Young Topologists Meeting 2015

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

This travel grant provides partial support for U.S. participation in the international event "Young Topologists Meeting 2015," held at the Federal Polytechnical School in Lausanne, Switzerland, July 6-10, 2015. First started in 2007, the Young Topologists Meeting (YTM) is an annual European conference for graduate students and young researchers in in the field of topology. The subject of topology, the mathematical study of geometric properties that are independent of deformation, has importance throughout mathematics as well as in a large number of applications that range from theoretical physics to data analysis to robotic motion planning. The YTM offers junior topologists the opportunity to present their work to a large international audience, giving the speakers experience as well as facilitating the dissemination of research results. In addition, the YTM hosts two mini-courses by senior topologists that offer introductions to advanced topics and provide gateways into these subfields for even relatively inexperienced participants. This year the two mini-courses will stress both of the great successes of algebraic topology: theory-building and applications. One course will offer an introduction to the theory of Infinity Categories from a simple and formal perspective. Infinity categories are a relatively new framework for understanding many tools arising in mathematics and physics, including homological algebra, model categories, locality in field theories, and theories of A- and L-infinity algebras. Although infinity categories can be identified as playing a role in many areas of mathematics, their usefulness can be limited by their combinatorial intractability -- a problem which will be addressed by introducing infinity categories from this new viewpoint. The second course will address applications of algebraic topology to data science. In particular, it will describe the theory of Persistent Homology, which is a tool used to extract meaningful inference from both large and multi-dimensional data sets. As data becomes more ubiquitous, developing mathematical methods for handling large amounts of data is paramount, and this course will introduce the next generation of topologists to these problems and possible solutions through topology. The conference website can be found at http://gr-he.epfl.ch/ytm2015.