# Math/Stat Colloquium

The colloquia are co-sponsored by the College of Arts and Sciences. In this lecture series, speakers will connect mathematics to a variety of disciplines within the college and beyond.

*Most talks* are scheduled for **Tuesdays, at 4:30 p.m. in IES 110.** See specific details below.

Attendees are invited to meet the speaker *30 minutes beforehand* over **Tea and Cookies.**

Organizers: Rafal Goebel & Aaron Lauve

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*Most talks will take place on the first floor of Loyola's new Institute of Environmental Sustainability (IES), room 110. (Changes will be noted within speaker details above.)*

The IES is located at southeast corner of W. Sheridan and N. Kenmore, on Loyola's lakeshore campus. (map)

Public parking available on-campus in the Parking Garage (building P1 on the campus map). To get to the Parking Garage, enter campus at the corner of West Sheridan Road and North Kenmore Avenue.

## Titles and abstracts of selected talks from the past

Jerry Bona, Mathematics, Statistics, and Computer Science, University of Illinois at Chicago (fall 2011)

*Large Waves on Deep Water: Rogue Waves and Tsunamis*

Large scale ocean waves have been of interest for centuries. Investigated here are some of the underpinnings of our attempts to understand such phenomena. The journey will take us through some 19th century history and culminate in more recent developments. We will be in a position to cast light on the genesis of such waves and understand how they can transmit coherent energy across thousands of miles of ocean.

Andrew Odlyzko, Digital Technology Center, University of Minnesota (spring 2011)*Cybersecurity, Mathematics, and Limits on Technology*

Mathematics has contributed immensely to the development of secure cryptosystems and protocols. Yet our networks are terribly insecure, and we are constantly threatened with the prospect of imminent doom. Furthermore, even though such warnings have been common for the last two decades, the situation has not gotten any better. On the other hand, there have not been any great disasters either. To understand this paradox, we need to consider not just the technology, but also the economics, sociology, and psychology of security. Any technology that requires care from millions of people, most very unsophisticated in technical issues, will be limited in its effectiveness by what those people are willing and able to do. This imposes strong limits on what formal mathematical methods can accomplish, and suggests that we will have to put up with the equivalent of baling wire and chewing gum, and to live on the edge of intolerable frustration.

Emily Peters, Mathematics, Northwestern University (fall 2012)*Knots, the four-color theorem, and proof by pictures. *

Your friend hands you two knots and asks you if they're the same 'Well, they're both knots!', you reply. 'What do you mean, the same?' Your friend convinces you that some things that look like knots really aren't knotted (like a necklace that's gotten tangled, but can be combed out with patience), while some other things really and truly are (like my bike frame and a bike rack and my bike lock, I hope). But now you want to know: how can you be sure? Knot invariants, which I'll introduce, can sometimes answer this. The rest of this talk will be variations on the theme of "proof by pictures" which emerges from talking about knot invariants. I'll try to convince you of the general usefulness of this point of view in math, by explaining how it can be used to prove the four-color theorem (a famous, simple-to-state-and-hard-to-prove fact about coloring maps). If time permits I'll also talk about some instances of "proof by pictures" in the field of operator algebras (ie, linear algebra in infinite dimensions).

Brian Adams, Sandia National Laboratories (spring 2012)*Applied Mathematical Sciences at Sandia*

Through this presentation I will relate my six year experience working in a mathematics and computer science research group at Sandia, a national security laboratory. The broad mission areas of the lab foster research in disciplines including engineering, materials, bioscience, energy and water, infrastructure security, scalable scientific computation, and beyond. Computational scientists support them with contributions ranging from theory and hardware to algorithms and software to solve application problems of national importance.

