Seminars and Colloquia

Future Seminars

Faculty Seminar Schedule

2012

• Martin A. Nowak, Harvard University, The Evolution of Cooperation
  Pi Mu Epsilon Ceremony and Colloquium, May 2, 2012.
• Victor Moll, Tulane University, The Evaluation of Integrals. There is More in it Than You Suspect.
  Abstract:  The question of providing a closed-form for the evaluation of definite integrals is one of the standard topics in elementary Calculus courses. This talk will show relations of this elementary question to a variety of areas in Mathematics. There will be some Number Theory, some Combinatorics and a surprising connection to Dynamical Systems. Many possible projects for students will be described.
  April 23, 2012.
• Ed Soares Statistical Evaluation of Pre-clinical Data: Power Analysis, Ratio Distributions, (h,phi) Divergence Measures, and ANOVA
  Abstract:  In the first part of the talk, I will discuss some recent work on performing a power analysis using a one-way layout Multivariate Analysis of Variance (MANOVA). This is the multivariate equivalent of the two-sample t-test under the assumption of equal variances between the two populations under consideration. I will present the theoretical underpinnings as well as curves that relate sample size required to identify a statistically significant difference versus the effect size. The curves will be parametrized by the correlation between the features.
  In the second part, I wish to discuss some open problems that need to be addressed in the evaluation of pre-clinical data. These include:
  1) Ratio distributions - useful when generating confidence intervals when longitudinal data have been normalized to the day 0 measurement
  2) (h,phi) divergence measures - useful when determining if two histograms describe the same probability distribution. I will focus on the use of the Bhattacharyya distance with application to segmented MRI images, used to evaluate muscle growth.
  3) If there is time, i will also discuss analysis of variance.
  April 19, 2012.
• Davide Cervone, Union College, The Hypercube and Hypersphere: Breaking Them Down and Building Them Up
  Leonard C. Sulski Memorial Lecture, March 2, 2012.
• Tom Cecil, Dupin Hypersurfaces With Four Principal Curvatures
  Abstract:  A hypersurface M embedded in the sphere Sⁿ is proper Dupin if the number g of distinct principal curvatures is constant on M, and each principal curvature is constant along each leaf of its corresponding principal foliation. This property was shown to be invariant under the group of Lie sphere transformations by Pinkall in 1981. Thorbergsson proved in 1983 that for a compact, connected proper Dupin hypersurface M ⊂ Sⁿ, g must be 1, 2, 3, 4 or 6, the same as Muenzner’s restriction for isoparametric hypersurfaces in Sⁿ. In 1985, P.J. Ryan and the author conjectured that every compact, connected proper Dupin hypersurface M ⊂ Sⁿ is equivalent to an isoparametric hypersurface by a Lie sphere transformation. The conjecture is true for g = 1, 2 and 3, but it was shown to be false in the case g = 4 in 1989 by in- dependent constructions due to Miyaoka-Ozawa and Pinkall-Thorbergsson. The construction of Miyaoka-Ozawa also provides counterexamples to the conjecture in the case g = 6. These counterexamples do not have constant Lie curvatures (invariants introduced by Miyaoka), which are the cross-ratios of the principal curvatures taken four at a time. A revised conjecture with the additional assumption of constant Lie curvatures is still open, and we will discuss recent progress on the revised conjecture in the case g = 4 by Q.-S. Chi, G. Jensen and the author.
  February 20, 2012.
• Gideon Maschler, Clark University, Kahler Metrics Conformal to Curvature-Distinguished Metrics
  Abstract:  On certain manifolds admitting a complex structure there exist Riemannian metrics with nice geometric properties, and these are called Kahler metrics. We describe various attempts to link Kahler metrics to metrics with distinguished curvature characteristics. Some applications will also be given if time permits.
  February 9, 2012.
• Andrew Hwang Constructing Kahler Metrics on the Total Space of a Line Bundle
  Abstract:  Explicit examples of metrics having specified scalar curvature are generally difficult to construct. Starting nearly from scratch, we'll review the basics of metrics and curvature, holomorphic manifolds and line bundles, and an ansatz (due to Calabi) for Kahler metrics on the total space of a line bundle, in which the scalar curvature becomes an explicit linear second-order differential expression in a single unknown function of one real variable.
  February 2012.

