Mid-Atlantic Topology Symposium: New Directions

Johns Hopkins University, Baltimore MD

Investigators

Abstract

The Mathematics Department at Johns Hopkins University is hosting a "Mid-Atlantic Topology Symposium: New Directions" at the Homewood campus in Baltimore, Maryland, Saturday-Sunday, March 12-13 2016. This meeting is inspired by a similar conference which took place in Spring 2015 at the University of Virginia. The PIs intend to establish a tradition of such meetings. Algebraic topology, geometry, and category theory are in the midst of a generational shift of language, techniques and paradigms, rooted in new ideas about higher homotopy-theoretic structures in geometry, physics, category theory, and data analysis. These fields are in ferment, with a forefront defined by a younger generation of researchers who bring new ideas from higher algebra to classical areas of geometry, physics, and applied mathematics. This conference is intended to help clarify the shifting boundaries and intersections in these closely related fields. Recent developments in computer science, physics, and big data are changing profoundly our notions of what constitutes geometry; in response, ideas from homotopy and category theory have provided new algebraic methods for (re)organizing our understanding of these questions, and how to approach them. The conference will focus on a developing new global language for both geometry and algebra, with connections to fields such as the following: 1. arithmetic geometry (new approaches to motives, for example, via motivic homotopy theory; new techniques in K-theory via Hochschild and cyclic homology; homotopy-theoretic methods in automorphic forms, with applications to classical homotopy theory) 2. geometric quantum field theory, for example, through various cobordism hypotheses (via chiral homology and related not-so-commutative ring spectra) 3. category theory (e.g., through Voevodsky's univalent foundations project and related work on homotopy type theory in computer science, and involving foundational work in and applications of higher category theory Demographic and intellectual developments in these areas have brought a diverse population of new researchers into the field, and the organizers hope that the conference will foster and encourage this development. The roster of speakers emphasizes junior researchers and diversity, but makes no compromises with the strength of the work under discussion. The speakers exemplify ground-breaking work in new directions, which points the way toward a new synthesis of algebra and geometry. This conference is an opportunity to expose graduate students and new researchers to these developments, and could have significant impact on their careers. A list of speakers and other details can be found at the conference website http://www.math.jhu.edu/matc/