Department of

Mathematics


Seminar Calendar
for Graduate Geometry/Topology Seminar events the year of Monday, April 16, 2018.

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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 19, 2018

4:00 pm in 241 Altgeld Hall,Friday, January 19, 2018

Organizational Meeting

Abstract: We'll get the schedule of talks for the semester worked out. There will be cookies.

Friday, January 26, 2018

4:00 pm in 241 Altgeld Hall,Friday, January 26, 2018

Ice cream geometry: a mathematical activity and coloring book

Melinda Lanius (UIUC)

Abstract: Come explore metrics I use in my dissertation research. In a souped-up color-by-numbers, we'll develop a general notion of circle and ball. In geodesic connect-the-dots, we'll see what happens when straight lines curve. In metric mazes, we'll come to appreciate the wonky ways of nonhomogeneous spaces. After exploring the geometries of the real and hyperbolic plane, sphere, cone, and cylinder, we'll conclude by building less familiar objects: surfaces with a Euclidean, cylindrical, conical, or hyperbolic-funnel end. Please bring your fun office supplies!

Friday, February 2, 2018

4:00 pm in 241 Altgeld Hall,Friday, February 2, 2018

Integrable systems in algebraic geometry

Matej Penciak (UIUC)

Abstract: In this talk I'll introduce the definition of an algebraic integrable system. The definition axiomatizes what it means to have an integrable system in algebraic geometry. After connecting the definition to the more common notion in differential geometry, I'll give a few examples of my favorite integrable systems. Possible examples are the Hitchin system on the space of Higgs bundles, the Calogero-Moser system, the Toda lattice hierarchy, and, if time permits, I'll try to give a hint of how all these systems are related via the gauge theory in physics.

Friday, February 9, 2018

4:00 pm in 241 Altgeld Hall,Friday, February 9, 2018

What are spectra?

Tsutomu Okano (UIUC)

Abstract: This is an introductory talk on stable homotopy theory. I will begin by discussing stable phenomena in homotopy theory that led to the definition of spectra. Spectra represent generalized cohomology theories, such as various kinds of K-theories and cobordism theories. This implies that results about cohomology theories can be proven in the category of spectra, using analogies from topological spaces. Unfortunately, the earlier category of spectra was defective in formal properties and it was not until the 1990's that suitable categories of spectra were defined. This formality leads to the study of other sorts of homotopy theories, such equivariant and motivic homotopy theories.

Friday, February 16, 2018

4:00 pm in 241 Altgeld Hall,Friday, February 16, 2018

Canceled

(UIUC)

Friday, February 23, 2018

4:00 pm in 241 Altgeld Hall,Friday, February 23, 2018

Unoriented Bordism and the Algebraic Geometry of Homotopy Theory

Brian Shin (UIUC)

Abstract: The classification of manifolds up to bordism is an interesting geometric problem. In this talk, I will discuss how this problem connects to homotopy theory. In particular, I will demonstrate that viewing the homotopy theorist's toolbox through the lens of algebraic geometry leads naturally to the solution for the classification of manifolds up to bordism.

Friday, March 9, 2018

4:00 pm in 241 Altgeld Hall,Friday, March 9, 2018

Cancelled

Friday, March 16, 2018

4:00 pm in 241 Altgeld Hall,Friday, March 16, 2018

Operations in complex K theory

William Balderrama (UIUC)

Abstract: In nice cases, the correct algebraic setup can exert a large amount of control over a geometric situation. I will illustrate this with the example of complex K theory.

Friday, March 30, 2018

4:00 pm in 241 Altgeld Hall,Friday, March 30, 2018

Optimizing mesh quality

Sarah Mousley (UIUC)

Abstract: I will talk about a project in computational geometry I worked on during a summer internship at Sandia National Lab. Our work builds on that of Mullen et al., who introduced a new energy function for meshes (triangulations) and an algorithm for finding low energy meshes. The energy is a measure of the mesh’s quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. While the motivation for this work is to obtain better solutions to PDEs, do not be turned off. I didn't solve a single PDE all summer. This is a geometry talk.

Friday, April 13, 2018

4:00 pm in 241 Altgeld Hall,Friday, April 13, 2018

What is group cohomology?

Elizabeth Tatum (UIUC)

Abstract: Group cohomology has many uses in algebra, topology, and number theory. In this talk, I will introduce group cohomology, give some basic examples, and discuss some applications to topology.

Friday, April 20, 2018

4:00 pm in 241 Altgeld Hall,Friday, April 20, 2018

The Volume Conjecture

Xinghua Gao (UIUC)

Abstract: It is a fundamental goal of modern knot theory to “understand” the Jones polynomial. The volume conjecture, which was initially formulated by Kashaev and later generalized by Murakami^2, relates quantum invariants of knots to the hyperbolic geometry of knot complements. In this talk, I will briefly explain the volume conjecture. No background in knot theory/hyperbolic geometry/physics required.

Friday, April 27, 2018

4:00 pm in 241 Altgeld Hall,Friday, April 27, 2018

Cannon-Thurston Maps

Elizabeth Field (UIUC)

Abstract: When a map between two objects extends to a continuous map between their boundaries, this boundary map is called the Cannon-Thurston map. When the objects at play are a hyperbolic group and a hyperbolic subgroup, there are two main questions which arise from this definition. First, when does the Cannon-Thurston map exist? Further, if such a map exists, can the fibers of this map be described in some nice algebraic or geometric way? In this talk, we will introduce the background needed to understand these questions. We will then briefly explore some of what is known about their answers, as well as some open questions which remain.