Joint Mathematics Meeting 2018

Страна: США

Город: San Diego

Тезисы до: 26.09.2017

Даты: 10.01.18 — 13.01.18

Область наук: Физико-математические;

Е-мейл Оргкомитета:

Организаторы: AMS


One of the fundamental problems faced by science and industry is that of making sense of large and complex data sets. To approach this problem, we need new organizing principles and modeling methodologies. One such approach is through topology, the mathematical study of shape. The shape of the data, suitably defined, is an important component of exploratory data analysis.  In this talk, we will discuss the topological  approach, with numerous examples, and consider some questions about how it will develop as mathematics. 


Motivated by questions arising in starkly different contexts, quandles have been discovered and rediscovered over the past century.  The axioms defining a quandle, an analogue of a group, simultaneously encode the three Reidemeister moves from knot theory and capture the essential properties of conjugation in a group.  Thus, on the one hand, quandles are a fruitful source of applications to knots and knotted surfaces; in particular, they provide a complete invariant of knots.  On the other, they inspire independent interest as algebraic structures; for instance, the set of homomorphisms from one quandle to another admits a natural quandle structure in a large class of cases.  We will illustrate the history of this theory through numerous examples and survey recent developments.



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