D.W.Weeks Lecture Series Archive
20122013
20100509  Maria Gorelik ((Weizmann Institute of Science)) TBA [Abstract] TBA 
20110926  Olivia Caramello (University of Cambridge) Toposes as 'Bridges' for Unifying Mathematics [Abstract] The notion of topos, introduced by Alexandre Grothendieck in the early sixties in the context of Algebraic Geometry, has an intrinsically eclectic nature; indeed, a topos can be seen as a generalized space, as a mathematical universe but also as a theory. In this talk, I will give an introduction to this fascinating concept with the aim of illustrating its potential role in 'unifying Mathematics'; specifically, drawing from my 
20111017  Cathy O'Neil (Intent Media) What's It Like to do Math in Business? [Abstract] Cathy O'Neil has worked as an academic in math (M.I.T. Moore Instructor 1999, assistant professor Barnard College 2005), as a quant at a hedge fund (2007), as a researcher at a financial risk software company (2009), and more recently (2011) as a data scientist at a New York internet marketing startup. She wants young mathematicians to know what's out there so they can their compare options and can prepare themselves for a 'real world' job if it turns out to be a good fit. She will also explain how modeling is used outside of academics, for good and for evil, and how mathematicians should educate themselves about how mathematics is used by some people to authenticate otherwise questionable practices. 
20111107  Rita MeyerSpasche (MPI fuer Plasmaphysik) Oscar Buneman, Douglas Hartree, and the Development of ParticleMethods [Abstract] Mathematical models for moving particles were developed first for studying the orbits of planets in a gravitational field. Later on the trajectories of charged particles in electric, magnetic and electromagnetic fields were studied. Today, numerical particle methods are wellestablished computational methods for various applications, including the generation of computer graphics on playstations. 
20111114  Monika Ludwig (Vienna University of Technology and NYU Poly) Valuations on Convex Bodies: From Hilbert's Third Problem to Recent Results [Abstract] Since Dehn's solution of Hilbert's Third Problem (concerning the elementary definition of volume) in 1902, valuations on convex bodies have played a prominent role in geometry. Here a realvalued function $\Phi$ defined on a family ${\mathcal C}$ of convex bodies (compact, convex sets) in ${\mathbb R}^n$ is called a valuation if 
20111201  Carla Cederbaum (Duke University) The Newtonian Limit of General Relativity [Abstract] 
20111205  Sarah Spence Adams (Franklin W. Olin College of Engineering) Complex Orthogonal Designs and their Associated SpaceTime Block Codes [Abstract] Complex orthogonal designs were first introduced in the 1970's, and the conditions for their existence are based on number theoretic results from the early 1900's. The application of these designs as spacetime block codes in multipleantenna wireless communications systems has led to a renewed interest in orthogonal design theory over the past decade. Spacetime block codes resulting from complex orthogonal designs perform well and enjoy a simple decoding algorithm. In this talk, we'll review some recent results in generalized complex orthogonal design theory, and we’ll explain the application of these results in the context of wireless communications systems. 
20120109  Tara Holm (Cornell University) and Janet Mertz (University of WisconsinMadison) () Speaker: Tara Holm (Cornell University) 
20120305  Julie Mitchell (University of Wisconsin  Madison) The Geometry of Molecules [Abstract] Abstract: Enzymes and antibodies are two types of molecules that are essential to survival. These molecules are proteins, which are formed as a linear sequence of amino acids. Folded proteins have unique geometric structures, much like pieces of a 
20120409  Emina Soljanin (Bell Labs, AlcatelLucent) Urns & Balls and Communications [Abstract] Urns and balls models refer to basic probabilistic experiments in which balls are thrown randomly into urns, and we are interested in various patterns of urn occupancy (e.g, the number of empty urns). These models are central in many disciplines such as combinatorics, statistics, analysis of algorithms, and statistical physics. After covering the fundamentals, we will show how some modern network and traffic communications scenarios give rise to problems that are related to the classical urns and balls questions. We will also describe some new models and problems that emerge in content delivery because information packets can be processed (e.g., by using finite field arithmetic) in a way their physical counterparts, urns and balls, cannot. 
20120423  Laura Miller (University of North Carolina Chapel Hill) Excitable Tissues in Fluids [Abstract] Abstract: A wide range of numerical, analytical, and experimental work in recent years has focused on understanding the interaction between fluids and elastic structures in the context of cardiovascular flows, animal swimming and flying, cellular flows, and other biological problems. While great progress has been made in understanding such systems, less is known about how these excitable tissues modulate their mechanical properties in response to fluid forces and other environmental cues. The broad goal of this work is to develop a framework to integrate the conduction of action potentials with the contraction of muscles, to the movement of organs and organisms, to the motion of the fluid, and back to the nervous system through environmental cues. Such coupled models can then be used to understand how small changes in tissue physics can result in large changes in performance at the organ and organism level. Two examples will be discussed in this presentation. The first example considers how active contractions generated by the cardiac conduction system can enhance flows in tubular hearts, particularly at low Reynolds numbers. The second example considers how the interactions between pacemakers in the upside down jellyfish can alter feeding currents generated by the bell pulsations. In both cases, the ultimate goal is to simulate the electropotentials in the nervous system that trigger mechanical changes in 1D fibers representing the muscular bands. The muscular contractions then apply forces to the boundaries that interacts with the fluid modeled by the NavierStokes equations. The computational framework used to solve these problems is the immersed boundary method originally developed by Charles Peskin. 
20120425  Joel Brewster Lewis (MIT) Math and Origami (but mostly origami) [Abstract] We'll discuss two of the many connections between origami and mathematics. First, we'll discuss origami as a constructive system of plane geometry, akin to the classical rules of compass and straightedge. Second, we'll apply some lovely results from graph theory to the problem of making attractive polyhedra from modular origami. Most of the talk will be devoted to folding paper, including angle trisection and the Sonobe unit. 
20120430  Youngmi Hur (Johns Hopkins University ) Searching for New Alternatives to Tensor Product in Wavelet Construction [Abstract] In the last few decades, wavelets have been proved to be a powerful tool for mathematical analysis and signal processing. Tensor product has been a predominant method in constructing multivariate wavelets. In this talk, I will first provide a brief overview of wavelets and the use of tensor product in constructing multivariate wavelets. Then, I will introduce a new alternative to tensor product, to which we refer as Coset Sum, and discuss the similarities and differences between the two methods. In particular, we will see that some of the known limitations of tensor product can be overcome, in a limited sense, by Coset Sum. 
20120509  Maria Gorelik (The Weizmann Institute of Science) Queer Lie Superalgebras [Abstract] The Lie superalgebras are generalizations of Lie algebras. The matrix Lie algebras have two close relatives in the 'superworld': the matrix Lie superalgebras and the queer Lie superalgebras. In my talk, we will get acquainted with these algebras. 
20120917  Elza Erkip (Polytechnic Institute of NYU) Energy Efficient Wireless Communication: Impact of Energy Harvesting and Processing Energy [Abstract] Energy efficiency in wireless devices, from smart phones to wireless sensors, is of paramount interest not only for ensuring continuous network operation despite battery limitations, but also for reducing the carbon footprint of communication systems. There are many demands on the power supply of a wireless device, including signal processing algorithms and the wireless modem. In particular, with the advance of complex multimedia tasks, and shorter communication distances (as in sensor or machinetomachine communications), the energy cost of signal processing becomes comparable to transmit energy. Battery limitations can be partly alleviated by energy harvesting, which corresponds to collecting various forms of energy such as solar, kinetic from the environment and then converting into electrical energy. 
