**Spring 2016**

Monday, February 22, at 5:30 in Cupples I, room 199Speaker: Professor Xiang Tang

Title: Can you comb a hairy ball?

Abstract: In this talk, we plan to discuss a math proof of the following result. ``One cannot comb a hairy ball without creating a cowlick." This theorem was first stated by Henri Poincare and first proved by Brouwer.

Tuesday, February 2, 2016, 5:30 p.m. in Cupples I room 199.

Speaker: Professor Rachel Roberts

Monday, Febraury 29, 5:30 p.m. in Cupples I, Room 199Speaker: Professor Xiang Tang

Title: Can you comb a hairy ball?

Abstract: In this talk, we plan to discuss a math proof of the following result. ``One cannot comb a hairy ball without creating a cowlick." This theorem was first stated by Henri Poincare and first proved by Brouwer.

Wednesday, March 30, at 5:30 in Cupples I, room 199

Speaker: Professor Carl Bender (Dept of Physics)

Topic: *Physics in the Complex Plane*

Monday, April 18th, at 5:30 in Cupples I, room 199

Student speaker: Kwok-hao Lee, at 5:30 in Cupples I, 199

Topic: *Law and Order: Group Actions on R^n (not the statistics language R, but the topologyical space!)*

Abstract: There is life beyond boring calculus. Step into the strange world of ordered groups - where familiar everyday objects, like the ball, torus or the Klein bottle correspond in a natural way to functions on the real number line.

**Fall 2015**

Monday, September 21, 5:30 in Cupples I, room 199

First meeting of the year with Professor Ari Stern as speaker**.**

October meeting

Speaker: Professor John Shareshian

Tuesday, November 3, at 5:30 p.m. in Cupples I room 199.

Speaker: Professor Matt Kerr

Topic: Power sums and alternating permutations

The talk explores properties of the sequence (aa, a2, ...,an, ...) where an is the number of "updown" sequences of length n:

i1 < i2 > i3 < i4 ... (a reordering of {1,2,...,n})

Tuesday, November 17, at 5:30 p.m. in Cupples I, 199

Speaker: Bennet Goeckner

Topic: Deomposing Simplicial Complexes

Abstract: Simplicial complexes lie in the intersection of combinatorics, topology, and abstract algebra, and can be studied using techniques from all three fields. I will provide an introduction to the study of simplicial complexes and an overview of my research, which focuses on decomposing these complexes. I will also talk about my time as an undergrad at Wash U and my experiences as a graduate student now. No prerequisite knowledge after (or including) Calculus will be assumed.Tuesday, November 17, at 5:30 in Cupples I, 199

*Note: Bennet is a former WU math major, graduated in May 2011, and now a Ph.D. student in the Department of Mathematics at the University of Kansas. He should also be able to answer some questions about graduate study in mathematics (particularly, of course, at University of Kansas)*

**Spring 2015**

Monday, January 26, 5:30 in Cupples I, room 199

Speaker: Professor Renato Feres

Topic: Geometry in Very High Dimensions

Abstract: Peculiar things happen to volumes when the dimension of space grows to very large values. In this talk we'll see some of these properties and how probability theory can help make sense of them

**Fall 2014 **

Tuesday, September 30, 5:30 p.m., in Cupples I, room 199

Speaker: Professor Hang Liang Gan, *Paradoxical Musings*

Abstract: A paradox is a statement or group of statements that leads to a contradiction or a situation which (if true) defies logic or reason, similar to circular reasoning. -Wikipedia. There are all sorts of paradoxes that people have thought up over the years. Logical paradoxes, philosophical paradoxes, chemical paradoxes, but by far the most interesting paradoxes are mathematical paradoxes. We'll see how good maths, some bad maths, some totally wrong maths, and some confusing maths can lead to counter intuitive conclusions. There will be an object with infinite surface area but finite volume, paradoxes about neckties, envelopes and even a paradox by a Saint!

