**Jun Li, Math Major 2017**

**Honors Lecture**

**Low-Dimensional Manifolds and**

**Open Book Decompositions**

**Wednesday, May 3**

**Refreshments, 4:00 p.m. ~ King 203**

**Lecture, 4:30 p.m. ~ King 239**

**Jad Salem, Math Major 2017**

**Honors Lecture**

**Dynamical Systems, Binary Expansions,**

**and Continued Fractions**

**Thursday, May 4**

**Refreshments, 4:00 p.m. ~ King 203**

**Lecture, 4:30 p.m. ~ King 239**

**Andrea Allen, Math Major 2017**

**Honors Lecture**

**Average Shortest Path Length in a**

**Novel Small-World Network**

**Thursday, April 27**

**Refreshments, 4:00 p.m. ~ King 203**

**Lecture, 4:30 p.m. ~ King 239**

The Mathematics Department

## WELCOMES

# Peter D Hislop

# 2017 Distinguished Visitor

Professor of Mathematics

University of Kentucky

## Wednesday, March 1, 2017

### Reception, 4:00 p.m., King 203

Lecture, 4:30 p.m., King 239

Resonances in Quantum **Mechanics**

Resonances in Quantum

Resonances are states of atomic systems with long lifetimes. They look like bound states on short time scales but eventually decay. It is diﬃcult to describe resonances in the mathematical theory of quantum mechanics. Resonant energies look like eigenvalues of the energy matrix, but have small imaginary parts that cause states to decay in time. However, the energy matrix is self-adjoint so has only real eigenvalues. The correct way to describe resonances is to go into the complex plane by meromorphically continuing certain functions. This talk will present some basic examples of resonances in quantum mechanics and show how resonances can be properly deﬁned and estimated. This talk will be accessible to students with a background in linear algebra, calculus, and basic analysis.

The Mathematics Department

## Welcomes

# Peter D Hislop

# 2017 Fuzzy Vance Lecture

###### Professor of Mathematics

University of Kentucky

## Thursday, March 2, 2017

### 7:30 p.m. - King 306

Reception following

# The Mathematics and Physics of Electrons in Solids

The propagation properties of electrons in solids have been studied since the beginnings of quantum mechanics. The quantum theory of a perfect crystal provides the basis of our understanding of insulators, semi-conductors, and conductors. However, for such a simple model, the conductivity is inﬁnite. When impurities are included in the model, the propagation properties of the solid are signiﬁcantly altered. This situation more closely models the ﬁnite conductivity properties of real solids. The mathematics needed to describe these properties is both fascinating and challenging, and draws from functional analysis and probability theory. This talk will concentrate on simple examples that illustrate and provide insight into Anderson localization and ﬁnite conductivity.

**mathematics pizza lunch**

**Professor Robert Bosch**

**OC students build bridges between math & art:**

** a report from Jyväskylä, Finland**

###### In August, four OC students --- Simon Ever-Hale,

###### Max Grusky, Hank Guss, and Sage Jensen (all

###### alumni of Bob Bosch's MATH 397 class) --- shared

###### some of their original mathematical artwork in

###### Jyväskylä, Finland at the Bridges conference, an

###### annual celebration of mathematical connections

###### to art, music, architecture, education, and culture.

###### Bob will talk about the conference, his students'

###### beautiful contributions, and identify upcoming

###### opportunities for combining math and art.

WEB SITES

Bob Bosch's Power Point Presentation

### Simon Ever-Hale '18

Max Grusky '16

Henry Guss '16

Sage Jenson '17

**MATHEMATICS DEPARTMENT**

*WELCOMES SPEAKER*

**Ilesanmi Adeboye**

###### Assistant Professor of Mathematics

###### Wesleyan University

### Friday, November 4, 2016

### Reception 4:00 p.m., King 203

### Lecture 4:30 p.m. , King 239

**Euler's Equation and the Philosophy of Numbers**

This talk will begin with the statement of Euler's equation: “the most remarkable formula in mathematics." We will then develop the number system from the natural numbers to the complex numbers, exploring why new numbers are defined and how basic operations are generalized. Next, calculus will be used to represent familiar functions in an unfamiliar way, in order to reveal a key relationship. Finally, our numbers and functions will be combined to give a proof of Euler's equation.