20121022  Sennur Ulukus (University of Maryland at College Park) InformationTheoretic PhysicalLayer Security [Abstract] Abstract: 
20121029  Bin Yu (UC Berkeley) Data and a Career in Statistics [Abstract] ***** This talk was cancelled due to Hurricane Sandy. It will be rescheduled. ***** 
20121105  Alice Guionnet (MIT) The Spectrum of NonNormal Random Matrices [Abstract] In this talk, we will give an introduction to spectral properties of nonnormal matrices; that is matrices which do not commute with their adjoint. We shall see that the spectrum of such matrices is in general not stable under small perturbation of the entries, but that it can be “stabilized” by adding a small random matrix. We will also review classical ensembles of random nonnormal matrices and the behavior of their spectrum as the dimension goes to infinity. No previous experience with random matrices is needed to follow this talk. 
20121114  Margaret Readdy (University of Kentucky) The Characteristic Polynomial [Abstract] Given a subspace arrangement, the characteristic polynomial is a polynomial in the variable t which weights each kdimensional intersection X by the Mobius function of X times t^k. I will describe many interpretations of the characteristic polynomial, including counting lattice points due to Blass and Sagan, Athanasiadis' modulo q interpretation, and the valuation approach of Ehrenborg and Readdy. We will also review Zaslavsky's work on specializing the characteristic polynomial at certain integer values of t, as well as Stanley's result on the number of acyclic orientations of a graph. Surprisingly all but one of these authors have some connection to MIT. 
20121126  Muriel Médard (MIT) To PHY or not to PHY  on the Capacity of Wireless Networks at Different Levels of SNR [Abstract] The intersection of network coding and wireless communications leads to potentially rich 
20121203  Carla D. Savage ( North Carolina State University) Lecture Hall Partitions [Abstract] Lecture hall partitions are finite sequences of nonnegative integers, constrained by a certain condition on the ratio of consecutive parts. They were introduced in 1996 by BousquetMelou and Eriksson, who discovered their remarkably simple generating function. Lecture hall partitions have been found to have surprising connections in combinatorics, algebra, geometry, and number theory. 
20121210  Agnes H. Chan (Northeastern University) Cloud Security [Abstract] In this talk, I will provide an overview of the security issues associated with cloud computing, in particular, I will discuss privacypreserving information retrieval schemes. Much work has been done on Private Information Retrieval (PIR) that allows retrieval of information from a database without letting the server know about the user’s access patterns. Most of these schemes incur enormous computation and communication overhead that outweigh any cost saving advantages of cloud computing. We present a practical, highly efficient protocol for PIR using MapReduce. The talk will end with an open discussion on the joy and obstacles of being a woman and an academician. 
20130107  ShanYuan Ho (MIT) Horse Racing, Information Theory, and the Optimal Portfolio [Abstract] If the sequence of outcomes in horse racing and stock market investments can be modeled as a stationary stochastic process, then information theory provides insight to optimal betting schemes on the horse race and optimal allocations for the portfolio. Specifically, the growth rate of an investment in a 'win bet' horse race is related to the entropy rate of that race. We discuss some simple portfolio strategies including constant rebalancing and show its optimality in a variety of situations. In particular, the exponential growth rate of wealth of the best strategy has at most a vanishing probability of growing at a greater rate than that of the constant balanced portfolio. This talk highlights some of Cover's seminal contributions to portfolio theory with a different representation. No previous knowledge is assumed. 
20130128  Nancy Reid (University of Toronto) Statistics in Research [Abstract] Statistical methods are an important part of research in nearly every field of study. Statistical theory provides the backbone on which these methods are developed. I will describe aspects of statistical theory close to my own research on likelihoodbased inference, and present some examples of problems in science, social science and humanities where statistical methods have been crucial to key advances. No special background is required. 
20130225  Tamar Friedmann (University of Rochester) From Representation Theory to Classification of Hadrons [Abstract] How much can elementary representation theory of groups like SU(n) tell us about the properties of particles? As it turns out, far more than one might expect. It is quite remarkable that particles can be viewed as basis vectors for the representations of a Lie algebra, where a corresponding Lie group describes some symmetry of the system. In this talk, we will elaborate on this statement and explain how the representation theory of Lie groups and Lie algebras lies at the root of the classification of certain particles known as hadrons. 
20130311  Silvia Sabatini (EPFL) The Geography of (some) Manifolds with Symmetries [Abstract] In mathematics, the problem of classifying manifolds (i.e. the higher dimensional analogues of curves or surfaces) is very hard and has many open problems. However the problem becomes much easier when the manifold admits a certain symmetry, i.e. there is a Lie group acting on it. In this talk I will introduce a special class of manifolds, namely symplectic manifolds, with a special type of actions, namely Hamiltonian actions, which also naturally arise in physics. I will explain that, if the group acting is 'big enough', these manifolds are completely characterized by a polytope with some special properties: this is the remarkable Delzant's theorem. I will illustrate 'how to reconstruct the manifold from the polytope': for example, how to obtain a 2dimensional sphere from a segment, and a complex projective space of complex dimension 2 from a triangle. 
20130318  Dana Randall (Georgia Institute of Technology ) Domino Tilings of the Chessboard: An Introduction to Sampling and Counting [Abstract] How many ways are there to tile an n x n chessboard with unmarked dominoes? This question dates back to the early 20th century, when physicists used domino tilings as a statistical mechanical model of diatomic molecules. For some regions (that are natural like the chessboard), we can exactly count the number of tilings with simple formulae, while for other regions we can count using efficient algorithms. We will introduce some of these methods and will show algorithms for generating random domino tilings approximately. As we shall see, random tilings reveal a rich underlying structure that has led to deep and beautiful mathematical discoveries. We will conclude with recent extensions in the biased setting where we favor certain tilings over others. 
20130320  Rongsong Liu (University of Wyoming) Interaction Between Plant Toxicity and Herbivores can Shape Landscapes [Abstract] In some areas of Alaska, it was found that after floods or forest fires willows became a dominant plant species. After about a duration of 10 years, willows were observed to become almost extinct, while alders became the dominant plant species. The reasons for the succession of willows and alders remain a puzzle in ecology. Some biologists suggest that a simple competitive advantage of alders is the cause of succession; however other biologists suggest that the interaction between the herbivores (snow hares and moose) and the plants is at play. In order to solve this puzzle, biologist J. P. Bryant conducted the ''haremoose exclusion' experiment from 1985 to 2000 and proposed that herbivore browsing and plant toxicity could lead to the elimination of willows from the ecosystem. In this talk, we show how mathematical models can be applied to rationalize the data above and describe the subtle willowalderherbivore system. The dynamics will be discussed to gain insight into the role of plant toxicity in the cycle of succession of plant species. 
