Department of

# Mathematics

Seminar Calendar
for events the day of Friday, December 1, 2017.

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events for the
events containing

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, December 1, 2017

12:00 pm in 243 Altgeld Hall,Friday, December 1, 2017

#### Dynamical Systems via Machine Learning

###### Lan Wang (UIUC)

Abstract: Machine learning has become an important technique to understand and predict the trends of large volume of data. While most machine learning models are static, static is hardly the case in real life. We need to create dynamical models by generalizing from past experience and results. In this talk, I will explore the usages of dynamical systems in machine learning. The talk will be divided into two parts. First, I will focus on the Kalman filter, a famous Bayesian model permitting exact inference in a discrete dynamical system, and its extensions. Then, I will discuss how to use continuous dynamical systems as a tool for machine learning, especially for deep neural networks. Some of the results are from my previous internship experience.

3:00 pm in 343 Altgeld Hall,Friday, December 1, 2017

#### Equations of Kalman Varieties

###### Amy Huang (University of Wisconsin)

Abstract: Given a subspace L of a vector space V, the Kalman variety consists of all matrices of V that have a nonzero eigenvector in L. I will discuss how to apply Kempf Vanishing technique with some more explicit constructions to get a long exact sequence involving coordinate ring of Kalman variety, its normalization and some other related varieties in characteristic zero. Time permitting I will also discuss how to extract more information from the long exact sequence including the minimal defining equations for Kalman varieties.

4:00 pm in 345 Altgeld Hall,Friday, December 1, 2017

#### Canceled

4:00 pm in 241 Altgeld Hall,Friday, December 1, 2017

#### Fireworks, balloons, and singularities of curves

###### Alyssa Loving (UIUC)

Abstract: The aim of this talk is to explore a rather explosive topic, namely what fireworks, balloons, and singularities happen to have in common. All three can be "blown up". This talk will focus on blowing up singularities of curves in the plane, which is a valuable method of resolving singularities such as self intersections or cusps. I will touch on the generalization of this, which involves blowing up schemes. We will not get to blowing up balloons; that will have to be saved for a future talk.