2017-2019 Talbot Workshops

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AbstractAward: DMS 1623977, Principal Investigator: Haynes R. MillerThis award provides support for the next three Talbot workshops to be held in 2017, 2018, and 2019. Since its initial meeting in 2004, the Talbot Workshop has introduced young researchers in algebraic topology to topics of contemporary interest. This annual workshop gathers about 35 young participants and one or two senior mathematicians for a week-long retreat; the participants, who are mostly graduate students, learn about the week's research topic by exchanging lectures and discussing the topic under the guidance of the mentors. The workshop has been extremely successful, inspiring the future research of many students and establishing numerous collaborations among the participants. The workshop's unique format, in which participants live and cook together in a rental house, helps to create and sustain the collaborative atmosphere.Past Talbot Workshops have focused on a wide variety of topics in homotopy theory and surrounding areas, from elliptic cohomology (2004) and Fukaya categories (2009) to non-abelian Hodge theory (2011) and, most recently (2016), the Hill-Hopkins-Ravenel solution of the longstanding Kervaire invariant problem (with Hill and Ravenel as mentors). The topics under preliminary consideration for 2017, 2018, and 2019 include: stability conditions on triangulated categories, trace methods in algebraic K-theory, conformal field theory, derived algebraic geometry, applied topology, and Heegaard Floer theory. As many of the participants are first- or second-year graduate students looking to get a start in a promising research area, the lectures begin with basics, such as an introduction to model categories and to equivariant homotopy theory in the 2016 workshop, and lead up to a presentation of open problems related to the workshop material. The web site for the Talbot workshops is http://math.mit.edu/conferences/talbot/.