Notices of the American Mathematical Society
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Constraint Maps and Free Boundaries
Alessio Figalli, André Guerra, Sunghan Kim and Henrik Shahgholian
In this survey we will focus on a specific but remarkably ubiquitous family of free boundary problems, those of obstacle-type. We will recount the historical development of the topic together with more recent advances, focusing in particular on vector-valued variational problems with constraints.
Introduction to Lie Algebras: Finite and Infinite Dimension
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Pierre Cartier: A Visionary Mathematician
Alain Connes and Joseph Kouneiher
This article reflects on the life and mathematical contributions of Pierre Cartier, a distinguished figure in 20th- and 21st-century mathematics. As a key member of the Bourbaki collective, Cartier played a pivotal role in the formalization and modernization of mathematics.
Stochastic Areas, Horizontal Brownian Motions, and Hypoelliptic Heat Kernels
Turing in the Shadows of Nobel and Abel: An Algorithmic Story Behind Two Recent Prizes
David Gamarnik
The goal of this article is to explain how the ideas pioneered by Giorgio Parisi and Michel Talagrand have led to a remarkably precise characterization of which optimization problems admit fast algorithms, versus those which do not, and furthermore to explain why this characterization holds true.
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