20130422  Fu Liu (University of California, Davis) Introduction to Ehrhart Polynomials [Abstract] Given an integral convex polytope P, for any positive integer m, we define its mth dilation to be mP = { m x  x in P}. We then denote by i(P,m) the number of lattice points inside mP. Eugene Ehrhart discovered in 1960s that the function i(P, m) is actually a polynomial in m of degree dim(P). So we often call i(P, m) the Ehrhart polynomial of P. 
20130429  Lynn Stein (Olin College) TBA [Abstract] TBA 
20102011
09/13/2010 
Alina Ioana Bucur (UCSD) Size Doesn't Matter: Heights in Number Theory [Abstract]
How complicated is a rational number? Its size is not a very good indicator for this. For instance, 1987985792837/1987985792836 is approximately 1, but so much more complicated than 1. We'll explain how to measure the complexity of a rational number using various notions of height. We'll then see how heights are used to prove some basic finiteness theorems in number theory. One example will be the MordellWeil theorem: that on any rational elliptic curve, the group of rational points is finitely generated. 
10/06/2010 
Tanya Khovanova (MIT) Modern Coin Weighing Puzzles [Abstract]
I will discuss several coinweighing puzzles and related research. Here are two examples of such puzzles: 
10/20/2010 
Lalitha Venkataramanan (Schlumberger) Moment Estimation of a Random Variable Using Mellin Transform [Abstract]
The search for oil and gas has three objectives: to identify and evaluate hydrocarbonbearing reservoirs; to bring hydrocarbons to the surface safely and costeffectively, without harming the environment; and to maximize the yield from each discovery. This talk will focus on applications of Nuclear
Magnetic Resonance (NMR) in Schlumberger, where experimental protocols have been developed to measure data represented by 
10/27/2010 
Amanda Folsom (Yale University) Mock Theta Functions in Number Theory and Combinatorics: A Legacy of Ramanujan [Abstract] With virtually no formal training in mathematics, it's a wonder that renowned number theorist G.H. Hardy "discovered" Ramanujan in 1913, the man behind hundreds of pages of scribbled formulas, some so deep that they remained a mystery for decades. In this talk, we will discuss the mathematics surrounding Ramanujan's mock theta functions, certain peculiar power series, and how they have had significant influence on fundamental areas of present day research in number theory and combinatorics. In particular, we will discuss how integer partitions (nonincreasing lists of positive integers that sum to a given positive integer), and modular forms (complex functions equipped with certain symmetries), play key roles. Prerequisites include only a basic knowledge of complex analysis (i.e. complex numbers); the talk will be for the most part selfcontained. 
11/3/2010 
Amy Cohn (University of Michigan) Planes, Politics, and Polyhedra [Abstract]
The U.S. Department of Transportation recently passed a regulation that says airlines can't keep passengers onboard for more than three hours in the case of a flight delay. Failure to follow this regulation can lead to multimillion dollar fines. Ironically, this ruling can actually make things worse for passengers in some cases. In this talk, I will explain how. I will provide an overview of the complexity of airline networks and an understanding of how this impacts decisions for dealing with delays. I will also talk about how the field of operations research, and in particular mixed integer programming, can be used both in better analyzing policy decisions and also in deciding how to recover from delays. 
11/10/2010 
Ragni Piene (University of Oslo) Some Counting Problems and Their Generating Functions [Abstract]
To a sequence of integers a_{1},a_{2},a_{3}... is associated with a generating function: the formal power series ƒ(x)=∑a_{n}X^{n}. The generating function provides a way of displaying the sequence. For example,if a_{n} denotes the number of ways one can write the integer n as a sum of positive integers, the generating function is the partition function p(x)=Π_{m≥1}(1  x^{m})^{1}, and hence one can compute a_{n} as the coefficient of x^{n} in the power series expansion of this function. 
11/15/2010 
Olgica Milenkovic (UIUC) Sorting Permutations by CostConstrained Transpositions [Abstract]
We address the problem of finding the minimum decomposition of a permutation in terms of transpositions with nonuniform cost. For arbitrary nonnegative cost functions, we describe polynomialtime, constantapproximation decomposition algorithms. For metricpath costs, we describe exact polynomialtime decomposition algorithms. Our algorithms represent a combination of Viterbitype algorithms for minimizing the cost of individual transpositions, dynamic programing algorithms for finding minimum cost cycle decompositions, and graphsearch techniques for minimizing the overall permutation decomposition cost. The presented algorithms have applications in information theory, bioinformatics, and algebra. In particular, they are essential components of trapdoor channel and flash memory error control decoding methods. At the same time, the described techniques can be used for reverseengineering the sequence of breakages in genomic sequences under the fragile DNA structure model. 
11/17/2010 
Natalia Rozhkovskaya (Kansas State University) Generalizations of Symmetric Polynomials With Origins in
Symmetric polynomials are polynomials of several variables that are invariant under the action of the symmetric group. Their applications to representation theory and algebraic geometry inspired many beautiful combinatorial results. Moreover, the connections with these areas of mathematics produce natural generalizations of symmetric polynomials. The topic of the lecture is the examples of generalizations that arise from representation theory of Lie algebras, quantum groups and from the theory of quantum integrable systems. 
11/29/2010 
Sarah Koch (Harvard University) Matings of Polynomials [Abstract]
Given two suitable complex polynomial maps, one can construct a new dynamical system by mating the polynomials; that is, by gluing together the Julia sets of the polynomials in a dynamically meaningful way. In this talk, we focus on quadratic polynomials  we begin with a brief discussion of parameter space for quadratic polynomials (the Mandelbrot set), we then define the mating of two quadratic polynomials, and finally we explore examples where the mating does exist, and examples where it does not. The operation of mating two polynomials was introduced by Douady and Hubbard in 1983. 
12/8/2010 
Giulia Sarfatti (UMI and University of Florence) Functions of a Quaternionic Variable [Abstract]
Since the beginning of last century, mathematicians tried to construct a theory of functions of a quaternionic variable, corresponding to the classical theory of holomorphic functions of one complex variable. Different definitions of regularity generate different theories. In this talk, I will introduce the class of slice regular functions and I will present both with some aspects of analogy and some of diversity with respect to the complex case. 
02/17/2011 
Elizabeth Chen (University of Michigan) Mandelbrot set + symmetry groups * higher dimensions = ? [Abstract] Come join us as we explore 3D fractals and pursue the holy grail, to construct a true 3D analog of the mandelbrot set. You may have heard of the mandelbulb, mandelbox... now we present the मण्डलबेथ (maṇḍalabeth), 3D, 4D, and higher dimensional fractals with various symmetry groups. They are constructed from bouquets of circles, using only basic complex analysis and linear algebra. 
02/28/2011 
Christina Sormani (CUNY GC and Lehman College) An Almost Isotropic Universe [Abstract]
In the Friedmann model of the universe, cosmologists assume that the spacelike universe has constant sectional curvature: so that it is either Euclidean, Spherical or Hyperbolic or a related space called a Space Form. Such spaces all have a Law of Cosines in which the length of the third side of a triangle is determined by two legs and the angle between them. This assumption is "justified" by saying that locally the universe is isotropic (looks the same under rotation) by Schur's Theorem. However, the universe is not exactly isotropic due to the fact that matter is not distributed uniformly. 
03/07/2011 
Trachette Jackson (University of Michigan) Mathematical Insights into Cancer Therapy [Abstract] As a group of genetic diseases, cancer presents some of the most challenging problems for basic scientists, clinical investigators, and practitioners. In order to design treatments that are capable of abating malignant tumor growth, it is necessary to make use of crossdisciplinary, systems science approaches, in which innovative, theoretical, and computational cancer models play a central role. The goal of this talk is to demonstrate how combining mathematical modeling, numerical simulation, and carefully designed experiments can provide a predictive framework for better understanding tumor development and for improving cancer treatment. 