**Spring 2014**

Tuesday, April 22, 5:30 p.m. uin Cupples I, room 199

Speaker: Professor Ron Freiwald, *Calculus and Infinitesimals*

Abstract: Early in the development of calculus, some mathematicians freely used “infinitesimals” in their arguments. An “infinitesimal” was a number “infinitely small but not 0.” Of course, the problem was that no such real numbers actually exist. Eventually infinitesimals were banished from pure mathematics by carefully developing the idea of “limit.” They remained only as an occasional shorthand for “a quantity with limiting value 0,” or as a heuristic device in physics and engineering. In the 1960s, a mathematician/logician named Abraham Robinson showed how to rigorously extend the real number system to a system of “hyperreals” that includes infinitesimals (and infinite) numbers. We will look at some features hyperreal numbers and illustrate how they could be used in elementary calculus operations.

Tuesday, April 8, a :30 p.m. in Cupples I, room 199

Speaker: Professor Ari Stern, *Scoring points vs. winning games: a fundamental problem in the mathematics of sports*

Abstract: Many sports and games are based on scoring, where the team (or player) with the highest score wins. Yet, due to chance, high-scoring teams sometimes lose, and low-scoring teams sometimes win. How can we determine whether a team is truly good, or merely lucky? (For example, how many games did the Cardinals really deserve to win last year?) What is the relative value of offense and defense? In this talk, I will discuss how these questions have been approached mathematically --- with widely varying degrees of sophistication and rigor --- and how this work might be put on more solid ground.

Tuesday, March 22, at 5:30 p.m. in Cupples I, room 199

Speaker: Professor John Patty (Department of Political Science)

Topics: *Game Theory and Political Coalitions*

Abstract: Game theoretic models of politics represent political situations as strategic interactions between multiple actors with potentially varying information, decisions, and goals. I will discuss a simple class of such models, known as asymmetric coordination games, and how one can apply these to the study of political coalitions: which ones form, how do they coordinate their actions, and how long do they tend to last?

Tuesday, March 4, at 5:30 p.m. in Cupples I, room 199

Speaker Professor Francesc Ferrer, Department of Physics

Topic: *The geometric theory of gravitation*

Abstract: In 1907 Einstein introduced the Principle of Equivalence of Gravitation and Inertia, and used it to calculate the red shift of light in a gravitational field. Six years later, a collaboration with the mathematician Marcel Grossman led Einstein to the view that the gravitational field must be identified with the metric tensor of Riemannian space-time geometry. Einstein subsequently worked out the field equations that relate the curvature of space-time to the energy and momentum of matter and radiation. We will discuss the geometrical foundations of General Relativity, and describe some of the implications such as the gravitational redshift, the existence of black holes, and the indirect evidence for gravitational waves that are being actively searched with laser interferometer observatories.

Thursday, February 13, at 5:30 p.m. in Cupples I, room 199

Professor John Shareshian*: Group Theory and Counting*

Abstract: A group is a set with a binary operation satisfying certain axioms. Groups arise in many areas of intellectual inquiry, in particular in any situation where symmetry exists. After introducing groups and presenting some examples, I will show how group theory can be used to solve some counting problems.

Professor Peter Luthy: *Analyzing Card Shuffling*

Abstract: Card shuffling can be viewed through a number of mathematical lenses: group theoretically, graph theoretically, linear algebraically, and probabilistically. In this talk we will discuss several of these different interpretations, discuss the computational difficulties surrounding this problem, and give a partial answer to the question of how many times I need to shuffle the deck. Time permitting, we will discuss a variety of shuffling strategies and how they compare to the standard riffle shuffle.

**Fall 2013**

Tuesday, December 3, at 5:30 p.m. in Cupples I, room 199

Speaker: Professor Blake Thornton

Topic: *Rational Tangles*

Thursday, November 21 at 5:30 p.m. in Cupples I, room 199

Speaker: Professor John McCarthy

Why were complex numbers invented?

Abstract: Nobody cared that you couldn't solve the equation x^2 + 1 = 0. Draw the graph, and it is obvious that no solution exists. But if you want to solve cubics like x^3 - 16x - 4 = 0, which by the intermediate value theorem has to have a real root between 4 and 5, the algebraic formula involves complex numbers. I will talk about the history of the cubic, and how to solve it.

Tuesday, October 29, 5:30 p.m. in Cupples I, room 199

Biostatistics: Dr. Jeannette Simino

Dr. Simino is on the faculty of the Division of Biostatistics at the School of Medicine. She will discuss the field of biostatistics and the MSIBS (Master of Science in Biostatistics) program.

