Department of

Mathematics


Seminar Calendar
for events the day of Friday, October 19, 2018.

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Friday, October 19, 2018

3:00 pm in 145 Altgeld Hall,Friday, October 19, 2018

Shadows of the Four Corner Cantor Set

Chi Huynh (Illinois Math)

Abstract: The set of particular interest will be $C(1/4) = C_{1/4} \times C_{1/4}$ where $C_{1/4}$ is the 1/4-Cantor set in $\mathbb{R}$. I will be presenting two proofs on the projections of $C(1/4)$ onto lines in $\mathbb{R}^2$. By utilizing the self-similar structure, these proofs present more detailed information on projections of $C(1/4)$ than the Marstrand projection theorem is able to. Due to time constraints, I will only go over one of the proofs in details, then sketch the proof of the sharper result by pointing out the necessary lemmas to obtain it.

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

An Introduction to Persistent Homology

Dan Carmody (UIUC)

Abstract: In this talk, I'll start by introducing the Cech and Vietoris-Rips complexes, then compute some basic examples of persistent homology using the python library Gudhi (Maria et al., 2014). I'll introduce one of the standard metric structures on the space of persistence diagrams, then end by surveying some of the applications of persistent homology to crop science and human biology.