03/16/2011 
Moon Duchin (University of Michigan) In Which We Think About Distance [Abstract]
In this talk, I'll focus on something basic  the definition of a metric, or a way of measuring distance  and I'll examine the work that it does. I'll spend a chunk of time on the padics, where distance between rational numbers is measured from the point of view of a prime p, and show a beautiful padic proof, due to Monsky, of an elementary theorem in plane geometry. I'll also talk about metrics on surfaces, and a metric on the space of metrics. 
03/30/2011 
Margaret Murray (University of Iowa and ACT, Inc.) Hiding in Plain Sight: Women Mathematicians in the United States [Abstract] Women have been part of the mathematical research community in the United States since the late 19th century, but the misconception persists that women have only recently joined the community of mathematicians. This misconception is shared by the general public, but also by plenty of people who ought to know better, including historians of science, social and cognitive psychologists, and university presidents. In this talk, I'll take a look at a few of the most egregious examples of this misconception, and carefully trace the participation of women in the U.S. mathematical community from the 1870s onward. 
04/04/2011 
Patricia Hersh (North Carolina State University) Interplay of Combinatorics and Topology through Posets [Abstract]
This talk will focus on how partially ordered sets help record topological structure, including mentioning some limitations in how much they can capture. I will briefly discuss my work on discrete Morse theory for order complexes of partially ordered sets and how this has been used e.g. to count by inclusionexclusion. Then, I'll turn things around and discuss more recent work on how topological structure of a stratified space can sometimes be gleaned from combinatorics of its closure poset, combined with codimension one topology. This is used to show that certain stratified spaces arising from combinatorial representation theory are regular CW complexes homeomorphic to balls. 
04/11/2011 
Erika Camacho (Arizona State University) Mathematical Models of the Human Eye [Abstract] The physics and biology of the overall vision process and of many individual parts is relatively well understood due to countless experiments that have been performed. However, the interactions of the various components within this process is far from complete, as the experiments almost always require the termination of the subject under investigation, and data over time is thus difficult to obtain. Analytic models of any components of the visual process are almost nonexistent. In an attempt to gain important insight into the role and interaction of melatonin levels within the eyes and of the interaction of the photoreceptors, we develop and analyze mathematical models with nonlinear differential equations. We examine equilibrium solutions and the stability and bifurcations of them. We are able to show the essential need for inclusion of various pathways and interactions in any comprehensive biological model of the eye. Knowledge of such pathways and interactions has implications in the understanding of certain abnormalities and diseases of the eye. 
04/20/2011 
Emily Peters (MIT) Knots, the Fourcolor Theorem, and von Neumann Algebras [Abstract] What do knots, the fourcolor theorem, and subfactors of von Neumann algebras have in common? All of these have the structure of a planar algebra. Planar algebras are a tool for doing computations by drawing pictures, often reducing complex problems in algebra or topology to simpler combinatorial calculations. In this talk, I'll begin with simple examples with cool applications, such as the TemperleyLieb algebra and its relation to the Jones polynomial, and the colorcounting planar algebra. I hope to end with a brief description of the study of subfactors (of von Neumann algebras) and why you should think of planar algebras for subfactors as a noncommutative generalization of Galois Theory. 
04/25/2011 
Susan J. Sierra (Princeton University) What is a Noncommutative Polynomial Ring? [Abstract]
The ring S:= C[x_1, x_2, ..., x_n] of polynomials in n variables is certainly the nicest possible commutative ring (that is not a field). What properties would a noncommutative generalization of S have? We'll talk about some possible answers and their positives and negatives. In the process, we'll discuss mathematics covering (at least) the period 1890 to 2011, with an appropriate pause to acknowledge Emmy Noether, the founder of ring theory. 
05/02/2011 
Marina Epelman (University of Michigan) Anisogamy, Expenditure of Reproductive Effort, and the Optimality of Having Two Sexes [Abstract]
No good formal arguments exist for a central question in biology: "Why, in species which have sexual reproduction, are there usually only 'males' and 'females'?" We present a nonlinear optimization model that supports the conclusion that having at most two sexes maximizes long run viability. This talk will introduce the classic KuhnTucker optimality conditions for constrained optimization problems. 
20092010
09/16/2009 
Johanna Franklin (Fields Institute) Defining Randomness [Abstract] What does it mean for an infinite binary sequence to be random? What does it mean for an infinite binary sequence to be nowhere near random? I will present three different approaches to defining randomness, show how they can be made to be equivalent, and describe some of the other properties that random binary sequences can have. Then I will present ways in which a real can be said to be "far from random," discuss whether or not these definitions are equivalent, and explore some of the other properties of these binary sequences. 
10/22/2009 
Julia Wolf (Rutgers University) What the Fourier transform can and cannot tell us about the integers [Abstract]
It is surprisingly straightforward to count the number of solutions to simple equations such
as x+y=2z (representing a 3term arithmetic progression) or xy=z2 (a square difference) in
a "randomlooking" subset of the integers. The discrete Fourier transform provides a natural
way of quantifying what we mean by randomlooking, but fails us once we start to consider
longer arithmetic progressions and other more intricate structures. This failure opens the
door to a rich and as yet largely unexplored theory of higherdegree Fourier analysis, which
we shall try and catch a glimpse of in this talk. 
10/26/2009 
Valentina Harizanov ( George Washington University) Priority methods [Abstract] In computable mathematics the existence of certain objects is often demonstrated by actually building them. We will present an example of a construction which will in a very simple setting illustrate the main ideas and give the flavor of a computability theoretic technique called the finite injury priority method. This method, which was invented in the 1950's and revolutionized computability theory, represents the first level in the hierarchy of priority methods. This intricate and powerful technique allows us to satisfy mutually conflicting requirements by fitting together opposite strategies. 
01/14/2010 
Alison Malcolm (MIT) Using Math to See Inside the Earth [Abstract] Seismic waves (similar to those excited by Earthquakes) are used all the time to make images of structures beneath the Earth. This is done for oil exploration, carbon sequestration, geothermal energy, contaminant monioring and slope stability studies to name just a few examples. Constructing images from these waves requires an understanding of how to compute the paths on which waves travel through the Earth. Through a series of examples, we'll see how simple techniques for solving equations can be applied to approximately compute these paths, quickly and accurately, and how the questions we ask in imaging the Earth also lead to new mathematical questions. 
01/12/2010 
Natasa Pavlovic (University of Texas, Austin) The Enigma of the Equations of Fluid Motion: a Survey of Existence and Regularity Results [Abstract]
The partial differential equations that describe the most crucial properties of the
fluid motion are the Euler equations. They are derived for an incompressible, inviscid
fluid with constant density. Some basic questions concerning Euler equations in 3
dimensions are still unanswered. For example, it is an outstanding problem to find
out if solutions of the 3D Euler equations form singularities in finite time.