2011

• Matthew Demers, (Ph.D. Candidate)  Northwestern University,  Pattern Formation in Multicomponent Membranes
  Abstract:  Multicomponent fluid membranes are found in many interesting physical systems. The presence of multiple components is an important feature, as it allows for the coupling of chemical and geometric properties, which can in turn lead to the formation of interesting shapes and patterns. I'll look at the example of three-component lipid vesicles and show some of the beautiful structures they can form.
  November 30, 2011.
• Giuliana Davidoff,  Mount Holyoke College,  Representations of Integers by Quadratic Forms and Generalizations
  Abstract:  One of the questions that drove the development of modern number theory was that of representation of integers by quadratic forms. For example, Fermat found, among other results, that a prime could be represented as a sum of two squares if and only if it is of the form p = 4n + 1, for some integer n. In modern language we write this as follows: p=x²+y² if and only if p ≅ 1 (mod4). With such statements, Fermat brilliantly connected the representation of integers by certain quadratic equations to the existence of primes in particular arithmetic progressions arising naturally from these equations. Further work by Euler, Legendre and Lagrange was brought into its fullest form by Gauss, who studied the most general form of quadratic equations in two unknowns, written as f(x,y)=ax² +bxy+cy². Gauss developed a rich theory of the representation of integers by such forms, which is still the most useful way of studying what eventually came to be called the arithmetic of quadratic extensions of the rational numbers. We will discuss this work and some recent extensions of it by Bhargava to number fields of higher degree.
  November 21, 2011.
• William B. Thompson,  University of Utah,  Visual Perception from a Computer Graphics and Virtual Environments Perspective
  Abstract:  Computer graphics produces images intended to be seen by people, yet relatively few practitioners in the field know much about the specifics of human vision. The first part of this talk will argue the importance of understanding human visual perception for computer graphics, scientific and information visualization, virtual environments, and related areas. The second part of the talk will provide an overview of current work in my research group involving embodied perception in virtual environments and computer animation.
  November 3, 2011.
• Catherine Roberts,  Improving our Children's Achievement in Mathematics, One Teacher at a Time
  Abstract:  This talk will describe the Intel Math Program, a professional development course for K-8 school teachers reaching thousands of teachers across the US, and my personal experience as an instructor for the program here in Massachusetts.
  October 20, 2011.
• Ben Coleman and Kevin Hartshorn,  Moravian College,  Game, SET, Math
  Abstract: The elegance of the card game SET® is found in the connection between simple game play and deep mathematical ideas. A portion of this talk will discuss the game and a variety of fascinating mathematical properties of the deck and game play. We will also discuss our own research to determine the number of structurally distinct ways to take 1 ≤ n ≤ 81 cards from the 81 cards of the deck. We will describe not only the technique that ultimately produced the answer, but also tell the story of our successes and failures along the way. In doing so, we will show how topics in discrete mathematics, linear algebra, geometry, computational complexity, and group theory can be seen in this fascinating game.  
  September 29, 2011.
• John Little, Toric Surface Codes -- Some New Observations
  Abstract: One of the central problems in coding theory is to find ways of constructing linear codes (that is, vector subspaces C of F^n -- F a finite field) that have good minimum distance properties (that is, such that any two distinct elements of C differ in as many coordinates as possible -- this is closely related to the error-correction capacity when the elements of C are used to encode information sent over a noisy channel). One construction that has received attention from a number of authors recently is the toric surface code construction. In concrete terms, this starts from a collection of integer lattice points (a,b) in the ordinary Euclidean plane. We construct elements of a code C over a finite field F by evaluating the corresponding monomials x^a y^b at all (x,y) in the (algebraic) torus (F^*)^2. In this talk, we will describe this construction in more detail, discuss some very good examples of codes that have been constructed this way, and summarize what is known about the minimum distances of these codes.
       Then we will consider what happens when we fix the collection of lattice points (a,b), but change the field F (either by taking algebraic extensions, or by just going to fields of larger size but different characteristic). We will see that in some cases, the codes we get for all sufficiently large F have the same minimum distance as the codes from the set of all lattice points in the convex hull of the original set. On the other hand, there are cases where some interesting arithmetic properties of algebraic (specifically elliptic!) curves over finite finite fields come into play and give unexpectedly different results 
  September 8, 2011.
• John Anderson, The Hull of Rudin's Klein Bottle
  Abstract: In 1981 Walter Rudin exhibited a totally real imbedding of the Klein bottle into C². I'll talk about the problem of finding holomorphic images of the unit disk in C with boundaries on Rudin's Klein bottle, and show that there are enough such disks so that their interiors fill an open subset of C². I'll also attempt to explain why this is interesting.
  May 2, 2011.
• Alisa DeStefano, Universal Observability of Dynamical Systems
  Abstract: A general question in control theory is whether the solution of a dynamical system is uniquely determined by a set of measurements of the system. If this is the case, the system is said to be observable. There are different ways to observe a dynamical system and some systems may be observable using only certain types of measurements. One might ask if there is a dynamical system that can be observed by any continuous function from the state space to the real numbers? If such a system exists, it is said to be universally observable. It might seem unlikely that such a system could exist. However, there are two known examples of such systems. We will discuss the history of the problem and then give the motivation and a brief outline of the construction of an elementary universally observable system on the two-dimensional torus. The ideas involved come from topological dynamics and small divisor problems. We also discuss an equivalence between universal observability and certain properties in the field of topological dynamics.
  April 18, 2011.
• Keith Ouellette, On the Fourier inversion theorem for PGL(2,Qp)
  Abstract: We will demonstrate our proof of the Fourier inversion and Plancherel formulae for spherical unramified principal series for the p-adic group PGL(2, Qp) where Qp is the quotient field of Zp, the p-adic integers. If time remains, we will apply the Fourier inversion theorem to transforms of some smooth compactly supported functions of PGL(2, Qp) for illustration.
  March 21, 2011.
• Carolyn Gordon, Dartmouth College, You Can't Hear the Shape of a Drum
  Abstract: In spectroscopy, one attempts to recover the shape or chemical composition of an object from the characteristic frequencies of sound or light emitted. Mark Kac's question "Can one hear the shape of a drum?" asks whether two membranes (drumheads) which vibrate at the same characteristic frequencies must have the same shape. We answer Kac's question negatively by constructing a pair of exotic shaped sound-alike drums. We also listen to a computer simulation, produced by Dennis DeTurck, of the sounds of these exotic drums.
  Leonard C. Sulski Memorial Lecture, March 9, 2011.
• Harold Connamacher, Albion College, The Satisfiability Threshold of Random Problems
  Abstract: A group of researchers attempting to classify the average difficulty of some notoriously hard problems (such as the NP complete problems) made an interesting discovery. For many problems, if you consider random instances with an increasing number of constraints, the probability that the instance has a solution undergoes a sudden transition at a specific constraint density. This threshold in the probability of having a solution attracted the attention of physicists and mathematicians because it seems similar to other thresholds in physical and mathematical structures such as thresholds encountered in random graphs and the transitions in an iron magnet as it cools. Despite over a decade of work on the subject, the major questions are still unresolved. This talk will survey the subject and describe some recent results.
  February 10, 2011.
• Kevin Walsh, Cornell University, Authorization in Nexus
  Abstract: We have little reason to trust computer systems. We do not know what software lurks on the other side of a network connection, or even what software runs on our own machines. We have few means to specify or reason about why we might trust a piece of software. And we do not have adequate authorization mechanisms in place to limit the damage that rogue software can inflict. In this talk I revisit the problem of authorization, and show how a combination of new secure hardware and a formal logic can result in a more trustworthy computer system.
  February 9, 2011.
• Audrey Lee-St.John, Mount Holyoke College, Rigidity Theory: from Foundations to Applications
  Abstract: I will present foundations for understanding rigidity properties of mechanical structures. Bar-and-joint frameworks, made up of rigid bars connected by universal joints, arise in important current applications; in engineering, they can model robots or buildings and, in biology, they can model proteins. Although such structures are the simplest type in a wide range of constraint systems, their mechanical properties (rigidity and flexibility) are still not fully understood.
  For certain types of constraint systems, combinatorial results have led to an elegant and efficient algorithm called the pebble game. I will present this algorithm and several generalizations, using Java applets and physical models for demonstration. In addition, I will describe current work that addresses constraint systems arising from the widely-used CAD (Computer Aided Design) software SolidWorks as well as applications in computational biology.
  February 7, 2011.
• David Kauchak, Pomona College, Learning to Simplify Sentences Using Wikipedia
  Abstract: The complexity and readability of text can vary widely. Compare, for example, a research article and a popular media article on the same topic. The articles may discuss the same material, but their usefulness for the reader can vary widely depending on the reader's background; while the fundamental concepts of the research article may be accessible, the language and structure of the article may prohibit the lay-reader from understanding these concepts.
  In this talk I will examine the problem of sentence simplification which aims to develop models to automatically reduce the reading complexity of a sentence. I will introduce a new data set that we have generated consisting of over a hundred thousand aligned Sentences from English Wikipedia and Simple English Wikipedia. Using this data set, we have developed a simplification system by extending work in statistical language translation. I will conclude with initial performance results.
  January 31, 2011.

