Calendar
- 27April 27, 2023
CMSA General Relativity Seminar: The localized seed-to-solution method for the Einstein constraints
I will discuss advances on asymptotically Euclidian initial data sets and the variational method introduced by J. Corvino and R. Schoen. This talk is based on joint papers with The-Cang Nguyen (Montpellier) and Bruno Le Floch (Sorbonne Univ. and CNRS). In the vicinity of any given reference data set, we define a “localized seed-to-solution” map, which allows us to parametrize the initial data sets satisfying the Einstein constraints (possibly with matter fields). The parametrization is defined over classes of data sets understood modulo the image of the dual linearized constraints. Our main contribution concerns the sharp behavior of solutions at infinity, which we can arbitrarily localize in asymptotic cones in the sense of A. Carlotto and R. Schoen. Most importantly, as we prove it, the solutions enjoy sharp decay estimates at the harmonic and super-harmonic levels. In the course of this analysis, we discover the notion of `asymptotic modulators’, as we call them, or “correctors” to the standard ADM invariants.
CMSA Active Matter Seminar: Competition at the front of expanding populations
20 Garden Street, Cambridge, MA 02138When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. (1) Based on symmetry considerations, we present a model that integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations on growth morphology are explored, providing a framework to study spatial competition, fixation, and differentiation, In particular, we find that ability to expand in space may overcome reproductive advantage in colonizing new territory. (2) Variations of fitness, as well as fixation time upon differentiation, are shown to belong to distinct universality classes depending on limits to gain of fitness.
This seminar will be held in person and on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/active-matter-seminar/
Thursday Seminar: Proof of the motivic Freudenthal Suspension Theorem
1 Oxford Street, Cambridge, MA 02138 USAIt’s been a long trek. In this talk I will put the pieces back together and explain the proof of the motivic Freudenthal suspension theorem.
Algebraic Dynamics Seminar: Marked cycle curves for quadratic polynomials and rational maps
We consider the algebraic curves obtained by marking a cycle of fixed period p in the space of quadratic polynomials. For each period, we produce a cell decomposition, whose combinatorics is closely related to the combinatorics of primitive components in the Mandelbrot set. This opens up many questions about their combinatorial and geometric structure. We also consider similar curves for the space of quadratic rational maps with a critical 2-cycle. Joint work with Caroline Davis, Malavika Mukundan, and Danny Stoll.For more information, please see: Algebraic Dynamics Seminar at Harvard
**please note change in time and location**