Department of

# Mathematics

Seminar Calendar
for events the day of Monday, September 10, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, September 10, 2018

2:00 pm in 464 Loomis,Monday, September 10, 2018

#### Aspects, Generalizations, and Applications of the Holographic Entanglement of Purification

###### Ning Bao (UC Berkeley)

Abstract: In this talk, we will define, and motivate the holographic entanglement of purification and several generalizations thereof. We will then make some comments on applications of these quantities in the context of quantum information theory, quantum error correction and bulk reconstruction.

3:00 pm in 243 Altgeld Hall,Monday, September 10, 2018

#### Lie 2-groups and their Lie 2-algebras

###### Eugene Lerman (University of Illinois at Urbana-Champaign)

Abstract: I will introduce Lie 2-groups and Lie 2-algebras and then discuss left-invariant vector fields on Lie 2-groups.

4:00 pm in 245 Altgeld Hall,Monday, September 10, 2018

#### Texture of Time Series, or Topological Data Analysis in Dimension 1

###### Yuliy Baryshnikov   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Persistent homology was created as a tool for topological inference, - reconstructing topological invariants of an unknown underlying model from noisy samples. In this picture, the information is contained in the long "bars", while the short bars are useless noise. In the past few years, practitioners realized that the short bars are an interesting descriptor of the data in many applied situations. I'll describe some underlying notions and results pertaining to the short bars, and will describe in some more details the structure of the corresponding point process for trajectories of Brownian motion.

5:00 pm in 241 Altgeld Hall,Monday, September 10, 2018

#### Slow continued fractions and permutative representations of Cuntz algebras

###### Chris Linden

Abstract: We will also discuss organization and start with Chris Talk Following the work of Bratteli and Jorgensen, I will show how permutative representations of the Cuntz algebras $\mathcal{O}_n$ arise from iterated function systems. I will then discuss a special case of this construction studied by Hayashi, Kawamura and Lascu where the function system is the Gauss map, which allows all (unitary equivalence classes of) irreducible permutative representations of $\mathcal{O}_{\infty}$ to be labeled by the orbits of a $PGL_2(\mathbb{Z})$ action. Finally, I will discuss my own work which extends this construction to $2 \leq n < \infty$ with the help of slow continued fraction algorithms.