2010

• Megan M Kerr, Wellesley College, Symmetries in Geometry: Exploring (different) Constant Curvature Spaces
  November 30, 2010.
• Sarah Wright, Graph C*-Algebras and Aperiodic Paths
  Abstract: Associating a visual object with a complicated mathematical structure is a popular and successful technique for teaching and discovering new ideas. We'll introduce the idea of a graph-algebra, where we associate a C*-algebra to some type of "graph". We'll discuss the "how's", "who's" and "why we cares" of this field of study. Once we have the basics, we can move on to the idea of aperiodicity. The condition "every cycle has an entry" first appeared in the literature in Kumjian, Pask, and Raeburn's paper on Cuntz-Krieger algebras of directed graphs, where it was called Condition (L). It provides a necessary condition for simplicity of the associated graph algebra. This condition has been generalized to aperiodicity conditions in the theory of topological graphs (Katsura), k-graphs (Kumjian, Pask), and the unifying theory of topological k-graphs (Yeend). We'll discuss the details of these generalizations as well as the theorems associated with them. We'll then introduce a Condition (F) on the finite paths of a topological k-graph that is equivalent to the corresponding aperiodicity condition. Hence we obtain a condition which is much easier to check than the aperiodicity of infinite paths.
  November 15, 2010.
• Cristina Ballantine, Powers of the Vandermonde determinant, Schur functions and the dimension game
  Abstract: Vandermonde determinants are ubiquitous in mathematics. Since every even power of the Vandermonde determinant is a symmetric polynomial, we would like to understand its decomposition in terms of the basis of Schur functions. Besides its obvious importance in mathematics, such a decomposition would shed light on the quantum Hall effect, in particular on the Slater decomposition of the Laughlin wave function. While we will not explore the problem from the point of view of physics, we will investigate several  combinatorial properties of the coefficients in the decomposition. In particular, I will give an inductive approach of computing some of the coefficients by building them up from tetris type shapes.
  November 8, 2010.
• Keith Ouellette, On the Fourier Inversion Formula for the Full Modular Group
  Abstract: We offer a new proof of the Fourier inversion and Plancherel formulae for Maass-Eisenstein wave packets. The proof  (presented in the case of the full modular group) uses truncation, basic analysis, and classical Fourier theory.  Brief sketches of the proofs due to Langlands, Lapid, and Casselman are then presented for comparison.
  October 25, 2010.
• Annalisa Crannell, Franklin and Marshall College, Fibonacci Harps and a Shift of Finite Type
  October 19, 2010.
• Dan Kennedy, The Baylor School (Chattanooga, TN)
  September 24, 2010.
• John Little, An Euler-Maclaurin Formula for Polytopes and Hirzebruch-Riemann-Roch for Toric Varieties
  Abstract: In its basic form, the classical Euler-Maclaurin summation formula relates the integral of a smooth function over an interval to the sum of the values of the function at points in the interval, with an error term involving Bernoulli numbers and derivatives of the function at the endpoints.  We will start out by looking at this elementary result and some of its applications.  In the 1990's, two (transplanted)  Russians, Khovanskii and Pukhlikov, published a generalization of Euler-Maclaurin where the interval above is replaced by a convex polytope in a higher dimensional Euclidean space.  We will look at their generalization, again in essentially elementary terms.  All of this is essentially generating function "magic."  But the generating function of the Bernoulli numbers,  f(x) = x/(1 - e^{-x}),  also quickly leads to Todd classes and the Hirzebruch-Riemann-Roch theorem.  Polytopes lead to projective toric varieties. Khovanskii-Pukhlikov gives an amazing proof of the Hirzebruch-Riemann-Roch theorem in this case. I hope to show you how it all works! 
  September 13, 20, 27, and October 4, 2010.
• Barbara Reynolds, S.D.S., Stritch University, Explorations in Plane Geometry with The Geometer's Sketchpad (GSP 5)
  Clavius Group Seminar, July 21, 2010.
• Tom Banchoff, Brown University, Piecewise Circular Space Curves 
  Clavius Group Seminar, July 20, 2010.
• Javier Leach, S.J., Universidad Complutense de Madrid, Mathematics and Reli
  

