From bird flocks to fish schools, animals move together and respond to their environment in remarkable ways; their natural collective motion patterns appear well choreographed and their collective survival strategies seem ingenious. These animal group behaviors inspire design for groups of mobile, sensor-equipped robots, where demanding cooperative sensing tasks, such as exploration and mapping in uncertain, dynamic environments in land, sea, air, or space, find their analogue in natural group behaviors, such as foraging and feeding. However, bio-inspired design of this kind is not immediate because the natural mechanisms are not well understood. Mathematical modeling and analysis play a critical role in addressing this joint challenge to explain the enabling mechanisms in animal groups and to define provable mechanisms for robotic groups.

A common framework based on notions of synchrony will be used to discuss connections among spatial pattern, information passing, and collective behavior in robot and animal networks. Applications to be presented include the design of an adaptive ocean observation system using a fleet of underwater robotic vehicles and an investigation of motion and decision-making in bird flocks and fish schools.

1) Did you ever wonder what protects your computer password when you log on, or your credit card number when you shop on-line, from hackers listening on the communication lines? 2) Is it possible for a group of people to play a (cardless) game of Poker on the telephone, without anyone being able to cheat? 3) Can you convince others that you can solve a tough math (or SudoKu) puzzle, without giving them the slightest hint of your solution? 4) Can two people who never met create a secret language in the presence of others, which no one but them can understand?

In this talk, I plan to survey some of the mathematical and computational ideas, definitions, and assumptions which underlie privacy and security of the Internet and electronic commerce. I will explain some of the magical consequences of this theory. For example, how the solution of question (1) enables a positive answer to questions (2), (3), and (4). I will also explain the fragility of the current foundations of modern cryptography and the need for stronger ones.

Probabilities and randomness arise whenever we’re not sure what will happen next. They apply to everything from lottery jackpots to airplane crashes, casino gambling to homicide rates, medical studies to election polls to surprising coincidences. This talk will explain how a “Probability Perspective” can shed new light on many familiar situations. It will also discuss Monte Carlo computer algorithms, which use randomness to solve problems in many branches of science.

As disruptive as the financial crisis has been, the important lessons to be learned from the spectacular failure of financial technologies gone awry may actually pave the way for some of the most significant achievements of the 21st century. In this talk, Prof. Lo will provide a brief overview of the origins of the crisis, the key role that mathematics played, and how a deeper understanding of human nature may allow financial engineers to focus the enormous power of global financial markets on some of society's most pressing challenges.

As an increasing amount of social interaction moves on-line, it becomes possible to study phenomena that were once essentially invisible: how our social networks are organized, how groups of people come together and attract new members, and how information spreads through society. With computational and mathematical ideas, we can begin to map the rich social landscape that emerges, filled with "hot spots" of collective attention, and behaviors that cascade through our networks of social connections.

The Arnold Family Lecture series is endowed by a generous gift from the Arnold Family Foundation.

Every time we go on-line to look up something or to make a purchase, we are exposing ourselves to a certain amount of risk. We risk having our identities hijacked and our private information exploited. How do we protect networks against intruders and keep information safe? We do this with cryptography. This lecture will tour the mathematical ideas behind encryption, public key encryption, digital signatures, and authentication.

In October 2006, Netflix kicked off a $1M competition by releasing 100 million movie ratings as a training set to be used to build a better recommendation system for their on-line movie rental business. This landmark data set generated intense interest from the statistics and machine learning communities, and attracted entries from over 3000 teams from academia and industry. In this talk, I will review our team's experience analyzing this data and document our journey towards winning a share of the million dollar prize. Some of the surprising lessons include the role of ensembles (of models and teams) in the drive for the top spot, the power of matrix decomposition techniques, and the interplay between collaboration and competitiveness during the contest.

Minnesota voters can appreciate the many troubling events associated with elections. Far more serious things can go wrong in the voting process, but most of us do not know how to look for them. The speaker exposes the many surprising problems that can occur in elections and explains how they are uncovered through the power of mathematics. Expect to leave this lecture troubled about whether the "right person" won in a recent election of importance to you.

The Arnold Family Lecture series is endowed by a generous gift from the Arnold Family Foundation.