12/02/2010 
Debra Borkovitz ( Wheelock College) SPECIAL PRESENTATION: Elementary Math is Not Elementary! Thoughts on Preparing Teachers. [Abstract]
For many years, it was commonly believed in the U.S. that future elementary school
teachers learned all the math content they needed to know by the end of high school.
Now it is widely recognized that for teachers to take school mathematics beyond
calculation without understanding, they need to develop a much deeper understanding
of elementary mathematics. There is a specialized body of math content knowledge for
elementary teaching, just as there are such bodies of knowledge for engineering and
other professions (and even people with Ph.D's in math have not necessarily mastered
this math content).

01/21/2010 
Lydia Bourouiba (MIT) Mathematics and the Mitigation of Disease Spread [Abstract]
H1N1 (swine) flu, SARS, H5N1 bird flu, Tuberculosis, and Poliomyelitis is only
a short list of numerous emerging or reemerging diseases with major human and
economic costs. The impact is clear when considering that the 19181919 (H1N1)
Spanish flu killed more than 40 million people. Most common infectious diseases
are preventable and their mitigation is the focus of organizations such as the Center
for Disease Control and the World Health Organization. In this ongoing mitigation and
prevention battle, mathematics is becoming a valuable ally, helping understand both
withinhost pathogen dynamics and population disease dynamics.