  gion: Our Language of Sign and Symbol 

  
  Clavius Group Seminar, July 20, 2010.
• Paul A. Schweitzer, S. J., Pontificia Universidade Catolica, Rio de Janeiro, The Structure of Reeb Components: An Elementary Presentation with Pictures
  Clavius Group Seminar, July 20, 2010.
• Pedro Suarez, Barry University, 
  Clavius Group Seminar, July 19, 2010.>
• Richard Freije, Sun Life Company, The Problem with the Internet
  Abstract: Some of the earliest legal cases involving the internet addressed liability of internet service providers. In particular, the cases asked if Compuserve, Prodigy, AOL and Netcom should be responsible for harassment, defamation or copyright infringement that occurred through use of theses services. After almost twenty years, and intervention by Congress, courts and commentators continue to argue the correct balance between freedom of speech and an open internet versus protection of intellectual property and the right to be free from cyberbullying or defamation.
  *The Problem with the Internet* is that it remains a platform for bad behavior; the biggest players in the technology world including Google, YouTube, Facebook and even Apple are benefiting; and no one can seem to figure out a reasonable balance between competing interests. This talk will address the history and current state of this ongoing concern. 
  Clavius Group Seminar, July 15, 2010.
• Marty Magid, Wellesley College, Timelike Minimal Surfaces via the Split-Complex Numbers 
  Clavius Group Seminar, July 15, 2010.
• Nelson Velandia, S.J., Universidad Nacional de Colombia, Space, Time and Gravity
  Clavius Group Seminar, July 15, 2010.
• Nelson Velandia, S.J., Universidad Nacional de Colombia, Particles in Schwarzschild Coordinates and Eddington - Finkelstein Coordinates
  Clavius Group Seminar, July 13, 2010.
• John Little, A Geometric View of Continued Fractions
  Abstract: "Ordinary" and "Hirzebruch-Jung" continued fraction expansions of rational numbers have very nice geometric interpretations involving sets of integer lattice points in polygons in the Euclidean plane. (This goes back ultimately to work of Felix Klein, but has been rediscovered independently several times.) We will develop this connection "from scratch" in the first hour, and then briefly indicate some applications in the theory of plane curve singularities and toric surfaces from algebraic geometry in the second. 
  Clavius Group Seminar, July 12 and 13, 2010.
• Gareth Roberts, Cyclic Central Configurations in the Four-Body Problem
  Abstract: We investigate the set of central configurations lying on a common circle in the Newtonian four-body problem. Such a configuration will be referred to as a cyclic central configuration (ccc). A central configuration is a special choice of positions where the gravitational force on each body is a scalar multiple of that body's position. Such a configuration leads to homothetic and homographic periodic solutions in the N-body problem. Using mutual distances as coordinates, we show that the set of ccc's with positive masses is a two-dimensional surface, a graph over two of the exterior side-lengths. Two symmetric families, the kite and isosceles trapezoid, are examined extensively. It is conjectured that if a ccc exists for a particular choice of masses, then it is unique. The techniques utilized in our work range from classical geometry (eg. the Cayley-Menger determinant and Ptolemy's Theorem) to modern computational algebra (eg. Grobner bases and Sturm's Theorem.) 
  Clavius Group Seminar, July 8, 2010.
• Mike Ackerman, Bellarmine University, Results on Graphs of Semigroups 
  Clavius Group Seminar, July 7, 2010.
• Tom Banchoff, Brown University, Self-Linking, Inflections, and Normal Euler Classes for Polygons and Polyhedra (part 1)
  Clavius Group Seminar, July 6, 2010.
• Ockle Johnson, Keene State College, Self-Linking, Inflections, and Normal Euler Classes for Polygons and Polyhedra (part 2)
  Clavius Group Seminar, July 6, 2010.
• Pat Ryan, McMaster University, Isoparametric Hypersurfaces in Complex Space Forms
  Clavius Group Seminar, July 6, 8, 9, 12, 13 and 16, 2010.
• Tom Banchoff, Brown University, Mike May, S.J., St. Louis University, and Barbara Reynolds, S.D.S., Stritch University, Pedagogy Meets Technology 
  Clavius Group Seminar, July 2, 2010.
• Thomas Cecil, Isoparametric Hypersurfaces in Spheres
  Clavius Group Seminar, June 29, July 1 and 2, 2010.
• Paul A. Schweitzer, S. J., Pontificia Universidade Catolica, Rio de Janeiro, Invariants of Legendrian Knots in T^3 and Similar 3-manifolds
  Clavius Group Seminar, July 1, 2010.
• Solomon Friedberg, Boston College, Stitching Primes Together
  Abstract: Whole numbers that are two or more have factorizations: they are products of a finite number of primes. Can we find a way to do something interesting with all the prime numbers at once?
  Pi Mu Epsilon Ceremony and Colloquium, April 14, 2010.
• Rick Miranda, Colorado State University, Musical, Physical, and Mathematical Intervals - how fretting a guitar is more complicated (and more simple) than one might think PDF
  Abstract: The intervals between frequencies of musical notes on a scale have been studied for millennia, and the Pythagorean method is to relate these intervals to ratios of small integers (e.g., an octave has frequency exactly twice the base note, and the fifth (e.g. a G above a C) has frequency 3/2 times the base note).  This leads to problems in transposing music, and the 'equal temperament' solution (from Renaissance times) finds a single ratio between half-notes (or adjacent frets on a guitar) that works fairly well. In 1743 Daniel Strahle (a craftsman with no apparent mathematical training) designed a simple geometric construction for placing the frets on a guitar that approximated the proper ratio.  It was wrongly dismissed at the time as being inaccurate (by mathematicians no less!), but over 200 years later, in the second half of the 20th century, it was shown to be related to two simple and important approximation techniques (for functions and for irrational numbers), and to be extremely accurate.
  In this lecture I'll review the basics from music theory, discuss a bit of history (Galileo is involved!) and then explain why Strahle's construction is so good.
  Leonard C. Sulski Memorial Lecture, March 12, 2010.

