Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, November 3, 2020.

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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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Tuesday, November 3, 2020

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, November 3, 2020

#### The Scattering Transform: a Wavelet-based Neural Network for Statistical Feature Extraction

###### Michael Perlmutter (UCLA)

Abstract: The scattering transform is a mathematical framework for understanding convolutional neural networks (CNNs) introduced by S. Mallat. Similar to more traditional CNNs, the scattering transform is a deep, feed-forward network featuring an alternating cascade of convolutions and nonlinearities. However, it differs by using predesigned, wavelet filters rather than filters that are learned from training data. This leads to a network that provably has desirable invariance and stability properties. In addition to preforming well on standard machine learning tasks such as image recognition. The scattering transform can also be used to extract statistical information about stochastic processes with stationary increments. The expected scattering moments are a novel form of nonparametric statistics which can be used to distinguish random textures with identical power spectrums. I will present Mallat's original construction as well as several novel variations designed for structured data such as graphs. In particular, I will discuss the use of one of the more recent construction to distinguish between different types of randomly generated graphs.

2:00 pm in Zoom,Tuesday, November 3, 2020

#### The threshold for the square of a Hamilton cycle

###### Jinyoung Park (Institute for )

Abstract: We will talk about a recent result of Jeff Kahn, Bhargav Narayanan, and myself stating that the threshold for the random graph $G(n,p)$ to contain the square of a Hamilton cycle is $1/\sqrt{n}$, resolving a conjecture of Kühn and Osthus from 2012. For context, we will first spend some time discussing a recent result of Keith Frankston and the aforementioned three authors on a conjecture of Talagrand (a fractional version of Kahn-Kalai "expectation-threshold conjecture").