01/26/2010 
Amanda Epping Redlich (MIT) Knitting and Math [Abstract] The aim of this talk is to teach mathematicians why knitting is useful, and to teach knitters why math is useful. Topics discussed include braid theory, Cartesian coordinates, Diophantine equations, Hamiltonian paths, knot theory, mobius strips, polar coordinates, the symmetric group, torii of arbitrary genus, Turing machines, cabling, circular needles, fair isle, Kitchener stitch, k2tog, M1, setin sleeves, stockinette, tinking, and YO. No prior knowledge of any of these topics will be assumed. 
01/28/2010 
Jill Pipher ( Brown University) Discrepancy Theory [Abstract]
I intend this talk to be accessible to undergraduates with an interest in mathematical
theory. I'll define everything, give some history, and indicate applications. I aim to
describe some open problems and new directions of research in this field for the more
advanced students in the audience.

02/22/2010 
Dr. Esther M. Pearson (Lasell College) Making the Connection: Ethnic and Cultural Effects of Mathematics (Special Lecture Celebrating Black History Month) [Abstract] This presentation examines chronological periods in history and how African Americans affected and were affected by mathematics. The African American experience from slavery through the Information Age is examined. Evidence within each period details how mathematics has profoundly affected the progress of African Americans. From their position as slaves to the representation of African Americans as 3/5th of a human; to their liberation, right to read, right to vote, and right to fight in the armed services. From their migration from the south to the north, from inner city to suburbia, from blue collar labor to white collar, from business employee to business owner. This talk brings into perspective the need for African Americans to embrace mathematics as never before so that academic, social, and economic gains can be maintained and advanced in America. Why then, has mathematics not been held closely or embraced like a friend to those of African descent? 
03/01/2010 
Megan M. Kerr (Wellesley College) Homogeneous Spaces: Differential Geometry with Lie Groups [Abstract]
Which Riemannian manifolds admit a metric of positive sectional curvature? This,
one of the original questions of global Riemannian geometry, has motivated deep
and beautiful mathematical results. And yet this is an area of geometry that is
characterized more by its open questions than by its known theorems. As an example,
the Hopf conjecture is easily stated and still open:

03/09/2010 
Barbara Csima (Computable Structure Theory) Mathematics and the Mitigation of Disease Spread [Abstract]
An infinite set of natural numbers is computable if there is a computer program that
decides membership in the set. Similarly, a function on the natural numbers is computable
if there is a computer program that on every input gives the same output as the function
value on the input.

03/17/2010 
Xiaomin Ma (Brown University) Introduction to Discrepancy Theory from Integration Estimation [Abstract] It is often impossible to calculate an exact value of the integral of an arbitrary Riemann integrable function defined, say, on the unit cube. There are a variety of numerical methods used to estimate integrals. The key issues in such methods include: 1) whether the estimate converges to the real solution, 2) the magnitude of the error, and 3) how the error term is controlled in terms of quantities that depend on properties of the functions. In this talk, we focus on quasiMonte Carlo estimation, which utilizes the theory of discrepancy. I will introduce the theory of discrepancy of point distributions and discuss constructions of low discrepancy sets. 
04/05/2010 
Tara Javidi (University of California, San Diego) FosterLyapunov Theorem and Routing in Wireless Networks [Abstract]
Routing is the process of selecting paths in a network along which the network traffic
is sent. Routing is performed for many kinds of networks, including the telephone
network, the electronic data networks (such as the Internet), and the transportation
networks. This talk is concerned primarily with routing in data networks, when information
is carried in the form of bits in a data packet. In data networks, routing directs
packet forwarding (the transit of logically addressed packets) from their source toward
their ultimate destination through intermediate nodes; typically hardware devices called
routers or switches. The manner, which routing algorithm directs packet forwarding,
impacts the delivery time of packets (per packet delay) and is the topic of this talk.
In particular, we will consider an abstract probabilistic model associated with routing
packets in a wireless data network.

04/14/2010 
Angelia Nedich (University of Illinois) Random Projection Algorithms for Convex Minimization Problems [Abstract] New applications in communication and control networks, as well as large data sets processing, have given rise to optimization problems with large and/or dynamically changing constraints. In this talk, we will consider such an instance where the constraint sets are unknown but they can be observed and learned over time. We will discuss algorithmic approaches for solving such problems with convex structure. The algorithms rely on random projections on the constraint sets, as the sets are learned. We investigate convergence properties of the algorithms and also provide some error bounds on the algorithms' performance both in time and asymptotic. 
04/21/2010 
Ragni Piene (University of Oslo) Some Counting Problems and Their Generating Functions (Cancelled) [Abstract]
To a sequence of integers a_{1},a_{2},a_{3}... is associated
with a generating \ function: the formal power series ƒ(x)=∑
a_{n}X^{n}. The generating function provides a way of displaying
the sequence. For example,\ if a_{n} denotes the number of ways one can
write the integer n as a sum of positive integers, the generating function is the
partition function p(x)=Π_{m≥1}(1  x^{m})^{1}, and
hence one can compute a_{n} as the coefficient of x^{n} in
the power series expansion of this function.