2009

• Siman Wong, UMASS-Amherst, How many primes are there?
  Abstract: For many of us, Euclid's argument that there are infinitely many primes is probably one of the first proofs we encountered. In this talk we will discuss variations and refinements of this well-known proof, both as a starting point of further investigations and as an illustration of how mathematicians tackle research problems.
  December 3, 2009.
• Stephen Abbott, Middlebury College, A Brief History of Integration from Cauchy to Riemann to Lebesgue to...Riemann
  Abstract: In the first half of the 19th century there was significant ambiguity about the proper definition of the integral--was it an area or an anti-derivative? Riemann's familiar integral from 1850--the one we still teach in calculus--was actually a modification of a proposal by Cauchy intended to divorce the integral from the derivative, but it was not without shortcomings. In particular, the collection of functions that could be integrated was lacking (i) limits of some convergent sequences and, more surprisingly, (ii) an entire class of derivatives. In 1901, Henri Lebesgue introduced a new definition of the integral whose elegant resolution to problem (i) propelled it to become the undisputed industry standard. There is, however, a modern and much less well-known integral that is more powerful than Lebesgue’s, simpler to define, and solves problem (ii) by providing the world’s shortest proof of the Fundamental Theorem of Calculus.
  Pi Mu Epsilon Ceremony and Colloquium, April 22, 2009.
• Joe McKenna, University of Connecticut, Suspension Bridges Behaving Badly
  Abstract: The Tacoma Narrows Bridge disaster in 1940 is one of the most spectacular and well documented bridge collapses. Originally it was thought that the collapse was due to resonance, a phenomenon associated with linear differential equations. However, new insights from modern analysis reveal that the collapse is better explained by properties of solutions of nonlinear differential equations.
  April 1, 2009.
• Paul A. Schweitzer, S. J., Pontificia Universidade Catolica, Rio deJaneiro, Asymptotic linking of volume-preserving R^k actions on domains in Rⁿ
  Abstract: V. Arnol'd studied asymptotic linking of the flowlines of volume-preserving (i.e. divergence-free) smooth flows on a compact convex domain in R³, related to the linking of closed curves in R³ and the helical twisting of the two flows. I shall describe Arnol'd's fascinating theory, with his two equivalent definitions of the asymptotic linking invariant: first, as a probabilistic integral involving Gauss' formula for linking of two disjoint simple closed curves in R³, and second, in terms of the differential forms dual to the vector fields that generate the flows. Then I shall briefly describe a generalization discovered by my doctoral student Jose Luis Lizarbe Chira to asymptotic linking of volume-preserving actions of R^k and $R^\ell$ on a convex domain in Rⁿ, where $k + \ell + 1 = n$.
  March 26, 2009.
• Paul A. Schweitzer, S. J., Pontificia Universidade Catolica, Rio deJaneiro, Surfaces and 3-dimensional Manifolds: How Geometry Comes to the Aid of Topology
  Abstract: The talk will begin with a short outline of the classification of closed surfaces, their Euler characteristic and curvature of metrics, and how the metric can flow to a constant curvature metric. We next talk about 3-manifolds, their geometries and Thurston's geometrization conjecture. Finally, we consider the idea of Perelman's proof of the geometrization conjecture, with a flow making the geometry as homogeneous as possible, distributing the curvature equally. The mathematical details are lengthy and difficult, so we shall emphasize the intuitive ideas with pictures, rather than giving proofs.
  Leonard C. Sulski Memorial Lecture, March 24, 2009.
• John Little, The Spectral Sequence of a Filtration
  Abstract: Spectral sequences are an important and useful tool in modern algebraic topology and algebraic geometry. But, unfortunately, their algebraic "overhead" has given them something of a bad reputation. The goal of these talks is to partially de-mystify the idea by considering a rather concrete situation that leads to a commonly-encountered type of spectral sequence. Namely, we will consider computing the homology of a topological space X with a (finite) filtration by subspaces: X_0 \subset X_1 \subset \cdots \subset X_n = X. (CW complexes are especially nice examples.) We will construct spectral sequences from such a filtration which converge to the homology or cohomology of the whole space and consider some examples from the theory of toric varieties.
  March 19, 2009.
• Helen Wong, Bowdoin College, Quantum invariants for 3-dimensional manifolds
  Abstract: Growing out of the Jones polynomial for links, the quantum invariant for 3-dimensional manifolds are an exciting and relatively new development in topology. Its construction is based on deep theorems in classical topology, its inspiration is from quantum mechanics, and the theory has applications from physics to quantum computation to combinatorics. A brief overview of how it is defined and give some applications to topological questions will be given.
  February 25, 2009.
• Reinier Broker, Worcester State College, Constructing cryptographic elliptic curves
  Abstract: Elliptic curves play a key role in Wiles' proof of Fermat's Last Theorem. Besides being of key importance in abstract mathematics, they have become increasingly important for crytography. They are being used in fast algorithms to factor integers in prime numbers, and they form the basis of an entire industry of cryptographic protocols.
  In this talk I will explain the basic ideas behind elliptic curve cryptography. As we will see, there are `good' crypto curves and `bad' crypto curves. I will present an efficient way to construct a `good' cryptographic curve. Many examples will be given.
  February 19, 2009.
• Gareth Roberts, On Central Configurations, II, February 12, 2009.
• Gareth Roberts, On Central Configurations, I
  Abstract: Central configurations (c.c.'s) play an important role in the Newtonian n-body problem. Physically speaking, a c.c. is a configuration of masses for which the gravitational force on each body points toward the center of mass (with an appropriate scaling). Mathematically, a c.c. is a solution to a complicated system of nonlinear algebraic equations. Three bodies of any mass placed at the vertices of an equilateral triangle is perhaps the most famous c.c. (Lagrange, 1772). C.C's play a vital role in spacecraft transport as ideal locations for observational spacecraft as well as helping determine low-energy trajectories to explore our solar system. In these talks, I will present an overview of the main results on central configurations, including the many different mathematical approaches to the subject (analytical, algebraic, topological, etc.) as well as the major open questions.
  February 05, 2009.

