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.


Graduate Student Analysis Seminar
4:00 pm   in 131 English Building,  Tuesday, March 7, 2017
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Submitted by compaan2.
Derek Jung   [email] (UIUC Math)
A variant of Gromov's H\"older equivalence problem for small step Carnot groups
Abstract: This is the second part of a talk I gave last semester in the Graduate Geometry/Topology Seminar. A Carnot group is a Lie group that may be identified with its Lie algebra via the exponential map. This allows one to view a Carnot group as both a sub-Riemannian manifold and a geodesic metric space. It is then natural to ask the following general question: When are two Carnot groups equivalent? In this spirit, Gromov studied the problem of considering for which $k$ and $\alpha$ there exists a locally $\alpha$-H\"older homeomorphism $f:\mathbb{R}^k\to G$. Very little is known about this problem, even for the Heisenberg groups. By tweaking the class of H\"older maps, I will discuss a variant of Gromov's problem for Carnot groups of step at most three. This talk is based on a recently submitted paper. Some knowledge of differential geometry and Lie groups will be helpful.

Friday, March 10, 2017

Graduate Geometry Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, March 10, 2017
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Submitted by penciak2.
Stefan Klajbor Goderich (UIUC Math)
Stability of relative equilibria and isomorphic vector fields
Abstract: We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth in his study of vector fields on differentiable stacks. Here we argue in favor of the usefulness of replacing an invariant vector field on a manifold by an isomorphic one to study nonlinear stability of relative equilibria. In particular, we use this idea to obtain a criterion for nonlinear stability. As an application, we sketch how to use this to obtain Montaldi and Rodrı́guez-Olmos’s criterion for stability of Hamiltonian relative equilibria.

Friday, March 17, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, March 17, 2017
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Submitted by dcarmod2.
Matthew Romney (UIUC Math)
A 50-minute peek into the quasi-world
Abstract: Quasiconformal geometry is the dominant research area which evolved from complex analysis in the 20th century and remains active today. This talk will give a friendly overview to the subject, from its roots in the classical Riemann mapping theorem and Liouville theorem on conformal mappings, to some of its compelling applications in other fields, including complex dynamics and geometric group theory.

Tuesday, March 28, 2017

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, March 28, 2017
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Submitted by cmalkiew.
Cary Malkiewich (UIUC)
Periodic orbits and topological restriction homology
Abstract: This talk is about an emerging connection between algebraic $K$-theory and free loop spaces on the one hand, and periodic orbits of continuous dynamical systems on the other. The centerpiece is a construction in equivariant stable homotopy theory called the "$n$th power trace," which relies on the equivariant norm construction of Hill, Hopkins, and Ravenel. This trace is a refinement of the Lefschetz zeta function of a map $f$, which detects not just fixed points but also periodic orbits of $f$. The applications so far include the resolution of a conjecture of Klein and Williams, and a new approach for the computation of transfer maps in algebraic $K$-theory. These projects are joint work with John Lind and Kate Ponto.

Friday, March 31, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, March 31, 2017
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Submitted by dcarmod2.
Sarah Mousley (UIUC Math)
Exotic limit sets of geodesics in Teichmuller space
Abstract: In 1975, Masur proved that the Teichmuller space of a surface of genus at least 2 is not Gromov hyperbolic. Since then, many have explored to what extent Teichmuller space has features of negative curvature. In a Gromov hyperbolic space, a geodesic ray converges to a unique point in the hierarchically hyperbolic space (HHS) boundary. We will present our result that a geodesic ray in Teichmuller space does not necessarily converge to a unique point in the HHS boundary of Teichmuller space. In fact, the limit set of a ray can be almost anything allowed by topology. The goal of this talk is not to prove the result, but rather to give necessary background to understand the statement. In particular, we will not assume knowledge of Teichmuller theory or HHS structures.

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)
Coassembly for representation spaces
Abstract: Abstract: I'll describe a homotopy-theoretical framework for studying the relationships between (families of) finite-dimensional unitary representations, vector bundles, and flat connections. Applications to surfaces, 3-manifolds, and groups with Kazhdan's property (T) will be discussed.

Tuesday, April 11, 2017

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, April 11, 2017
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Submitted by cmalkiew.
Kate Ponto (U Kentucky)
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

Tuesday, May 2, 2017

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, May 2, 2017
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Submitted by rezk.
Nathan Perlmutter (Stanford)
To Be Announced