times for at least one component.
Neural Networks, Cost Functions, and What Happens When You Ignore Math
Convolutional Neural networks are the current state-of-the-art in image processing, far surpassing other popular strategies in terms of performance. These network models are built on heuristics, though, and have a limited foundation of mathematical guarantees. This talk will cover the basics of modern Neural network architectures and provide an overview of notable cases where they fail in unexpected, unpredictable ways.
Numerical schemes for the 2d Navier-Stokes equations: Strong rate of convergence.
"Khinchine’s Inequalities. 3.”
Eulerian and Almost Injective Maps
"Khinchine’s Inequalities. 2.”
The Shattered Urn
Graduate Student Panel Discussion
Come to hear from 6 graduate students from the mathematics department at Pitt. This discussion is not meant to favor nor oppose graduate school, but merely for undergraduates to seek more information about graduate school.