Thursday, October 15, 2013

Professor David Wright: Mathematics and Music

Abstract: It has been observed that mathematics is the most abstract of the sciences, music the most abstract of the arts. Mathematics attempts to understand conceptual and logical truth and appreciates the intrinsic beauty of such. Music evokes mood and emotion by the audio medium of tones and rhythms without appealing to circumstantial means of eliciting such innate human reactions. Therefore it is not surprising that the symbiosis of the two disciplines is an age old story. The Greek mathematician Pythagoras noted the integral relationships between frequencies of musical tones in a consonant interval; the 18th century musician J. S. Bach studied the mathematical problem of finding a practical way to tune keyboard instruments. In this talk, some musical and mathematical notions will be brought together.

Thursday, September 26, 2013

Professor Ari Stern: An Introduction to LaTeX

Abstract: LaTeX is a powerful open-source software tool for typesetting documents, especially those containing mathematics. While it is used almost universally among professional mathematicians, it has an unfortunate reputation for having a steep learning curve, and many books and tutorials are woefully out of date. This talk will give a gentle introduction ot LaTeX--as it's used today, with historical baggage kept to a minimum-- and will discuss installation, creation of basic documents, useful packages, and various tips and tricks.

Thursday, September 12, 2013

A screening of the movie Fermat's Last Theorem

**Spring 2013**

Monday, April 22, 2013 at 5:40 p.m. in Cupples I, room 199

Professor Killian Weinberger (Department of Computer Science and Engineering)

Topic: *What is Machine Learning?*

Abstract: In this talk I give a brief introduction of the discipline of Machine Learning, its history and the problems it attempts to solve. In addition, I provide a brief overview over a few simple approaches (nearest neighbors, logistic regression and artificial neural networks) and demonstrate them live on several examples.

Monday, March 25, 2013 at 5:40 p.m. in Cupples I, room 199

Professor John P. Cunningham (Department of Biomedical Engineering)

Topic: *R^100 is a big place*

Abstract: Remarkable things happen in high-dimensional Euclidean space. I will discuss some examples of this phenomenon, known to some as the curse of dimensionality, to others as the blessing of dimensionality, and to others as just weird. I will talk about intuition-breakdown in high-dimensional statistics, an issue which is becoming increasingly important in the modern world of huge data sets and important statistical challenges. We will discuss hypercubes, hyperspheres, high-dimensional Gaussian vectors, Fisher's LDA, correlation, concentration of measure, etc. I presume a basic knowledge of statistics, linear algebra, and calculus, and I will try to keep measure theory out of it.

Monday February 25, 2013 at 5:40 p.m. in Cupples I, room 199

Jeff Gill (Department of Political Science)

Topic: *The variable effect of war on longterm childhood mental health outcomes*

Abstract: While children are routinely exposed to armed conflicts ranging from minor skirmishes to full-scale national wars, there is relatively little scholarship on the psychological and emotional consequences they face in either the short or long term. Through continued partnership with the AMPATH network of clinics (a collaborative effort between Indiana University and Moi University Schools of Medicine), we have access to the health clinic patient population in Eldoret, western Kenya. How does the severity and variety of exposure to political violence affect children differently? Can this causal process be modeled with a monotonic biological gradient? Are there clustering and transmission patterns that can be identified? Do there exist interaction effects between subjects, outcomes, or geographic regions that are supported by empirical data? We propose using a case-control study to test the effects of violent conflict, understanding sampling effects and potential bias, estimating expected precision and validity, as well as obtaining demographic, political, and geographic background data. The core of the statistical analysis is the specification of a Bayesian hierarchical model to directly incorporate grouping that results from clustering of effects, geography, and affliction, as well as demographics.

Date: Monday February 11, 2013 at 5:40 p.m. in Cupples I, room 199

David Levine (John H. Biggs Distinguished Professor of Economics)

Topic: *Nash, Hirsch and all that*

Abstract: What is a Nash equilibrium, why do economists care about it, and what do entropy and retracts have to do with it? All these questions and more will be answered.

