## Population Games and Evolutionary Dynamics

**April 14, 2014**

**Speaker:** Bill Sandholm (Economics)

**Abstract:** Population games provide a general model of strategic interactions among large numbers of agents; highway congestion, multilateral externalities, and natural selection are among their many applications. To model the dynamics of behavior in population games, we introduce revision protocols, which provide explicit stochastic descriptions of how individual agents make decisions.

## Elliptic Curve Cryptography

**April 7, 2014**

**Speaker:** Megan Maguire

**Abstract:** Public-key cryptography refers to cryptographic algorithms that require both a secret key and a public key that are mathematically linked. The public key is used to encrypt and the private key is used to decrypt. Since the public key is public information, the mathematical relationship between the public and private keys needs to be sufficiently difficult to determine without knowledge of the private key. The elliptic curve discrete logarithm problem (ECDLP) provides such a framework for generating public and private keys. We will learn the basics of elliptic curves over finite fields, the elliptic curve discrete logarithm problem, and how they are used in cryptography.

## Game Theory and Economics: Some Classic and Open Problems

March 24th 2014

**Speaker: **Marzena Rostek (Economics)

**Abstract: **Game theory studies behavior in strategic situations, that is when agents payoffs depend on behavior of others as well as their own. This talk will give an introduction to how economics and game theory draw on mathematics. We will discuss some classic games and new economic and game theoretic problems, where novel conceptualizations and/or tools are needed

As always, there will be **free** food.

**When: **Monday, March 24th 2014, 4:35pm

## Some Surprising Issues Relating to Curvature

March 3, 2014

**Speaker: **Betsy Stovall

**Abstract:** In multivariable calculus, we learn about a few simple, yet fundamental curved surfaces, such as the paraboloid, the sphere, and the cone. These simple surfaces give rise to some concrete, but very hard (and still unsolved) problems in a field called harmonic analysis. These problems also have surprising connections to some completely geometric questions about sets in euclidean space. In this talk, we will give a friendly introduction to some of the questions and ideas in this area.

## Multistability and Hidden Attractors

February 24, 2014

**Speaker:** Clint Sprott, UW Department of Physics

**Abstract:** One characteristic of nonlinear dynamical systems is that they can have more than one stable equilibrium. Perturbations of the variables or changes in the parameters can cause the system to abruptly switch from one equilibrium to the other from which it is hard to recover (what Al Gore calls a "tipping point"). Furthermore, equilibria can become unstable and give birth to periodic oscillations and even chaos. Hence, in addition to static attractors, there can be limit cycles and strange attractors, and several such attractors can coexist in even simple systems. Sometimes these attractors are "hidden" in the sense that they cannot be found by starting from the vicinity of an unstable equilibrium. Such hidden attractors can be catastrophic if the system is a building, a bridge, or an airplane wing. Examples of such behavior will be illustrated in very simple systems of differential equations and with simple demonstrations.

## Heavenly Clues to the Fundamental Laws of Physics

February 17, 2014

**Speaker**: Daniel Chung

**Abstract:** Observations of the heavens have played an important role in the development of the fundamental laws of physics. I will survey the current status of this interplay between cosmology and the fundamental laws of nature. Topics covered will include dark matter, dark energy, Higgs bosons, the matter/antimatter asymmetry, inflation, and the multiverse.

## Using Pentagrams to Conjure Solitons

November 11, 2013

**Speaker:** Gloria Mari-Beffa

**Abstract: **The pentagram map was defined by Richard Schwarz over 20 years ago and, after a somehow dormant period, it has recently become a very active area of research. In this talk I will describe the basic construction of the pentagram map and its relation to the Boussinesq equation, a well-known water wave equation with soliton solutions. I will also describe some of what is known and not known about the map, and variants like pentagram spirals.

## Curve Shortening and Bicycle Tracks; Life as a math major at EPIC

November 4, 2013

**Speakers:** Sigurd Angenent; Renee Schuppener

**Abstract:** **Dr. Sigurd Angenent** will answer three old questions in his talk: Can you tell from a pair of bicycle tracks which is the front track, and which is the rear? If you know the track of the front tire, can you draw that of the rear tire? What about the other way around?

Also on Monday, **Renee Schuppener** will be speaking about life as a math major at Epic Corporation, a leading medical software company that regularly hires math majors.

## The Geometry of Molecules

April 29, 2013

Speaker: Julie Mitchell

Abstract All of us have grown up doing puzzles. But, did you know that your body works by matching the geometries of molecules? For example, this is how you become immune to a disease. Your immune system works to create a shape that is a match to the invader.

## Non-standard analysis and hyperreal numbers

April 22, 2013

Speaker: Uri Andrews

Abstract Newton and Leibniz invented calculus using infinitesimals: positive numbers smaller than every positive real number. The math-world had come to reject the idea of infinitesimals on the (silly) grounds that no positive real number is smaller than every positive real number. We'll talk about how to fix that pesky problem and use infinitesimals to give a different approach to analysis.