Calendar

Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a result, in collaboration with Xinliang An, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/event_category/general-relativity/

Understanding the geometry of The Mandelbrot set, which records dynamical information about every quadratic polynomial, has been a central task in holomorphic dynamics over the past forty years. Near parabolic parameters, the structure of the Mandelbrot set is asymptotically self-similar and resembles a parade of elephants. Near parabolic parameters on these “elephants”, the Mandelbrot set is again self-similar and resembles another parade of elephants. This phenomenon repeats infinitely, and we see different parades of elephants at each scale. In this talk, we will explore the implications of controlling the geometry of these elephants. In particular, we will partially answer Milnor’s conjecture on the optimality of the Yoccoz inequality, and see potential connections to the local connectivity of the Mandelbrot set.

For more information, please see: https://people.math.harvard.edu/~demarco/AlgebraicDynamics/