I will survey a number of application problems whose solution relies on mathematics, statistics, disciplinary science, and high-performance parallel computing. These are used in creating computational models (simulations) that scientists and engineers use for insight and decision making. I will also introduce optimization and uncertainty quantification algorithms and discuss their application to nuclear reactor performance assessment, water network security, micro-electro-mechanical system (MEMS) design, and disease spread modeling. I will touch on challenges of simulation credibility, or knowing that computer models are appropriate in the context in which they are used.

Aaron Greicius, Mathematics and Statistics, Loyola University Chicago (fall 2011)*Music is Applied Mathematics*

Well, at least according to the Pythagoreans, who related consonant intervals to ratios of small integers and subsumed music into their mathematical quadrivium along with arithmetic, geometry and astronomy. Since then the strong connection between music and mathematics has been much trumpeted; however, explanations seldom go beyond this first point of contact. We hope to improve on this by taking a deeper look at the musical parameters of pitch, harmony, rhythm and timbre. One-upping Pythagoras, we will see how pitch-space is naturally represented by a circle, and how the space of dyads (two-note chords) can be considered as a Möbius strip. Regarded in this light, a musical composition comes to resemble exactly the sort of structure that abstract mathematics is concerned with. As a result, relatively sophisticated mathematics can be applied both to the understanding of these structures (musical analysis), and to their construction (composition). Musical examples will abound. At the end the speaker will raise the philosophical question of whether we have really come any further in establishing the supposed deep link between these two disciplines, and then quickly duck out of the room.

Jon Bougie, Physics, Loyola University Chicago (spring 2011) *Pattern Formation in Granular Materials: Nonlinear Dynamics in a Sandbox *

Systems composed of grains are all around us, but there is much still to be learned about their behavior. Granular materials are found in many forms, including sand on a beach, wheat in a hopper, boulders in an avalanche, and pills at a pharmaceutical factory. While the behavior of individual grains can be quite simple, interactions between many grains can lead to very complex and interesting behavior. Therefore, despite the fact that granular materials are common in nature, agriculture, and industrial applications, the basic equations governing granular systems are not yet known. In this talk, I will illustrate these ideas by examining spontaneous pattern formation in vertically shaken granular layers. When a layer of grains is placed on a vertically oscillating plate, the layer leaves the plate at some point in the oscillation if the maximum acceleration of the plate is greater than that of gravity. If the acceleration increases above a critical value, standing waves form in the layer. These waves spontaneously order themselves to create patterns such as stripes, squares, and hexagons. I will discuss the phenomenon of pattern formation in these systems as an example of pattern formation in nonlinear systems. I will also compare these patterns to those found in shaken fluid layers, and discuss whether this analogy with fluid dynamics can lead us to a set of “granular hydrodynamic” equations governing granular flow.

Cary Huffman, Mathematics and Statistics, Loyola University Chicago (fall 2011)*From CDs to Deep Space *

Why can you still play a CD even after it is scratched? How does NASA get perfect pictures from Saturn? This talk will examine how error-correcting codes are used in CD/DVD recording and deep space communications. Really cool pictures will be shown.

Karen Smilowitz, Industrial Engineering and Management Sciences, Northwestern University (fall 2012)

*Operations research for non-profit settings*

This talk will discuss opportunities and challenges related to the development and application of operations research techniques to transportation and logistics problems in non-profit settings. Much research has been conducted on transportation and logistics problems in commercial settings where the goal is either to maximize profit or to minimize cost. Significantly less work has been conducted for non-profit applications. In such settings, the objectives are often more difficult to quantify since issues such as equity and sustainability must be considered, yet efficient operations are still crucial. This talk will present several research projects that introduce new approaches tailored to the objectives and constraints unique to non-profit agencies, which are often concerned with obtaining equitable solutions given limited, and often uncertain, budgets, rather than with maximizing profits. This talk will assess the potential of operations research to address the problems faced by non-profit agencies and attempt to understand why these problems have been understudied within the operations research community. To do so, we will ask the following questions: Are non-profit operations problems rich enough for academic study? Are solutions to non-profit operations problems applicable to real communities?