MSRI-UP 2020: Branched Covers of Curves
July 3, 2020
Dr. Andrea Arauza Rivera, California State University, East Bay
Analysis on fractals: Also what are fractals?
We will begin with a "you know it when you see it" introduction to fractal sets. For many years mathematicians avoided working with fractals and referred to them as the "monsters" of mathematics. Recently, however, mathematicians have begun to explore fractals, as they can be used to describing the chaotic nature of the real world. We will talk about some of the fundamental properties that make fractals so monstrous, and dare to wonder how one might do calculus on fractals.
July 10, 2020
Dr. Renée Brady-Nicholls, Moffitt Cancer Center
July 17, 2020
Dr. Alex Cayco Gajić, École Normale Supérieure
Complex dynamics in feedforward networks of neurons
In this talk, I will present two approaches to modeling feedforward networks of neurons. In the first part of the talk, I will present my graduate research studying how complex firing patterns emerge in feedforward networks of binary neurons, by analyzing the eigenstructure of a mean field Markov chain describing layer to layer transmission of activity. In the second part of the talk, I will describe my recent work understanding a feedforward network in the cerebellum, a region of the brain that coordinates movements. Classic and recent theories have shown that this feedforward structure speeds associative learning, in analogy with a multilayer perceptron, if the feedforward circuitry generates a high dimensional representation. I will show recent work inferring the intrinsic dimensionality of the cerebellar neural code based on data from awake mice.