2008

• Alex Popa, Applications of Modular Forms, II,
  December 02, 2008.
• Gabe Weaver, Computing with Diagrammatic Content: Lessons Learned from Archimedes
  Abstract: The Episteme Project focuses on developing tools for increasing accessibility to and awareness of Ancient Scientific and Mathematical works. Unique to Episteme is its focus on representing and computing with diagrammatic information. Rather than treating diagrams as images, Episteme treats diagrams as a unique data type capable of representing a dynamic process in static form. Using this approach, both person and computer can interact with diagrams in terms of what they represent rather than how they are drawn. More specifically, Episteme explores the traditional operations of navigation, production, and logical assertion on diagrams through the lens of computation. In addition, non-traditional modes of interacting with diagrams such as querying become feasible.
  Particular attention will be paid to the development of the Diagram Markup Language (DML) and the architecture of the DML compiler. The compiler is unique in that programs written in DML are not compiled into assembly code, but rather into SVG images, annotated with logical content encoding their meaning.
  More information is available at http://www.episteme.ws/
  November 19, 2008.
• Alex Popa, Applications of Modular Forms, I,
  November 18, 2008.
• Casey Douglas, Rice University, Perturbed, Genus-One Scherk Surfaces and Their Limits
  Abstract: The singly periodic, genus one helicoid is conjectured to be the limit of a one parameter family of doubly periodic minimal surfaces referred to as Perturbed Genus One Scherk Surfaces. Using both classical elliptic function theory and more recent handle-addition techniques for minimal surfaces, we prove the existence of these perturbed surfaces and verify their conjectured limit.
  November 11, 2008.
• Ed Soares, Evaluation of pharmaceutical treatments for cancer models, II,
  October 28, 2008.
• Ed Soares, Evaluation of pharmaceutical treatments for cancer models, I
  Abstract: The talk describes joint work with Jack Hoppin and his new company inviCRO (along with Northeastern U, UNM, etc). The idea is to evaluate pharmaceutical treatments for cancer models. One acquires SPECT data from mice (control and treatment groups), derives activity and concentration measures of cancerous tumors, and evaluates these measures longitudally. A multivariate analysis of variance is used to test the null hypothesis that there is no difference between control and treatment groups. I am running this methodology on some real data to see if the statistical test will bear out what we see visually. Again, PCA is also used.
  October 21, 2008.
• John Anderson, Hardy spaces
  Abstract: I will give a brief introduction to the theory of classical Hardy spaces and their modern counterparts, with particular attention to the duality between the Hardy space H^1 and the space BMO of functions of bounded mean oscillation.
  October 07, 2008.
• Jack Hoppin, Co-Founder InviCRO, LLC, The Role of SPECT in Pre-Clinical Molecular Imaging,
  Abstract: The recent development of micro-imaging systems has resulted in new research opportunities for scientists and businesses. Using animal models of disease, coupled with increased image spatial resolution, these entities use small-animal imaging to better identify disease pathways and the effectiveness of drug treatments. By fusing structural x-ray computed tomographic (CT) images to emission images, such as single-photon emission computed tomography (SPECT), one can better identify regions of increased tracer uptake, which is common to cancerous tissue.
  October 6, 2008.
• Tom Cecil, Lie Sphere Geometry and Dupin Hypersurfaces, III, September 30, 2008.
• Tom Cecil, Lie Sphere Geometry and Dupin Hypersurfaces, II, September 23, 2008
• Tom Cecil, Lie Sphere Geometry and Dupin Hypersurfaces, I, September 16, 2008.
• Robert Benedetto, Amherst College, The abc Conjecture: An Introduction, Department of Mathematics and Computer Science Pi Mu Epsilon Ceremony and Colloquium,
  April 30, 2008.
• Donal B. O'Shea, Holyoke College, The Shape We're In: The Poincare Conjecture, Leonard C. Sulski Memorial Lecture,
  April 22, 2008.
• Gareth Roberts, The Planar, Circular, Restricted Four-Body Problem
  Abstract: An interesting case of the Newtonian four-body problem arises when one infinitesimal body interacts with three larger ones (primaries) fixed at the vertices of a rotating equilateral triangle. This problem, a planar, circular, restricted four-body problem (PCR4BP), can be characterized by a special potential function V. We investigate the number and location of the critical points of V (equilibria or "parking spaces") as a function of the masses of the three primaries. In particular, we prove that the number of critical points is finite for any choice of masses. A version of Saari's conjecture, that the only solutions to the n-body problem with a constant total size are rigid rotations, is also investigated for the PCR4BP. Techniques from computational algebraic geometry are employed such as Gröbner bases, resultants and BKK theory.
  April 17, 2008.
• Cristina Ballantine, Expander graphs - hard and easy constructions
  Abstract: I will present a construction of an infinite family of Ramanujan bigraphs (i.e., bipartite, biregular graphs which are asymptotically optimal expanders) based on representation theory. This provides the first known infinite family of Ramanujan bigraphs. I will also discuss the zig-zag product of graphs due to Reingold, Vadhan and Wigderson. This is a purely combinatorial construction that gives infinite families of constant degree expander graphs which are close to being Ramanujan. The first part of the talk is joint work with Dan Ciubotaru.
  February 29, 2008.

