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In this talk we explore electromagnetic models arising in the context of magnetohydrodynamic (MHD) generators or accelerators (which are analogous to traditional turbo-machinery generators and electric motors). The plasma found in MHD generators is different from more well-understood plasmas in that it is not particularly conductive (called restive plasma), it exhibits the Hall-effect (which is a non-linear dependence of current-densities on the magnetic field), and has low magnetic Reynolds number (meaning that the plasma does not induce much magnetic field).
Launched by Alexander Grothendieck in the 1980s, the modern theory of dessins d'enfants (children's drawings) provides a geometric illustration of the absolute Galois group. One of the most important results in this theory is that the action of the absolute Galois group via conjugation is faithful on dessins of genus g. We look at a sketch of the proof for dessins of genus 0 on the Riemann sphere. We will also look at some examples of plane trees, their corresponding Belyi functions, and some full Galois orbits.
I will describe the basics of variational inequalities and in particular some classical results for the parabolic case. Then I will introduce a new application to biofilm models for which some (many) open questions remain.
In this talk I present a framework to address participation in the mathematics classroom. This framework represents my journey through mathematics education research from a largely cognitive approach (with a focus on understanding and beliefs) to a sociocultural perspective (with a focus on context and valorization of knowledge). Some of the questions I discuss are: what does it mean to be good at math? Whose knowledge and experiences are represented? Whose and what approaches are valued? Which language(s) and forms of communication get privileged?