## Earle Raymond Hedrick Lecture Series

### Nonlinear Dispersive Equations and the Beautiful Mathematics That Comes with Them

*Lecture 1: Thursday, August 2, 11:00 a.m. – 11:50 a.m.*

*Lecture 2: Friday, August 3, 10:30 a.m. – 11:20 a.m.*

*Lecture 3: Saturday, August 4, 10:00 a.m. – 10:50 a.m.*

**Gigliola Staffilani**, *Massachusetts Institute of Technology*

*image by Bryce Vickmark*

#### Abstract

In these lectures I will give an overview of the rich mathematical structures that characterize the wave solutions of some of the most important nonlinear partial differential equations, such as the Schrödinger equation. In doing so I will illustrate how beautiful pieces of mathematics, developed using different tools, not just coming from analysis, have been generated over the years in order to answer some of the most fundamental questions for these equations, such as existence and uniqueness of solutions for example. Along the way I will formulate open questions and possible new directions of investigation.

#### Gigliola Staffilani Bio

Gigliola Staffilani is the MIT Abby Rockefeller Mauze' Professor of Mathematics since 2007. She received the B.S. equivalent from the University of Bologna in 1989, and the M.S. and Ph.D. degrees from the University of Chicago in 1991 and 1995. Following a Szego Assistant Professorship at Stanford, she had faculty appointments at Stanford, Princeton and Brown, before joining the MIT mathematics faculty in 2002. At Stanford, Professor Staffilani received the Harold M. Bacon Memorial Teaching Award in 1997, and was given the Frederick E. Terman Award for young faculty in 1998. She was a member of the Institute for Advanced Study in 1995-96 and again in 2003-04. She was a Sloan Fellow from 2000-02 and a Fellow at the Radcliffe Institute for Advanced Study at Harvard in 2009-10. In 2013 she became an AMS Fellow and a member of the Massachusetts Academy of Sciences. In 2014 she was inducted into the American Academy of Arts and Sciences. In 2017 she received a Guggenheim Fellowship and a Simons Fellowship. In 2017 she also received an inaugural *MITx* Prize for Teaching and Learning in MOOCs.

## AMS-MAA Invited Address

### Gravity's Action on Light: A Mathematical Journey

*Thursday, August 2, 10:00 a.m. – 10:50 a.m.*

**Arlie Petters**, *Duke University*

#### Abstract

The gravitational fields of stars, black holes, and galaxies act on light propagating near them, casting magnification patterns in space. Such optical phenomena have wide-ranging physical applications, including detecting extrasolar planets and testing for a fifth dimension of the universe. Assuming no background in astrophysics or cosmology, this talk will take you on a mathematical journey unveiling the intriguing properties of these beautiful magnification patterns.

## MAA Invited Address

### Inclusion-exclusion in Mathematics: Who Stays in, Who Falls out, Why It Happens, and What We Should Do about It

*Friday, August 3, 11:30 a.m. - 12:20 a.m.*

**Eugenia Cheng**, *School of the Art Institute of Chicago*

#### Abstract

The question of why women are under-represented in mathematics is complex and there are no simple answers, only many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women. I will present the field of Category Theory as a particularly congressive subject area, accessible to bright high school students, and contrast it with the types of math that are often used to push or stimulate those students. No prior knowledge will be needed.

#### Eugenia Cheng Bio

Eugenia Cheng is a mathematician and concert pianist. She is Scientist In Residence at the School of the Art Institute of Chicago and won tenure at the University of Sheffield, UK. She has previously taught at the universities of Cambridge, Chicago and Nice and holds a PhD in pure mathematics from the University of Cambridge. Alongside her research in Category Theory and undergraduate teaching her aim is to rid the world of "maths phobia". Eugenia was an early pioneer of maths on YouTube and her videos have been viewed over 10 million times to date. She has also assisted with mathematics in elementary, middle and high schools for 20 years. Her first popular maths book "How to Bake Pi" was featured on the Late Show with Stephen Colbert, and "Beyond Infinity" was shortlisted for the Royal Society Science Book Prize 2017. She also writes the Everyday Math column for the Wall Street Journal, and recently completely her first mathematical art commission, for Hotel EMC2 in Chicago. She is the founder of the Liederstube, an intimate oasis for art song based in Chicago. Her next book, "Thinking Better: The Art of Logic in an Illogical World" is due out in 2018.

## MAA Invited Address

### Snow Business: Scientific Computing in the Movies and Beyond

*Saturday, August 4, 11:00 a.m. - 11:50 a.m.*

**Joseph Teran**, *University of California Los Angeles*

#### Abstract

New applications of scientific computing for solid and fluid mechanics problems include simulation of virtual materials in movie visual effects and virtual surgery. Both disciplines demand physically realistic dynamics for materials like water, smoke, fire, and soft tissues. New algorithms are required for each area. Teran will speak about the simulation techniques required in these fields and will share some recent results including: simulated surgical repair of biomechanical soft tissues; extreme deformation of elastic objects with contact; high resolution incompressible flow; and clothing and hair dynamics. He will also discuss a new algorithm used for simulating the dynamics of snow in Disney’s animated feature film, “Frozen”.

## MAA Invited Address

### Mathematical Medicine: Modeling Disease and Treatment

*Thursday, August 2, 9:00 a.m. - 9:50 a.m.*

**Lisette de Pillis**, *Harvey Mudd College*

#### Abstract

Immune system dynamics have proven to play an increasingly central role in the development of new treatment strategies for immune-related diseases such as type 1 diabetes and certain cancers. The critical importance of the immune system in fighting such diseases has been verified clinically, as well as through mathematical models.