Date: Monday January 28, 2013 at 5:40 p.m. in CUpples I, room 199

Professor Mark Alford (Department of Physics): *Field theory, the Higgs particle and superconducting metals*

Abstract: The recently discovered Higgs particle and the long-known superconductivity of a cold metal are two aspects of the same basic phenomenon, which is spontaneous symmetry breaking. I will discuss how physicists understand this phenomenon in terms of field theory.

**Fall 2012**

Date: Monday, November 26, 2012

Speaker: Professor John Shareshian*Some divergent series studied by Euler, and permutation statistics*

Abstract: For a positive integer n, a permutation of n is a list of the integers 1 through n in any of the n! possible orders. A permutation statistic is a function that assigns a nonnegative integer to each permutation. Certain permutation statistics are called ``Eulerian", due to their connection with work of L. Euler on divergent series. One example of an Eulerian statistic is the excedance statistic, which assigns to each permutation w of n the number of elements i in {1,...,n} such that the number found in the i^th position of w is larger than i. For example, the permutation 13542 has two excedances, found in the second and third positions. Other statistics are called ``Mahonian", as the first difficult results on such statistics were found by P.A. MacMahon. One example of a Mahonian statistic is the inversion number, which assigns to each permutation w of n the number of pairs (i,j) of elements of {1,...,n} such that i is less than j but i appears after j in w. For example, 13542 has 4 inversions, namely, the pairs (2,3), (2,4), (2,5) and (4,5). After describing Euler's work and its connection to Eulerian statistics, I will (time permitting) discuss modern work on joint distributions involving one Eulerian statistic and one Mahonian statistic. In such work, given a Mahonian statistic f and an Eulerian statistic g, one tries to understand, for each n, the two-variable polynomial obtained by summing, over all permutations w of n, the monomial q^f(w) t^g(w).

Date: November 5, 2012

Speaker: Professor Victor Wickerhauser*What Haar, Walsh, Hadamard and Rademacher did with 0, 1, and -1*

Abstract: The four mentioned mathematicians found efficient ways to express arbitrary functions as linear combinations of simple functions taking just the values 0, 1, and -1. We will look at their ingenious constructions and discover some of the beautiful connections among their ideas.

Date: Monday, October 22,

Speaker: Professor Anton Weisstein

Professor Weisstein is visiting the Biology Department at W.U. this fall, from Truman State University where he an Associate Professor of Biology. He is an "alumnus" math major from W.U.Topic:* The Beauty of Untidiness: an Overview of Mathematical Biology*

Abstract: The long-standing collaboration between mathematics and physics has yielded enormous benefits to both fields. By contrast, the complexity of most biological systems has made them far harder to mathematize, leading to the life sciences being viewed as essentially non-mathematical. owever, ththe development of technologies such as massively parallel genomic sequencing and ultrafast molecular modeling have generated new biological questions that require more specialized mathematical analysis. ust as the study ofof planetary movements stimulated the development of trigonometry and calculus, these new biological questions offer opportunities for advances in graph theory, statistical inference, and multiscale modeling. n this talk, I I will give an overview of mathematical biology, focusing on five specific areas of collaboration. No specialized biology background is assumed.

Date: October 8, 201

Speaker: Professor Ari Stern

Topic: *Simulating dynamical systems: classic methods and modern challenges*

Abstract: Ordinary differential equations (ODEs) are central to many areas of mathematics, and have a vast range of applications in science and engineering. However, most nonlinear ODEs cannot be solved in closed form. Fortunately, all hope is not lost: "numerical integrators" allow us to simulate these dynamical systems, obtaining approximate solutions to an arbitrary degree of accuracy. This talk will introduce a few classic methods for numerical integration, along with the theory used to analyze their stability and convergence. I will also discuss some recent research developments in the area of "geometric numerical integration," explaining why certain methods perform much better than others for simulating physical systems.

Date: Monday, September 24

Speaker: Professor Math Kerr

Topic: * Finite Fourier transforms and Bernoulli polynomials*

Abstract: I've often wondered why undergraduate courses in linear algebra don't cover finite Fourier transforms, considering future mathematicians might use them in number theory and engineers in MATLAB. What I'll try to explain in this talk is what the two things in my title are, and how together they give you a beautiful way to compute the sums of a nice big set of infinite series -- elementary number theory at its best. I'll say something about more applied uses of finite FT's too.