2007

• Burt Tilley, Olin College, You Pick: Using Popular Science in a Mathematical Modeling Course, Department of Mathematics and Computer Science Colloquium,
  November 26, 2007.
• Arvind Bhusnurmath, University of Pennsylvania, Flows and Cuts in Computer Vision, Department of Mathematics and Computer Science Colloquium,
  November 14, 2007.
• Viraj Kumar, A sublinear space, polynomial time algorithm for directed s-t connectivity
  Abstract: For many algorithmic software verification techniques (model checking, conformance testing, etc.), the central problem reduces to exploring graphs efficiently. A software program can be viewed as a graph, where each vertex represents the state of the program (a tuple consisting of the program counter, the values of all variables, and the stack configuration) at a given time, and each edge from vertex u to vertex v represents the possibility of switching from state u to state v in one step. Since the number of states is exponential in the number of variables, the entire graph cannot be represented in memory and the challenge is to explore the graph using as little memory as possible.
  Undirected graphs with n vertices can be explored very efficiently (in time polynomial in n, using O(log n) space) via random walks. Graphs that model software programs, however, are usually directed since computation steps are typically nonreversible. Random walks perform poorly on directed graphs with n vertices (they can require time exponential in n). This talk will present a deterministic sub-linear space, polynomial time algorithm by Barnes et. al. (1992) for the directed s-t connectivity problem, where one is given a graph and asked to find a (directed) path from s to t if one exists. Details of the paper are given below:
  A sublinear space, polynomial time algorithm for directed s-t connectivity; G. Barnes, J. F. Buss, W. L. Ruzzo and B. Schieber; Structure in Complexity Theory (1992), pp. 27 -- 33.
  November 01, 2007.
• Steve Levandosky, Stability of Solitary Waves of a Fifth-Order KdV Equation II,
  October 26, 2007.
• Steve Levandosky, Stability of Solitary Waves of a Fifth-Order KdV Equation
  Abstract: For a certain class of fifth-order KdV-like equations, one can use a constrained minimization problem to prove the existence of a 2-parameter family of solitary waves. Their stability is determined by the concavity of a function of one of the parameters (the wave speed c). Unfortunately, the explicit form of this function is known only in special cases. To remedy this situation, numerical calculations are required. I'll give an overview of the existence and stability theory, and then explain how an important scaling identity can be used to greatly reduce the scope of the numerical calculations. This scaling property also leads to some partial analytical results.
  October 19, 2007.
• Andy Hwang, Extremal Kähler metrics
  Abstract: This talk will introduce and briefly survey a differential-geometric variational problem whose solutions include the metrics of constant Gaussian curvature on a compact Riemann surface. In higher dimension, existence of solutions is not guaranteed, and leads to fascinating, subtle criteria. We'll see a geometric hint of what can go wrong in a minimizing sequence by looking at explicit complex surfaces.
  September 28, 2007.
• Richard P. Stanley, Massachusetts Institute of Technology, Plane Tilings, Leonard C. Sulski Memorial Lecture,
  April 24, 2007.
• Paul Blanchard, Boston University, Newton's Method: Complex Numerics and Complex Dynamics, Department of Mathematics and Computer Science Pi Mu Epsilon Ceremony and Colloquium,
  April 19, 2007.
• Tanya Leise, Amherst College, The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google, Department of Mathematics and Computer Science Colloquium,
  March 28, 2007.
• Noam D. Elkies, Harvard University, Canonical Forms: A Mathematician's View of Musical Canons, Interdisciplinary Colloquium,
  February 19, 2007.

2006

• Steven Sherwood, Dept. of Geology and Geophysics, Yale University, Global Climate Change: What We Know and Don't Know, Interdisciplinary Colloquium, November 20, 2006.
• Dave Damiano and Andrew Hwang, HC, The Poincare Conjecture, Department of Mathematics and Computer Science Colloquium, October 20, 2006.
• Michele Intermont, Kalamazoo College, On Calculus and Derivatives . . . the Goodwillie Kind, Clavius Group Seminar, July 14, 2006.
• Jennifer Beineke, Western New England College, Great Moments of the Riemann Zeta Function, Department of Mathematics and Computer Science Pi Mu Epsilon Ceremony and Colloquium, April 26, 2006.
• Andrew Swift, Dept. of Mathematical Sciences, WPI, An Introduction to Bayesian Statistics, Department of Mathematics and Computer Science Colloquium, April 5, 2006.
• Michele Intermont, Kalamazoo College, The Sound of Algebra, Leonard C. Sulski Memorial Lecture, March 22, 2006.
• David Vella, Skidmore College, The Higher Chain Rule and Composite Generating Functions, Department of Mathematics and Computer Science Colloquium, February 15, 2006.

2005

• Robert L. Devaney, Boston University, The Fractal Geometry of the Mandelbrot Set, Department of Mathematics and Computer Science Colloquium, December 1, 2005.
• John Little, HC, Symmetry in Music, Department of Mathematics and Computer Science Colloquium, November 16, 2005.
• Catherine A. Roberts, HC, How does the solution grow?, Department of Mathematics and Computer Science Colloquium, October 20, 2005.
• Edward Burger, Williams College, Conjugate Coupling: The Romantic Adventures of the Quintessential Quadratic, Department of Mathematics and Computer Science Pi Mu Epsilon Ceremony and Colloquium, April 13, 2005.
• Frank Morgan, Williams College, Soap Bubble Geometry, 200 B.C. - 2005 A.D, Leonard C. Sulski Memorial Lecture, April 7, 2005.
• Neil Heffernan, WPI, Learning about Learning, Department of Mathematics and Computer Science Colloquium, March 30, 2005.
• Marian Batton, GIS Senior Analyst, Johnson, Mirmiran and Thompson, GIS: Solving Problems With a Geometric Network, Department of Mathematics and Computer Science Colloquium, March 21, 2005.
• William J. Martin, WPI, The Math Behind the Compact Disk, Department of Mathematics and Computer Science Colloquium, January 26, 2005.

