This proposal will provide support for participants from institutions in the U.S. to attend the Fourth Arolla Conference on Algebraic Topology. The conference will be held August 20th - 26th, 2012 in the village of Arolla, Switzerland. The goal of the Arolla conferences is to bring together experts from a wide variety of fields within homotopy theory and K-theory to learn of current ground-breaking work throughout these disciplines. The following individuals have agreed to give plenary lectures at the upcoming conference: Arthur Bartels (Munster), Mark Behrens (MIT), Gunnar Carlsson (Stanford), Michael Ching (Amherst), Daniel Dugger (Oregon), Teena Gerhardt (Michigan State), Ian Leary (Ohio State), Ib Madsen (Copenhagen), Niko Naumann (Regensburg), Angelica Orsono (Chicago), Kari Ragnarsson (DePaul), Goncalo Tabuada (MIT), and Antoine Touze (Paris XIII). These plenary speakers have made significant contributions to many subfields of algebraic topology, including K-theory, L-theory, equivariant stable homotopy theory, homotopy theory and algebraic geometry, applied and computational algebraic topology, group representations and cohomology, homotopical algebra, Goodwillie calculus and operads, and higher category theory. There will be 10-12 contributed lectures, chosen from abstracts submitted by registered participants so as to cover a wide range of topics. For more details about the conference, visit the conference website at

Algebraic topology is a field of mathematics that uses algebraic tools to study properties of shapes that are preserved under continuous deformations. It developed as a distinct discipline within mathematics in the late 19th/early 20th century and has played a major role in 20th and 21st century mathematics. The Arolla conferences are among the few continuing established conferences that cover a broad range of topics within algebraic topology. The conferences bring together researchers from around the world who work in many specialties within algebraic topology to exchange ideas and learn of new developments in the field. The conferences particularly encourage participation from young researchers. Funding from this proposal will support U.S.-based speakers at the 2012 conference, thereby enabling conference participants to learn of work that is taking place in the U.S. It will also support participation by young researchers and those from groups that are traditionally underrepresented in mathematics in the U.S., providing them with opportunities to learn more about what is happening in the field, share their work with others, explore ideas for new research, and develop professional networks in Europe.

Project Report

took place August 20th - 26th, 2012, in the village of Arolla, Switzerland. The goal of this international mathematics conference was to give researchers in the field of algebraic topology an overview of ground-breaking work currently being carried out in a wide range of subfields within topology. Over 80 participants from colleges and universities in Europe, North America, and Asia attended the conference. The conference featured invited lectures by the following established and emerging leaders in the field of algebraic topology: Arthur Bartels (WWU Muenster Mathematisches Institut), Gunnar Carlsson (Stanford University), Daniel Dugger (University of Oregon), Teena Gerhardt (Michigan State University), Ian Leary (Ohio State University), Ib Madsen (University of Copenhagen), Angelica Osorno (University of Chicago), Kari Ragnarsson (Google), Goncalo Tabuada (MIT), and Antoine Touze (University of Paris 13). In addition, there were 17 contributed lectures given by other conference participants. Through the lectures, conference participants learned about significant new results in algebraic topology. Through informal interactions between the lectures, participants had the opportunity to share their work with others, and to collaborate on projects of common interest. Funding from the National Science Foundation made it possible for 15 researchers from institutions in the US to attend and participate in the conference, including 11 graduate students and early-career mathematicians. The Arolla Conferences on Algebraic Topology are among the very few established, regularly recurring international conferences in algebraic topology that seek to bring together researchers from the full range of specialties within homotopy theory and algebraic K-theory. Participation from U.S.-based researchers at Arolla is important for them to learn of new developments throughout algebraic topology. The Union College Mathematics Conference took place October 19th-20th, 2013 at Union College in Schenectady, NY. The conference consisted of parallel sessions in algebraic topology, big data analytics, category theory, commutative algebra, and differential geometry. Funding from the National Science Foundation was used to partially support participation in the algebraic topology session. Though smaller in scope than the Arolla Conference, the Union Conference also offered an important opportunity for researchers in algebraic topology to share their work and learn of new developments. Through our featured speakers for the session, Gunnar Carlsson (Stanford) and Kathryn Hess (EPFL), whose work overlaps significantly with the interests of the participants in the big data analytics and category theory sessions respectively, we were able to increase the level of interaction between researchers in these fields.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
Standard Grant (Standard)
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Joanna Kania-Bartoszynska
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Union College
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