Date: Monday, September 10, 5:40 - 6 :30, in Cupples I, room 199

Topic: *The Geometry of Eero Saarinen's Gateway Arch * (a DVD presentation by geometer Robert Osserman)

**Spring 2012**

Date: Tuesday, April 24,2012 at 5:40 p.m. in Cupples I, room 199

Speaker: Professor Hiro Mukai, Systems Science and Mathematics

Topic: *Linear Programming: Linear Optimization*

Date: Tuesday, April 10,2012 at 5:40 p.m. in Cupples I, room 199

Speaker: Mr. Josh ORear, Agricultural Statistician USDA, National Agricultural Statistics Service

Topic: *Statistics in the agricultural market*

Date: Tuesday, March 27, 2012 at 5:40 p.m. in Cupples I, room 199

Speaker: Ping Wang, Seigle Family Professor, Department of Economics

Topic: *Optimal Control: From Shooting Rocket to Economic Decision-Making*

Tuesday, March 6, 2012 at 5:40 p.m. in Cupples I, room 199

Speaker: Professor Tzyh Jong Tarn (Systems Science and Mathematics)

Topic: *Systems Science: Past, Present, and Future*

Tuesday, February 21, 2012 at 5:40 p.m. in Cupples I, room 199

Speaker: Professor Ivan Horozov

Topic: *Iterated Integrals in Number Theory and Differential Geometry*

Abstract: A key ingredient in the talk will be the notion of "differential forms". I will introduce them in an intuitive way. Then we will use them to define iterated integrals. After that I am going to use iterated integrals for special values of arithmetically important functions such as Riemann Zeta Function and Multiple Zeta Functions. The relations will be of the type "a special value of above function = an iterated integral". At the end of the talk, I will describe a unified approach for all of such equalities, which could be a first step in Differential Geometry.

Tuesday, February 7, in Cupples I, room 199, at 5:40 p.m.

Speaker: Professor Matt Kerr

Title: *Introduction to p-adic numbers*

Abstract: You have long been comfortable (or not) with real numbers having infinite decimal expansions to the right. But have you ever wondered whether a viable theory of numbers could be made with infinite *leftward* expansions? In fact you can make infinitely many such systems, one for each prime p, and in this talk I'll at least try to explain some basic operations like addition, subtraction, multiplication, and square root. Subtraction is really strange, almost as strange as the fact that any point inside a p-adic circle is its center. Far from being a novelty item, however, p-adic numbers are an essential tool in diverse areas of number theory, including Galois theory, the study of Diophantine equations, and the proof of Fermat's last theorem.

Tuesday, January 24, 2012 in Cupples I, room 199, at 5:40 p.m.

Title: The Optimal Packings of Three Equal Circles on Flat Tori

Speaker: Jennifer Kenkel (junior math major)

Abstract: The study of maximally dense packings of disjoint equal circles is a problem in Discrete Geometry. The optimal densities and arrangements are known for packings of small numbers of equal circles into hard boundary containers, including squares, equilateral triangles and circles. In this presentation, we will explore packings of three equal circles into a boundaryless container called a flat torus. Using numerous figures we will introduce all the basic concepts (including the notion of a flat torus, an optimal packing and the graph of a packing), demonstrate many maximally dense arrangements, and outline the proofs of their optimality. This research was conducted as part of the 2011 REU program at Grand Valley State University.

**Fall 2011**

Title: What does a negatively-curved space look like?

Speaker: Professor Tejas Kalelkar

Date/Time/Place: Tuesday, November 29, 2011 in Cupples I, room 199 at 5:40 pm

Abstract: A few centuries back, people assumed the world was flat and now we scoff at such claims. A few decades back people assumed the universe was flat, post-Einstein now we think we know better. It makes sense then to ask of the possible shapes space can take as long as there are some basic common-sensical rules that must be obeyed. We shall talk, in particular, of a negatively-curved space called Hyperbolic space, and some of its weird properties. We shall then briefly run through a typical day for someone living in a Spherical, Euclidean or a Hyperbolic universe.