Many open questions remain, however, including what may lead to non-uniform patient responses to treatments, and how to optimize and personalize therapy strategies. Mathematical models can help to provide insights into the mechanisms that may be influencing patient outcomes. In this talk, we will present a sampling of mathematical models that help us to simulate immune system interactions, disease dynamics, and treatment approaches that may slow, or even stop, disease progression.

## MAA James R.C. Leitzel Lecture

### The Relationship between Culture and the Learning of Mathematics

*Saturday, August 4, 9:00 a.m. - 9:50 a.m.*

**Talitha Washington**, *Howard University and National Science Foundation*

#### Abstract

How do we ensure that our mathematics is culturally inclusive? Why have issues with minority participation not been resolved? Unfortunately, even with our best intentions, our implicit biases impact the mathematics we teach and learn. We all can take an active role to ensure the strength of our future mathematical community, which should also be a reflection of our Nation. I will share how to infuse various cultures in learning mathematics that can better help educate those of diverse backgrounds which will broaden the participation of those doing mathematics.

## AWM-MAA Etta Zuber Falconer Lecture

### Finding Ellipses

*Friday, August 3, 9:30 a.m. - 10:20 a.m.*

**Pamela Gorkin**, *Bucknell University*

#### Abstract

Ellipses make frequent appearances in our lives: Kepler’s laws of planetary motion involve ellipses and a medical procedure involving kidney stones known as lithotripsy uses them as well. We see ellipses in architecture and in President’s Park South we find a park called simply “The Ellipse.” What properties of the ellipse make it so important? How can we construct an ellipse? We begin with questions like these, providing some unfamiliar answers. Then we study three seemingly unrelated problems in mathematics, chosen from linear algebra, complex analysis, and projective geometry, and we show how the solution to each of these problems relies on finding ellipses.

## MAA Chan Stanek Lecture for Students

### FAIL: A Mathematician's Apology

*Thursday, August 2, 1:30 p.m. - 2:20 p.m.*

**Laura Taalman**, *James Madison University*

#### Abstract

The job of being a mathematician primarily consists of long periods of failure punctuated by short bursts of success which later seem to be somewhat obvious...but that’s what we love about it! And, as it turns out, 3D printing kind of works the same way. In this talk we’ll take a journey through many mathematical and 3D printing failures and try to laugh about it the best we can.

#### Laura Taalman Bio

Laura Taalman is a Professor of Mathematics at James Madison University whose research has included algebraic geometry, knot theory, and games. Dr. Taalman also publishes Calculus textbooks and Sudoku puzzle books, blogs at Hacktastic and Shapeways, and designs and shares hundreds of models with the 3D printing community, where she is known as “mathgrrl”. She consults for 3D printing companies as an “expert amateur”, a completely real thing which here means “a person who is good at doing things that they aren’t particularly good at.” Dr. Taalman is a Project NExT Fellow, a recipient of the Alder Award, Trevor Evans Award, and SCHEV Outstanding Faculty Award, and has been featured on Thingiverse, Adafruit, and Science Friday.

### The Singular Uniformity of Large Random Systems

*Wednesday, August 1, 8:00 p.m. - 8:50 p.m.*

**Peter Winkler**, *Dartmouth College*

#### Abstract

A random structure could be anything, yet somehow, when that structure is composed of many small parts, it often turns out to be shockingly predictable---at least, in a probabilistic sense. A random graph on a million vertices, for example, has a long list of characteristics each with high probability.

In an attempt to understand this phenomenon, we'll take a little tour from zero-one laws to variational principles, contrasting graphs and permutations along the way.

## NAM David Harold Blackwell Lecture

### Continuous, Discrete, or Somewhere in Between: An Introduction to Time Scales with Applications

*Friday, August 3, 1:00 p.m. - 1:50 p.m.*

**Raegan Higgins**, *Texas Tech University*

#### Abstract

Since Stefan Hilger's landmark paper in 1988, progress has been made in the unification and extension of discrete and continuous analysis. While many results about differential equations correspond to ones for difference equations, other results appear to lack a discrete analogue. The study of dynamic equations on time scales reveals such discrepancies. The broad idea is to prove a result once for a dynamic equation where the domain of the unknown function is a time scale \(\mathbb{T}\), which is an arbitrary, nonempty, closed subset of the real numbers.

Using the exponential function \(e^{pt}\), we will introduce to the theory of time scales. We will then use the fact that \(e^{pt}\) is the solution of \(x^{\prime} = px, \; x(0)=1\) to define a generalized exponential function on a time scale \(\mathbb{T}\) and derive several important properties of the exponential function. Examples and applications will be given.

In this talk, we consider the second-order linear delay dynamic equation \(\begin{eqnarray*} \left( p(t)y^{\Delta}(t) \right)^{\Delta}+ q(t)y(\tau(t)) =0 \end{eqnarray*}\) on a time scale \(\mathbb{T}\). By employing the Riccati transformation technique, we establish some sufficient conditions which ensure that every solution oscillates. The obtained results unify the oscillation of second-order delay differential and difference equations. We illustrate our results with examples.

Our interest in delay equations has lead us to study a certain area of mathematical physiology. We are using mathematical models to understand how behavioral disruption of the circadian clock can lead to glucose dysregulation. Specifically, we are interested in whether the timing and content of meals (exogenous input to glucose levels) impact the degree to which circadian misalignment alters glucose metabolism. In this talk, we present some preliminary results.