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Folded nodes occur in generic slow-fast dynamical systems with two slow variables. Open regions
of initial conditions flow into a folded node in an open set of such systems, so folded nodes are an
i...
Dissimilarity maps on trees and the representation theory of $GL_n(\C)$
Dissimilarity maps trees the representation theory Algebraic Geometry
2011/9/14
Abstract: We revisit the representation theory in type $A$used previously to establish that the dissimilarity vectors of phylogenetic trees are points on the tropical Grassmannian variety. We use a di...
Periods of rational maps modulo primes
p-adic dynamics Mordell-Lang conjecture Algebraic Geometry
2011/9/6
Abstract: Let $K$ be a number field, let $\phi \in K(t)$ be a rational map of degree at least 2, and let $\alpha, \beta \in K$. We show that if $\alpha$ is not in the forward orbit of $\beta$, then th...
March 18, 2007，An international team of 18 mathematicians, including two from MIT, has mapped one of the largest and most complicated structures in mathematics. If written out on paper, the calculatio...