Title: From Quantum Coherence to Quantum Computer by Molecular Spectroscopy

Speaker: Professor Tom Lin, Department of Chemistry

Date/Time/Place: November 1, 2011 in Cupples I, room 199 at 5:40 pm.

Abstract: We apply group theory and density matrices techniques in our quantum computer study. The experimental tool is electron spin echo spectroscopy which studies the quantum coherence effect and quantum computer feasibility of organic triplet states (paramagnetic states) in solids upon laser excitation and in the presence of microwave pulses. The math tools and quantum concepts needed in this research are essential which allows us not only to simplify our computation protocol but also facilitate detailed calculations with minimum efforts.

Title: Billiards, Markov chains, and statistical physics

Speaker: Professor Renato Feres

Date/Time/Place: October 25, 2011 in Cupples I, room 199 at 5:40 pm.

Abstract: A widely studied mathematical version of the game of billiards has long provided a valuable tool to explore and develop the dynamical theory of both "integrable" and "chaotic" dynamical systems. In this talk I wish to describe certain types of Markov chains derived from billiard dynamical systems that help to understand basic thermodynamic concepts such as temperature and thermal equilibrium.

Title: Error Correcting Codes

Speaker: Professor Edward Spitznagel, *Error Correcting Codes*

Date/Time/Place: October 11, 2011 in Cupples I, room 199 at 5:40 pm.

Abstract: Have you ever wondered how Compact Digital (CD) disks can suffer so many scratches and still play perfectly? Have you ever wondered how those fantastic pictures of Saturn and its rings get from "there" to "here" with apparently no degradation? The answer to these and similar questions lies in error correcting codes. I will give a very gentle introduction to these unsung heroes of the information age, showing a wee bit of the college-level mathematics that lies beneath them. There are no prerequisites for my talk. The ideas are simple, but they open doors into a great expanse of modern mathematics.

Title: The Beauty of Geometry

Speaker: Professor Quo-Shin Chi

Date/time/place: Tuesday, September 27, 5:40 pm in Cupples I 199

Abstract: I will walk through several decisive developments and their prevailing impacts in the long history of geometry.

Title: A viewing of the movie: *PROOF*

Date/time/place: Tuesday, September 13, 5:40 pm in Cupples I 199

Summary: The daughter of a brilliant but mentally disturbed mathematician, recently deceased, tries to come to grips with her possible inheritance: his insanity. Complicating matters are one of her father's ex-students who wants to search through his papers and her estranged sister who shows up to help settle his affairs.

**Spring 2011**

Title: Symmetry and the Laws of Physics (or, How to Derive Everything from Basically Nothing)

Speaker: Tim Wiser

Date/time/place: Tuesday, April 19, 5:30 pm in Cupples I 199

Abstract: Symmetry is a powerful mathematical tool for solving problems, both in pure mathematics and in physics. Symmetry is often used informally to solve physics problems quickly, but one can also use abstract mathematical statements about symmetry to derive concrete facts about physical systems. One example is Noether's Theorem, which relates every continuous symmetry of a system to a conserved physical quantity (e.g. energy or momentum). Even more powerfully, our best model (currently) of the interactions of elementary particles is completely determined by symmetry alone. (Such a theory is called a "gauge theory"). I will prove Noether's Theorem for classical mechanics, and demonstrate the connection between symmetry and conservation laws. If time permits, I will briefly discuss gauge theories.

Title: Math and Music

Date/Time/Place: Tuesday, April 5, 5:30 p.m. in Cupples I, room 199

Speaker: Professor David Wright, Department of Mathematics

Abstract: This talk is about interrelationships between mathematics and music using several aural examples and demonstrations. We will discuss equal temperament, relate the chromatic scale it uses to modular arithmetic, and show why the musical staff is like a logarithmic scale for pitch. We will discuss how overtones are related to the integers and show how harmony derives from the overtone series. We will identify the mathematical relationships between pitches in consonant intervals and chords, and discuss the historical obstacles (going back to Pythagoras) to tuning a musical scale which gives mathematically precise harmony in all keys. The relationship between musical tones and periodic functions will be discussed, showing how a tone's timbre is determined by it's harmonics, and how this relates to trigonometry. Musical examples ranging from Tibetan throat singing to American jazz will be played to demonstrate such things as overtones, chords, timbres, and tuning.