When we look out on a clear night, the universe seems infinite. Yet this infinity might be an illusion. During the first half of the presentation, computer games will introduce the concept of a "multiconnected universe." Interactive 3D graphics will then take the viewer on a tour of several possible shapes for space. Finally, we'll see how recent satellite data provide tantalizing clues to the true shape of our universe. The only prerequisites for this talk are curiosity and imagination. For middle school and high school students, people interested in astronomy, and all members of the university and surrounding communities.

The principles of origami, the centuries-old Japanese art of paper-folding, can be used to solve a wide range of folding problems, from how to compress an airbag into a steering wheel to how to design complex folding telescopes. These math-based origami concepts are used in product development, architecture, and designs seen all around us. For example, the University of Minnesota's Weisman Art Museum is an origami-inspired structure. The speaker is an artist and a consultant who applies origami principles to engineering problems.

This question appeared in a recent newspaper headline, but was based on a study involving only 14 people. How can we interpret the statistics behind headlines? What does statistically significant really mean? How do statistics get manipulated to further an agenda? The field of statistics is essential to understanding most current issues. It informs economics, health care, and environmental protection. The speaker calls statistics mathematical social work; it helps science progress, so it is important to understand its power.

Wavelets are used in the analysis of sounds and images, as well as in many other applications. The wavelet transform provides a mathematical analog to a music score: just as the score tells a musician which notes to play when, the wavelet analysis of a sound takes things apart into elementary units with a well defined frequency (which note?) and at a well defined time (when?). For images wavelets allow you to first describe the coarse features with a broad brush, and then later to fill in details. Because wavelets allow you to do a similar thing in more mathematical terms, the wavelet transform is sometimes called a “mathematical microscope.” Wavelets are used by many scientists for many different applications. Outside science as well, wavelets are finding their uses: wavelet transforms are an intergral part of the image compression standard JPEG2000. The talk will start by explaining the basic principles of wavelets, which are very simple. Then they will be illustrated with some examples, including an explanation of image compression.

Sensor networks are poised to affect our societies in dramatic ways. They are embedded into products we use each day, such as airbags, hearing aids, and networked cell phone systems. Sensors are tiny devices that collect information. When connected to a larger network, they manage vast amounts of data. Managing that data so we don't drown in it requires answers from mathematics.

Sensor networks monitor environmental changes in rain forests and are used in nanotechnology and biomedical testing. They are widely used in law enforcement and in homeland security. "These networks are changing our lives and our social rules," Ghrist says. "And the impacts we are seeing today are incomparable to changes that are coming." He will describe a recent calculus for sensor network data, whose origins lie in algebraic topology.

Major League Baseball is a multi-billion dollar per year industry that relies heavily on the quality of its schedule. Teams, fans, TV networks, and even political parties (in a way revealed in the talk) rely on the schedule for profits and enjoyment. Only recently have the computational tools of operations research been powerful enough to address the issue of finding "optimal" schedules. Trick will discuss his experiences in scheduling college basketball, major league baseball, and other sports, and show how operations research is revolutionizing the way sports scheduling is done.

Systems as diverse as the world wide web, Internet or the cell are described by highly interconnected networks with amazingly complex structure. Recent studies indicate that the evolution of these complex networks is governed by simple but generic laws, resulting in apparently universal architectural features. I will discuss this amazing order characterizing our interconnected world, and its implications to how we perceive the impact on communications and medicine.

Recently, algebraic methods have been developed to unify and advance a variety of techniques of statistical analysis, providing new and improved tools for computational biology. Professor Sturmfels, one of the founders of the new field of algebraic statistics, will introduce the subject and describe its emerging applications to genome science and developmental biology. He will be assisted by a fictional character named DiaNA who plays hopscotch and rolls tetrahedral dice with faces labeled “A”, “C”,“G”, and “T”.

M.C. Escher is among the most mathematical of artists. In 1956 he challenged the laws of perspective with his graphic Print Gallery, and found himself trapped by an impossible barrier. His uncompleted master-piece quickly became the most puzzling enigma of modern art, for both artists and scientists. Half a century later, mathematician Hendrik Lenstra took everyone by surprise by drawing a fantastic bridge between the intuition of the artist and his own, and completed Escher's work mathematically. This story is presented in the 52 minute film Achieving the Unachievable by documentary filmmaker Jean Bergeron. After the screening, the film's U.S. premier, Bergeron will be available to answer questions.

