Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, January 24, 2019.

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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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Thursday, January 24, 2019

11:00 am in 241 Altgeld Hall,Thursday, January 24, 2019

#### Some statistics of the Euler phi function

###### Harold Diamond (Illinois Math)

Abstract: Questions about the distribution of value of the Euler phi function date to work of Schoenberg and Erdos. This talk will survey this theme and include a result of mine in which two applications of the Perron inversion formula are applied to count the number of points (n, phi(n)) lying in a specified rectangle.

12:00 pm in 243 Altgeld Hall,Thursday, January 24, 2019

#### Stretch Factors Coming From Thurston's Construction

###### Joshua Pankau (U Iowa)

Abstract: Associated to every pseudo-Anosov map is a real number called its stretch factor. Thurston proved that stretch factors are algebraic units, but it is unknown exactly which algebraic units are stretch factors. In this talk I will discuss a construction of pseudo-Anosov maps due to Thurston, and discuss my recent results where I classified (up to power) the stretch factors coming from this construction. We will primarily focus on a specific class of algebraic units known as Salem numbers. This talk is intended to be accessible to everyone.

1:00 pm in 347 Altgeld Hall,Thursday, January 24, 2019

#### Constraining neural networks with spiking statistics

###### Andrea Barreiro (Mathematics, Southern Methodist University)

Abstract: As experimental tools in neuroscience have advanced, measuring whole-brain dynamics with single-neuron resolution is becoming closer to reality. However, a task that remains technically elusive is to measure the interactions within and across brain regions that govern such system-wide dynamics. We propose a method to derive constraints on hard-to-measure neural network attributes --- such as inter-region synaptic strengths --- using easy-to-measure spiking statistics. As a test case, we studied interactions in the olfactory system. We used two micro-electrode arrays to simultaneously record from olfactory bulb (OB) and anterior piriform cortex (PC) of anesthetized rats who were exposed to several odors. We were able to make several predictions about the network, notably that inhibition within the OB and inhibition within PC were constrained to a narrow slice of possible values. As time permits, I’ll describe ongoing work in which we are applying the same techniques to determine how peripheral sensation and lateral inhibition combine to shape dynamic selectivity within the OB.

2:00 pm in 347 Altgeld Hall,Thursday, January 24, 2019

#### Introduction to Percolation Theory

###### Grigory Terlov (UIUC Math)

Abstract: This is the first part of two talks designed to introduce students to Percolation Theory. We will describe the model, talk about infinite clusters, prove the existence of the phase transition, introduce the universality principle and more.