Schedule: Spring 2018 Midwest Topology Seminar

Schedule

9:00-10:00 9:00	Coffee and snacks in Rawles Hall Lounge
10:00-11:00 10:00	Charles Weibel (Rutgers), The Real Topological Analogue of the Witt Group
11:00-11:30 11:00	Coffee in Rawles Hall Lounge
11:30-12:30 11:30	Guillem Cazassus (IU), Towards extended Floer field theories
12:30-2:30 12:30	Lunch at Local Restaurants
2:30-3:30 2:30	Jonathan Campbell (Vanderbilt), Combinatorial K-theory, Devissage and Localization
3:30-4:00 3:30	Coffee and cookies in Rawles Hall Lounge
4:00-5:00 4:00	Julie Bergner (Virginia), 2-Segal sets arising from graphs and their associated Hall algebras
5:15- 5:15	Party in Rawles Hall Lounge

Talks will be in Swain East 105 (map) and breaks will be in Rawles Hall 107 (map)

Time Zone

Bloomington, Indiana, is in the Eastern time zone and observes daylight saving time. See timeanddate.com to compare with your local time.

Abstracts

2-Segal sets arising from graphs and their associated Hall algebras

Julie Bergner, University of Virginia

The notion of 2-Segal set allows us to consider structures which behave like categories but for which composition may not always exist or may be multiply-defined. While many examples only have partially defined composition, the 2-Segal set associated to a graph gives a nice example where maps can be composed in different ways. Thus, it gives a good way to explore the general properties of 2-Segal structures. In particular, following a definition of Dyckerhoff and Kapranov, this 2-Segal set has an associated Hall algebra which is much smaller than most natural examples of such algebras and has a curious description as a cohomology ring.

Combinatorial K-theory, Devissage and Localization

Jonathan Campbell, Vanderbilt University

What sorts of categories can K-theory be defined for? We know that exact categories and Waldhausen categories can be used as appropriate input. However, there are geometric categories where we would like to define K-theory where we are only allowed to cut and paste rather than quotient — examples of these include the category of varieties, and the category of polytopes. I'll define a more general context where one may talk about the algebraic K-theory of these categories, and outline a proof of a geometric version of Quillen's devissage and localization. I'll outline applications to studying derived motivic measures and the scissors congruence problem. This is joint work with Inna Zakharevich.

Towards extended Floer field theories

Guillem Cazassus, Indiana University

Donaldson polynomials are powerful invariants associated to smooth four-manifolds. The introduction by Floer of Instanton homology groups, associated to some 3-manifolds, allowed to define analogs of such polynomials for (some) four-manifolds with boundary, that have a structure similar with a TQFT.

Wehrheim and Woodward developed a framework called Floer field theory which, according to the Atiyah-Floer conjecture, should permit to recover Donaldson invariants from a 2-functor from the 2-category Cob_{2+1+1} to a 2-category Symp they defined, which is an enrichment of Weinstein's symplectic category.

I will outline a possible way of extending such a 2-functor to lower dimensions. This should permit to define new invariants in Manolescu and Woodward's symplectic instanton homology (sutured theory, equivariant version). This is work in progress.

April 28, 2018

Schedule

Time Zone

Abstracts

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