Mathematical models are enabling advances in increasingly complex areas of engineering and technology. Recent developments in multiscale geometrical modeling have opened the way to progress in modeling such complex systems as the human circulatory system and the climate system. Professor Quarteroni leads a team which has harnessed mathematical modeling to design improved cardiac surgical interventions and to optimize the design of the twice winning America's cup yacht Alinghi. He will talk about this work, and their efforts to confront some of the great environmental challenges that face us.

Optimization, one of the most utilized branches of applied mathematics, is the study of problems which can be formulated as maximizing some quantity of interest by controlling related quantities. The idea of optimization is intimately connected with modern science. Pioneers like Galileo, Fermat, and Newton, were convinced that the world had been created by a benevolent god who had established the laws of nature as the most efficient way to achieve his purposes: in short, this is the best of all possible worlds, and it is the task of science to find out why and how. Gradually this view was overturned, leaving optimization as an important tool for the human-engineered world. More recently, game theory has come to replace optimization for describing situations where a multitude of individuals with conflicting interests make decisions based on imperfect information. In this lecture, Professor Ekeland will guide us along the path from Fermat to modern economic theory, and from optimization to game theory.

Some problems in life are very hard (achieving world peace) while others are, at least for many of us, pretty easy (eating a good breakfast). How can we figure out which are which? Math can often tell us precisely how hard real-world problems are—but not always. We'll look at easy problems, hard problems, the sources of hardness, and puzzling instances where problems are invariably easier than today's math says they should be.

The world around us often seems terribly complex, chaotic and difficult to understand. We encounter this every day: in the weather, social networks, sophisticated machinery, the internet. Frequently this complexity arises from the interaction of widely diverse scales in time and space. For example, the weather can turn in minutes, while the climate persists for many many years. Can math and science help us to make sense of all this complexity, or is it a study doomed from the start? Illustrating with many examples, Professor Budd will show that all is not lost. He will explain how simple properties often emerge from seemingly very complex systems, and how we can use these properties to gain understanding.

Regular patterns appear all around us: from vast geological formations to the ripples in a vibrating coffee cup, from the gaits of trotting horses to tongues of flames, and even in visual hallucinations. The mathematical notion of symmetry is a key to understanding how and why these patterns form. In this lecture Professor Golubitsky will show some of these fascinating patterns and explain how mathematical symmetry enters the picture.

During the past decade, complex networks have become increasingly important in communication and information technology. Vast, self-engineered networks, like the Internet, the World Wide Web, and Instant Messaging Networks, have facilitated the flow of information, and served as media for social and economic interaction. In social networks, the ease of information flow goes by many names: the "small world" phenomenon, the "Kevin Bacon phenomenon," and "six degrees of separation"—the claim that any two people on earth can be connected through a chain of acquaintances with at most five intermediaries. Unfortunately, many of the properties that facilitate information transmission also facilitate the spread of viruses in both technological and social networks. Dr. Chayes uses simple mathematical models to explain these epidemics and to examine strategies for their containment.

The human brain contains about 100 billion neurons, each making about 1000 synaptic connections with other neurons. This huge dynamical system communicates with itself and its environment via electrical impulses called spikes. How is incoming information turned into spikes, and how do spikes create decisions and behaviors? I will show how mathematics helps us model and analyze such questions, involving events from single neural spikes to decisions that change our lives.

All too often we see mathematics and the arts as two sides of the science/humanities coin. In this talk we'll see a place in which the two come naturally together in exciting new research. In today's world in which almost all aspects of life are brought to the common medium of the computer, it is now possible to quantify and extract the style of an artist via computation. Examples are gleaned from the literary, visual, and dance arts, and include applications to the problem of authentication. Taken together this work reveals just how stylish math can be.

Shadow patterns are all around us. We drive through them on the way to work and swim among them in pools. Similar patterns are also cast throughout the universe by the gravitational fields of stars and galaxies. We unveil some of the cosmic and mathematical secrets of these mysterious and beautiful patterns.

Sometimes the way a magic trick works is even more amazing than the trick itself. I will illustrate with some performable tricks that seem to fool magicians. The math involved has application to breaking and entering, robot vision, cryptography, random number generation, and DNA sequence analysis.