Title: Some evolutionary consequences of superexponential population growth in humans; or, why do humans have so many rare variants?

Date/Time/Place: Tuesday, March 29, 5:30 p.m. in Cupples I, room 199

Speaker: Professor Alan Templeton, Department of Biology

Abstract: A recent DNA sequencing survey on nearly 15,000 humans revealed that rare variants are much more common than expected from standard population genetic theory. Standard theory assumes a population size that is roughly stable over time, but humans have experienced superexponential growth for at least the last 10,000 years. Probability generating functions are used to investigate the impact of such population growth upon the survival of a new mutant. It is shown that population growth greatly increases the probability of survival of a mutant, and even highly deleterious mutants can have a finite probability of persisting indefinitely. These results have a profound impact on our understanding of genetic risk factors to disease in humans, and can help explain the anomaly of "missing heritability" in genetic epidemiology studies.

Title: Common Knowledge

Speaker: Professor John Nachbar (Department of Economics)

Date/Time/Place: Tuesday, March 1, 5:30 p.m. in Cupples I, room 199

Abstract: In a very short, very beautiful, very readable paper, Robert Aumann provided a formal definition of "common knowledge" and used it to show that, assuming an auxiliary condition called the common prior assumption, experts cannot "agree to disagree" (Annals of Statistics, 1976, 1236-1239). Aumann himself noted that this conclusion is contradicted by everyday experience. Why is reality so different from this seemingly straightforward theory? I will cover Aumann's original paper and then, as time permits, survey some of the paper's extensive legacy, such as the no trade theorems and the epistemic foundations of equilibrium in games.

Title: Declared-Strategy Voting and Approval Ratings

Speaker: Professor Ron Cytron (Department of Computer Science and Engineering)

Date/time/place: Tuesday, February 15, 5:30 pm in Cupples I 199

Abstract: Computational social choice is a new discipline that explores issues at the intersection of social choice theory and computer science. In contrast to the security and reliability issues associated with using computers as ordinary voting devices, this new field studies the application of computation to enable new, interesting, and effective social choice mechanisms. We begin with a discussion of declared-strategy voting systems. While traditional voting systems elicit only the outcome of a participant's strategic thinking, a declared-strategy system accepts such strategies directly. Each voter's strategy is then evaluated to compute the voter's behavior in the election. We present a rationally optimal model for plurality elections in which voters need disclose only their cardinal preferences for the alternatives. We present results from applying this system in diverse social choice settings. Approval-rating polls already serve an important role in assaying the views of an electorate on some subject of interest. Sites such as Rotten Tomatoes and Metacritic.com collect and display the results of

approval-rating polls for movies and games. Moreover, sites such as Amazon and eBay collect approval ratings to estimate the worthiness of their buyers and sellers. We demonstrate the extent to which such polls can be manipulated. We then discuss mechanisms that avoid manipulation, including a declared-strategy system. Finally, we summarize our current investigations into comparing declared-strategy systems for more general approval elections.

Title: F = ma in the complex plane

Speaker: Professor Carl Bender (Department of Physics)

Date/time/place: Tuesday, February 1, 5:30 pm in Cupples I 199

Abstract: Classical mechanics and quantum mechanics are two very different theories: In classical mechanics the motion of a particle is governed by Newton's laws and we can say exactly where the particle is and how fast it is going at all times. The energy of a classical particle in a potential takes on a continuum of values. In quantum mechanics, on the other hand, particles display wavelike properties and predictions are probabilistic in character. The energy of a quantum particle in a potential can only take on a discrete set of allowed "quantized" values. Many years ago, mathematicians generalized the real number system to the complex number system. By doing this, mathematicians can understand and explain the real number system more clearly. What happens if we follow the mathematicians and generalize real physics to complex physics? In this talk I will show what happens when we generalize ordinary real classical mechanics to complex classical mechanics. We will see that, despite the enormous differences between classical mechanics and quantum mechanics in the real world, these differences melt away in the complex world and these two theories behave in an eerily similar fashion.