In this hands-on workshop we will do a mathematics activity leveraging the 5 practices for orchestrating productive mathematical discussions to debrief it. We will then examine each practice and have time for reflection about how you can incorporate these ideas in your classroom.
5 practices of Orchestrating Productive Mathematics Discussions
Apr. 25, 2025 3:35pm (MATH 2…
PDE/Analysis
Maja Taskovic (Emory University)
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The wave kinetic equation is one of the fundamental models in the theory of wave turbulence, and provides a statistical description of weakly nonlinear interacting waves.
This talk will address the global in time well-posedness of the spatially inhomogeneous wave kinetic equation by applying techniques inspired by the analysis of the Boltzmann equation – another model of statistical mechanics that describes evolution of rarefied gases in which particles undergo predominantly binary interactions.
We will also discuss the well-posedness of the wave kinetic hierarchy – an infinite system of coupled equations closely related to the wave kinetic equation. Two essential tools for obtaining these results are the Hewitt-Savage theorem, which allows us to lift the existence result for the equation to the hierarchy, and the Klainerman-Machedon board game argument, which allows us to control the factorial growth of the Dyson series and consequently prove uniqueness of solutions.
This is a joint work with Ioakeim Ampatzoglou, Joseph K. Miller and Natasa Pavlovic.
On the inhomogeneous wave kinetic equation and its associated hierarchy Sponsored by the Meyer Fund
5 practices of Orchestrating Productive Mathematics Discussions