04/26/2010 
Vera Hur (UIUC and IMA) Symmetry or Not? [Abstract] Many problems in analysis appear symmetric, yet their solutions are sometimes nonsymmetric. I will present a number of examples for this. One of them is Newton's body of minimal resistance, one of the oldest problems in the calculus of variations. I will present a collection of tricks on how to prove symmetry for solutions of PDEs or of variational problems. If time permits, I will also present a research problem on symmetry of surface water waves, accessible to graduate students. 
05/10/10 
Marina Meila ( University of Washington) Statistics and Computing with Permutations [Abstract]
When data comes in the form of permutations, statisticians and computer scientists
turn to combinatorics in order to analyze it. I will describehow combinatorics,
algorithms, and statistics come together in this endeavor from defining interesting
but simple distributions over permutations, to algorithms for fitting them to the
data, and to predicting their properties.

20082009
02/12/2009  Susan Landau Sun Microsystems √2 + √3: Four Different Views [Abstract]
How much time does it take to factor polynomials?
How can you efficiently tell if a polynomial has roots expressible in terms of
radicals? Is there a fast method to decompose a polynomial into
lowerdegree components? Suppose it is claimed that
; how can you check if it is true? 
02/19/2009  Matilde Lalin University of Alberta So you think you can count? [Abstract] In the study of curves, zeta functions codify information about the number of solutions over finite fields, but we expect them to have more information. In particular, there is a big interest in studying the distribution of zeros of zeta functions (and L functions).

03/03/2009  Rebecca Weber Dartmouth What is computability theory? [Abstract] If it is possible to write a computer program to execute a given function, we can call that function "computable". It is clear, then, how to prove that a function _is_ computable, but how do you show that it is _not_ computable? That requires a more precise definition, something not affected by advances in technology and also something to which we can apply proof techniques. Once we have such a definition, a whole world opens up  there are more noncomputable functions than computable ones, and we can explore their properties and compare "how noncomputable" they are. Examples of noncomputable objects include the Halting Problem, also seen in computer science, and random sequences. Avoiding as many technical details as possible, we'll define computability and tour the world of the noncomputable.

03/17/2009  Rina Anno University of Chicago The geometry of flag varieties and Springer fibers [Abstract] A flag in a linear space V is a configuration of subspaces 0=V_{0} ⊂ V_{1} ⊂ ... ⊂ V_{n}=V of given dimensions. The flag variety is simply the space of all flags (for a given V and a given type of a flag). If we add a linear endomorphism Z of V into the play, we can define a Springer fiber over Z as the space of all flags with ZV_{i} ⊂ V_{i} for all i.

3/19/2009  Angela Hicks University of California, San Diego Combinatorics of the Diagonal Harmonics [Abstract] The space of diagonal harmonics has emerged as one of the key ingredients in a program initiated by Garsia and Haiman to give a representationtheoretical proof of some conjectures in the theory of Macdonald polynomials. The study of this particular space has provided a remarkable display of connections between several areas, including representation theory, symmetric function theory, and combinatorics. Over two decades since the introduction of the diagonal harmonics, the bivariate Hilbert series of the diagonal harmonics has been the object of a variety of algebraic and combinatorial conjectures.

3/30/2009  Tai Melcher University of Virginia Brownian motion on curved spaces [Abstract] Consider a perfume particle released from position x at time 0, and let B_{t}^{x} describe the position of the particle at any later time t>0. The dynamics of this random trajectory are well understood: B_{t}^{x} is Brownian motion. In particular, we know the transition probabilities of the particle, the function p_{t(x,y)} that gives the probability of the particle transitioning to position y in time t. The function p_{t(x,·)} is called the heat kernel of B_{t}^{x}.

4/1/2009  Ioana Dumitriu University of Washington Linear computations: faster, bigger, better. Random?! [Abstract] Why should one care that the increasing processormemory gap signals the end of Moore's Law? How can we build a faster matrix multiplication algorithm, and if we can, will it be reliable? What is "fast" linear algebra, and how can random matrices and block algorithms help us make it faster? These are all very relevant questions in today's numerical linear algebra, and I will attempt to answer them without resorting to esoterica.

4/15/2009  Andrea Young University of Arizona Curvature Flows [Abstract] In the past several decades, curvature flows, such as the Ricci flow, have proven to be remarkably useful tools for studying geometric objects. In this talk, I will discuss two equations related to the Ricci flowthe Ricci YangMills flow and the cross curvature flowand will examine some applications.

5/5/2009  Sara Billey University of Washington How To Get A Ph.D. In Mathematics In A Timely Fashion And What To Do From There [Abstract] This will be an informal discussion about taking the next
step in your mathematical career. I will present some advice I have
collected on how to transition from a classoriented
testtakingmachine to a full fledged mathematician. In particular,
there are two major transitions along the way: becoming a mathematical
researcher culminating in your Ph.D. and becoming an independent
researcher as a postdoc or assistant professor.

5/8/2009  Bridget Tenner DePaul University Mathematics and Voting [Abstract] Why are there so many voting procedures? How many ways can there be to tally the votes? Do different ways lead to different outcomes? What is the most "fair" option?
