Seminar Calendar
for Graduate Geometry 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.

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

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.

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.

Friday, April 7, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, April 7, 2017
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Submitted by dcarmod2.
William Balderrama (UIUC Math)
Stable Phenomena in Algebraic Topology
Abstract: A phenomenon might be called stable if it happens the same way in every dimension. For example, if $C_\bullet$ is a chain complex, then $H_\ast C_\bullet = H_{\ast+1}C_{\bullet+1}$: ``taking homology'' is done the same in every dimension. In some cases, a construction might not be stable, but can be stabilized. For example, if $M$ is a smooth closed manifold, choice of distinct embeddings $i,j\colon M\rightarrow \mathbb{R}^n$ give rise to possibly nonisomorphic choices of normal bundles $N_iM$ and $N_jM$. However, we can stabilize this by adding trivial bundles: $N_iM\oplus k \simeq N_jM \oplus k$ for sufficiently large $k$, leading to the notion of the stable normal bundle. In this talk, I will introduce this notion of stability, and propose spectra, the main objects in stable homotopy theory, as a good way for dealing with it.

Friday, April 14, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, April 14, 2017
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Submitted by dcarmod2.
Chris Gartland (UIUC Math)
Net and Filter Convergence Spaces
Abstract: A net or filter convergence space is a set together with a collection of data that axiomatizes the notion of convergence to an element of that set. In this sense, convergence spaces generalize topological spaces. More specifically, we will define the (equivalent) categories of net and filter convergence spaces and show that they contain the category of topological spaces (Top) as a full subcategory. We'll highlight some of the advantages these categories have over Top, especially in relation to Tychonoff's theorem. This talk is based off a series of blog posts by Jean Goubault-Larrecq, http://projects.lsv.ens-cachan.fr/topology/?page_id=785.

Friday, April 21, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, April 21, 2017
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Submitted by dcarmod2.
Joshua Wen (UIUC Math)
It’s hard being positive: symmetric functions and Hilbert schemes
Abstract: Macdonald polynomials are a remarkable basis of $q,t$-deformed symmetric functions that have a tendency to show up various places in mathematics. One difficult problem in the theory was the Macdonald positivity conjecture, which roughly states that when the Macdonald polynomials are expanded in terms of the Schur function basis, the corresponding coefficients lie in $\mathbb{N}[q,t]$. This conjecture was proved by Haiman by studying the geometry of the Hilbert scheme of points on the plane. I’ll give some motivations and origins to Macdonald theory and the positivity conjecture and highlight how various structures in symmetric function theory are manifested in the algebraic geometry and topology of the Hilbert scheme. Also, if you like equivariant localization computations, then you’re in luck!