Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, August 30, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, August 30, 2016

11:00 am in 345 Altgeld Hall,Tuesday, August 30, 2016

#### Perspectives on the telescope conjecture

###### Mark Behrens (University of Notre Dame)

Abstract: Mahowald-Ravenel-Schick attempted to disprove the telescope conjecture using the localized Adams spectral sequence, and described a very precise hypothesis. I will describe work, with Beaudry-Bhattacharya-Culver-Ravenel-Xu, where we consider what the unlocalized tmf-resolution, and the motivic localized Adams spectral sequence have to say about the telescope. While these tools alone don't seem to resolve the conjecture, they do make the MRS hypothesis eminently believable.

1:00 pm in 345 Altgeld Hall,Tuesday, August 30, 2016

#### On adjoint functors in the categories of graphs and digraphs

###### Jan Foniok (Manchester Metropolitan University)

Abstract: We consider the category of digraphs and their homomorphisms, as well as its full subcategory of graphs and several variations. These adjunctions have many applications in areas such as graph colouring and computational complexity of constraint satisfaction problems. I will present a characterisation and discuss some of the applications and some open problems. Examples include: a simple proof that deciding the existence of a homomorphism to C_5 is NP-complete; a circular Gallai-Roy theorem; Hedetniemi's conjecture (that the chromatic number of the product of two graphs is equal to the minimum of the chromatic numbers of the factors). Much of the content is based on joint work with Claude Tardif.

3:00 pm in 241 Altgeld Hall,Tuesday, August 30, 2016

#### Some applications of the container method in discrete geometry

###### Jozsef Balogh (Illinois Math)

Abstract: The container method proved to be applicable in several areas of combinatorics. I will discuss some new applications. 1. We consider a problem of Erdos about point sets in the plane in (almost) general position. 2. We discuss epsilon-nets, where the underlying set is a subset of points in the plane, and the ranges are collinear point tuples. Though we have not completely solved any of the problems, maybe our improvements are of some interests. It is joint work with Jozsef Solymosi.

3:00 pm in 243 Altgeld Hall,Tuesday, August 30, 2016

#### Modules over factorization spaces, and moduli spaces of parabolic G-bundles

###### Emily Cliff (Illinois Math)

Abstract: Beilinson and Drinfeld introduced the notion of factorization algebras, a geometric incarnation of the notion of a vertex algebra. An advantage of working with factorization algebras is that they admit non-linear analogues, called factorization spaces, which can be viewed as both generalizations of and ways to produce examples of factorization algebras from algebraic geometry. The resulting factorization algebras can then be studied via the geometry of the spaces from which they arise. Just as vertex algebras admit interesting categories of representations, so too do factorization algebras and factorization spaces. In this talk we will review the definitions of a factorization algebra and factorization space before introducing the notion of a module over a factorization space. As an example and an application we will construct a moduli space of principal G-bundles with parabolic structures, and discuss how it can be linearized to recover modules over the factorization algebra corresponding to the affine Lie algebra associated to a reductive group G.