Seminar Calendar
for Topology Seminar events the next 12 months of Sunday, January 1, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, January 20, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, January 20, 2017
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Submitted by dcarmod2.
Organizational Meeting
Abstract: This is the organizational meeting to get the schedule of talks down for the spring. If you think you might be interested in giving a talk at some point, please attend!

Friday, January 27, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, January 27, 2017
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Submitted by dcarmod2.
Daniel Carmody (UIUC Math)
Galois Categories and the Topological Galois Correspondence
Abstract: Classical Galois theory for fields gives a correspondence between closed subgroups of the Galois group of a Galois extension and intermediate subfields. The theory of covering spaces in topology gives a correspondence between connected coverings of nice spaces and subgroups of the fundamental group. The purpose of this talk is to explain the relationship between (and generalization) of these two theorems.

Tuesday, January 31, 2017

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, January 31, 2017
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Submitted by rezk.
Charles Rezk (Illinois)
Complex analytic elliptic cohomology and Looijenga line bundles
Abstract: I'll explain how, by taking the cohomology of suitable spaces and messing around a bit, you can get things like: the moduli stack of (analytic) curves, the universal curve, and Looijenga line bundles over these. This seems to have some relevance for the construction of complex analytic elliptic cohomology.

Friday, February 3, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, February 3, 2017
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Submitted by dcarmod2.
Marissa Loving (UIUC Math)
Train Tracks on Surfaces
Abstract: Our mantra throughout the talk will be simple, "Train tracks approximate simple closed curves." Our goal will be to explore some examples of train tracks, draw some meaningful pictures, and develop an analogy between train tracks and another well known method of approximation. No great knowledge of anything is required for this talk as long as one is willing to squint their eyes at the blackboard a bit at times.

Friday, February 10, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, February 10, 2017
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Submitted by dcarmod2.
Georgios Kydonakis (UIUC Math)
Opers and non-abelian Hodge theory
Abstract: We will describe two different families of flat $G$-connections over a compact Riemann surface for a complex, simple, simply connected Lie group $G$. The first is the family of $G$-opers, which for $G=\text{SL(2}\text{,}\mathbb{C}\text{)}$ can be thought of as global versions of the locally defined second order Schrödinger operators. The second comes from a particular subfamily of solutions to the so-called $G$-Hitchin equations. The physicist Davide Gaiotto conjectured that for $G=\text{SL(}n\text{,}\mathbb{C}\text{)}$ the second family in a scaling limit converges to a limiting connection which has the structure of an oper. We will describe a proof of this conjecture. This is joint work with Olivia Dumitrescu, Laura Fredrickson, Rafe Mazzeo, Motohico Mulase and Andrew Neitzke.

Friday, February 17, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, February 17, 2017
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Submitted by dcarmod2.
Melinda Lanius (UIUC Math)
Hyperbolic taxi cabs and conic kitty cats: a mathematical activity and coloring book
Abstract: In this extremely interactive talk, we will develop intuition for various metrics that I have encountered in my own research. We’ll work our way through understanding more familiar spaces such as the real plane as well as hyperbolic plane and disk, to less familiar objects: such as a surface with a Euclidean, cylindrical, or hyperbolic-funnel end. Some markers and colored pencils will be provided, but please feel free to bring your own fun office supplies.

Friday, February 24, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, February 24, 2017
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Submitted by dcarmod2.
Bill Karr (UIUC Math)
Geometry of convex hypersurfaces
Abstract: A convex hypersurface in Euclidean space or Minkowski space is the boundary of an open convex set. Smooth convex hypersurfaces have non-negative sectional curvature and indicate properties of more general Riemannian manifolds with non-negative curvature. I will discuss some properties of convex hypersurfaces. Finally, I will describe a problem that arises from Lorentzian geometry involving convex hypersurfaces and geodesic connectedness and discuss a possible solution to this problem.

Tuesday, March 7, 2017

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, March 7, 2017
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Submitted by rezk.
Guillaume Brunerie (IAS)
Invariant homotopy theory in homotopy type theory
Abstract: This talk will be about homotopy type theory and in particular the branch of it known as invariant homotopy theory, or synthetic homotopy theory.

The main idea is that homotopy type theory is a formal language which can be used to talk about "spaces-up-to-homotopy-equivalence". The basic objects can be thought of as spaces, but the language has the property that all the structures, properties, constructions and proofs that we can express are invariant under homotopy equivalence.

One advantage is that every construction or proof done in this setting is expected to be automatically valid in every infinity-topos, not just in the infinity-topos of spaces, while still looking elementary. In this sense, we can see homotopy type theory as an internal language for infinity-topoi. Moreover, such proofs are also amenable to computer formalization, as homotopy type theory is strongly related to computer proof assistants.

I will present the basic concepts and show what a few proofs and constructions look like in invariant homotopy theory. In particular, we will see the universal cover of the circle, the Hopf fibration, cohomology, and the Steenrod operations.


Tuesday, April 4, 2017

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, April 4, 2017
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Submitted by rezk.
Dan Ramras (IUPUI)
To Be Announced

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, April 4, 2017
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Submitted by rezk.
Dan Ramras (IUPUI)
To Be Announced

Tuesday, April 18, 2017

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, April 18, 2017
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Submitted by rezk.
Nathan Perlmutter (Stanford)
To Be Announced

Tuesday, April 25, 2017

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, April 25, 2017
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Submitted by rezk.
Carmen Rovi (Indiana)
To Be Announced