Top 10 math.ias.edu Wettbewerber

mathoverflow.net

Q&A for professional mathematicians

projecteuclid.org

In 1691, James (Jacob) Bernoulli proposed a problem called elastica problem: What shape of elastica, an ideal thin elastic rod on a plane, is allowed? Daniel Bernoulli discovered its energy functional, Euler-Bernoulli energy function, and the minimal principle of the elastica. Using it, Euler essentially solved the problem in 1744 by developing the variational method, elliptic integral theory and so on. This article starts with a review of its mathematical meaning and historical background. After that we present one of its extensions, statistical mechanics of elastica as a model of the DNA and the large polymers. We will call it a quantized elastica, and show that it is connected with the modified Korteweg-de Vries hierarchy, loop space, submanifold Dirac operators, moduli spaces of the real hyperelliptic curves and so on. By reviewing the other extensions of the elastica problem, we will see that elastica is in the center of mathematics even now.

ams.org

Advancing research. Creating connections.

arxiv.org

A system of non-tradable credits that flow between individuals like karma, hence proposed under that name, is a mechanism for repeated resource allocation that comes with attractive efficiency and fairness properties, in theory. In this study, we test karma in an online experiment in which human subjects repeatedly compete for a resource with time-varying and stochastic individual preferences or urgency to acquire the resource. We confirm that karma has significant and sustained welfare benefits even in a population with no prior training. We identify mechanism usage in contexts with sporadic high urgency, more so than with frequent moderate urgency, and implemented as a simple (binary) karma bidding scheme as particularly effective for welfare improvements: relatively larger aggregate efficiency gains are realized that are (almost) Pareto superior. These findings provide guidance for further testing and for future implementation plans of such mechanisms in the real world.

math.mit.edu

the official website for the department of mathematics at mit

math.uchicago.edu

the department of mathematics at the university of chicago

math.columbia.edu

Resources For Current Students Your Academic Advisor is the Program Director: Jaehyuk Choi E: jc6569@columbia.eduT: 212-854-2643426 Mathematics Building (Office Hours) The Career Development Advisor: Gloria