**Mathematics Department**

*Welcomes Speaker*

*Welcomes Speaker*

**Ken Kleinman**

**The University of Mass Amherst**

**Department of Biostatistics**** **

** ****Monday, October 10, 2016**

**Reception 3:30 pm – King 203**

**Lecture 4:00 pm King 343**

** **

**The life of a statistician in a medical school: ****three examples from practice**

In this talk I review one example from each of the three main elements of what statisticians in practice do: 1) educate about statistical methods and interpretation; 2) develop statistical methods needed for situations that arise; and 3) collaborate on projects my colleagues are pursuing. I begin with the problem of how to interpret odds ratios from logistic regression-- a seemingly simple issue that has actually generated errors, papers, and workarounds. I then talk about surveillance for bioterrorism using doctors' visits, and a statistical method I worked on to speed up a computationally onerous test. Finally, I discuss my colleagues' use of a specialized study design-- the cluster-randomized trial-- and how I worked with them to develop an approach to make their studies more robust.

### Jeffrey Witmer

Professor of Mathematics

###### I spent a week in Kenya with my son Joel (OC class of 2003), who was there to shoot a documentary film on the East Africa Dairy Development, a project of Heifer International. We spent some time on safari in the Masai Mara National Game Reserve, which included the following memorable event, told here by Joel:

###### Our driver took us two hours out on as legitimate a road as you get in these parts, and then got onto what can generously be described as a path, and at this point I'm thinking unpleasant thoughts. Just how long is it going to take to get back now? And for what? We are headed deeper into the savannah. Everything is savannah. Going into the middle of it isn’t any better than seeing it from the road because there is no ‘middle of it’ in any real sense. It’s an open space. And now we’re just inconveniently situated in it. This was a mistake. That’s what I’m thinking.

###### An hour into the path we are in a narrow valley between two sizable hills and I see a bloody zebra carcass at eye level a few feet up one hill. It's slumped against the base of a tree. This is interesting because until now every carcass I've seen has been well worn, if not skeletal. This one is red with blood. This excursion is paying off.

###### We drive forward a few feet, eyes still on the zebra because, you know, it's black and white and red all over. It's hard to look away. That is, until you clear the tree and on the other side you see a lion, tired but regal, her cub playing a few feet up the hill. She too is eye level. The adrenaline rushes and instinctively I contemplate death. I don't know how else to put it. Here is a mom protecting both her very young child — the guide later estimated the cub was 2-3 months old — and dinner for the next week and I'm sitting in an open air vehicle, completely vulnerable, sitting 20 feet away. Measuring in distance almost seems laughable, actually. A more accurate measure would be Seconds Left Alive Should This Lion Pounce. I'm guessing 3-5.

###### We sit there quietly, mostly. Any sound we make catches the lion's attention. She greets it with a stare. We remain still. But after a few minutes I start hearing noises on the opposite side of the truck. Not stealthy noises either. Noises that suggest the creature making them does not care about the situation, or maybe does not know. Oblivious or indifferent, it's causing a stir. Now the lion is looking beyond me, through the truck, to the noise machine a few yards away. I turn and see an elephant. This just got more interesting. We are idling between a killing machine made of fast twitch muscle fiber and an animal made of battering rams.

###### Anyway, this is getting long and we didn’t die, obviously. But what a way to go if we had!

Kevin Woods

### Associate Professor of Mathematics

Last summer, I visited the Universidad de los Andes, in Bogota, Colombia, to work with Tristram Bogart (Oberlin College '01) and John Goodrick. We've finished up a paper called "Parametrized Presburger arithmetic: logic, combinatorics, and quasi-polynomial behavior" which is available on my website http://www.oberlin.edu/faculty/kwoods/papers.html. Here's a picture of me in the cloud forests of Colombia.