Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, October 29, 2019.

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Tuesday, October 29, 2019

11:00 am in 347 Altgeld Hall,Tuesday, October 29, 2019

Topological Quillen localization of structured ring spectra

Yu Zhang (Ohio State University)

Abstract: Homotopy groups and stable homotopy groups of spaces are main invariants in algebraic topology. Homotopy groups are very powerful but difficult to compute in practice. Stable homotopy groups, on the other hand, are easier to work with, at the expense of losing unstable information. Structured ring spectra are spectra with certain algebraic structure encoded by the action of an operad O. For such O-algebras, the analog of stable homotopy groups is played by Topological Quillen (TQ) homology groups. In this talk, we will discuss the following question: What information can be seen by TQ-homology? In particular, we will discuss TQ-localization of O-algebras and show the TQ-Whitehead theorem for homotopy pro-nilpotent O-algebras.

1:00 pm in 347 Altgeld Hall,Tuesday, October 29, 2019

The Abnormally Normal Behavior of the Nonlinear Schroedinger Equation

Katelyn Leisman (Illinois Math)

Abstract: The Nonlinear Schroedinger Equation (NLS) is an important partial differential equation that models many different physical applications, including super-fast lasers, Bose-Einstein condensates, and light traveling in optical fibers and wave guides. The goal in studying this equation is to know how its solutions (and thus the physical systems they model) behave over time. One way to do this for linear ("normal") equations is by finding a relationship between the wavelength and the frequency, called the dispersion relation. Unfortunately, the traditional dispersion relation approach does not work for nonlinear waves (like the NLS). However, I've found that some numerical solutions of the NLS have an effective dispersion relation. In this talk, I'll discuss this important equation and this apparent abnormally "normal" behavior. This talk will be accessible to a general audience.

2:00 pm in 243 Altgeld Hall,Tuesday, October 29, 2019

A bandwidth theorem for locally dense graphs

Andrew Treglown (University of Birmingham Math)

Abstract: A fundamental topic in extremal graph theory is to find minimum degree conditions that force a spanning substructure in a graph. One of the most general results in this direction is the so-called Bandwidth Theorem of Boettcher, Schacht and Taraz. This result gives a minimum degree condition which forces a graph G to contain every spanning subgraph of bounded chromatic number, bounded degree and sublinear bandwidth. In this talk I will describe a version of the Bandwidth Theorem where now one substantially lowers the degree condition at the expense of ensuring the host graph G is "locally dense". This is joint work with Katherine Staden.