2004

• Allison Pacelli, Williams College, Polynomials, Primes, and Fermat's Last Theorem, Department of Mathematics and Computer Science Colloquium, December 8, 2004. 
• Andrew Hwang, HC, Topology and Curvature of Polyhedra, Department of Mathematics and Computer Science Colloquium, November 17, 2004.
• John Geddes, Olin College of Engineering, Oscillations in Microvascular Bloodflow, Department of Mathematics and Computer Science Colloquium, November 6, 2004.
• Tom Hull, Merrimack College, The Secrets of Super-Complex Origami Design, Department of Mathematics and Computer Science Colloquium, April 19, 2004.
• Gil Pontius, Clark University, International Development, Community and Environment (IDCE) Department & Graduate School of Geography, Environmental Studies, Educational Technology, and the Department of Mathematics & Computer Science Colloquium, March 25, 2004.
• Frank Farris, Santa Clara University, The Edge of the Universe: Non-Euclidean Wallpaper, Leonard C. Sulski Memorial Lecture, March 22, 2004.

2003

• Robert Devaney (Holy Cross '69), Boston University, The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence, Department of Mathematics and Computer Science Pi Mu Epsilon Ceremony and Colloquium, April 28, 2003.
• Kresimire Josic, University of Houston, Singularly Perturbed Quadratic Maps, Department of Mathematics and Computer Science Colloquium, April 25, 2003.
• Mark Lawrence, HC, Analytic Continuation in Several Complex Variables, Department of Mathematics and Computer Science Colloquium, April 11, 2003.
• Gregory Buck, Saint Anselm College, Physical Knot Theory, Pi Mu Epsilon Ceremony and Colloquium, April 9, 2003.
• Kathleen Shannon, Salisbury University, Pascal's Triangle, Cellular Automata and Serendipity: A Mathematical Tale, Leonard C. Sulski Memorial Lecture, April 2, 2003.
• Dave Damiano, HC, Knot Theory: Ribbon = Slice?, Department of Mathematics and Computer Science Colloquium, March 19, 2003.
• Diana M. Thomas, Department of Mathematical Sciences, Montclair State University, A Characterization for the Length of Cycles of the N Number Ducci Game, Mathematics Colloquium, February 24, 2003.
• Anne Schwartz, Westfield State College, Modular Functions and Almost Modular Functions and Why We Care, Department of Mathematics and Computer Science Colloquium, February 21, 2003.
• Andy Hwang, HC, An Introduction to Kaehler Geometry, and a Survey of Einstein and Extremal Kaehler Metrics, III, Department of Mathematics and Computer Science Colloquium, February 12, 2003.
• Andy Hwang, HC, An Introduction to Kaehler Geometry, and a Survey of Einstein and Extremal Kaehler Metrics, II, Department of Mathematics and Computer Science Colloquium, February 5, 2003.
• Andy Hwang, HC, An Introduction to Kaehler Geometry, and a Survey of Einstein and Extremal Kaehler Metrics, Department of Mathematics and Computer Science Colloquium, January 29, 2003.

2002

• Carlos Morales, Worcester Polytechnic Institute, A Rough Introduction to Roughness Estimation, Mathematics Colloquium, December 5, 2002.
• Stanzi Royden, HC, Seeing Through our Illusions: How the Brain Mechanisms Underlying Heading Perception Explain a Visual Illusion, Department of Mathematics and Computer Science Colloquium, November 20, 2002.
• Ann Trenk, Wellesley College, Professors who Snooze and those who Steal:An Introduction to Interval Graphs, Mathematics Colloquium, November 14, 2002.
• Gareth Roberts, HC, Central Configurations and Their Importance in the N-Body Problem, continued, Department of Mathematics and Computer Science Colloquium, November 13, 2002.
• Gareth Roberts, HC, Central Configurations and Their Importance in the N-Body Problem, Department of Mathematics and Computer Science Colloquium, November 6, 2002.
• John Little, HC, Fast Fourier Transforms and Polynomial Multiplication, Department of Mathematics and Computer Science Colloquium, October 30, 2002.
• Cristina Ballantine, HC, Rolle's Theorem for Local and Finite Fields, Department of Mathematics and Computer Science Colloquium, October 9, 2002.
• John Little, HC, Primes in P continued, Department of Mathematics and Computer Science Colloquium, September 25, 2002.
• John Little, HC, Primes in P, Department of Mathematics and Computer Science Colloquium, September 18, 2002.
• Dennis DeTurck, University of Pennsylvania, Coiling and Writhing in Geometry, Biology and Physics, Leonard C. Sulski Memorial Lecture, April 18, 2002.
• Jack Hoppin '98, University of Arizona, Comparing Estimation Tasks in Medical Imaging Without a Gold Standard, Mathematics Colloquium, February 28, 2002.
• Elizabeth Sweedyk Dimacs, Rutgers University, Approximating the Shortest Common Superstring, Department of Mathematics and Computer Science Colloquium, February 26, 2002.

2001

• Laurie King, HC, Runtime Execution of Reconfigurable Hardware in a Java Environment, Department of Mathematics and Computer Science Colloquium, November, 2001.
• Rosalind Picard, MIT Media Lab, Toward Computers that Recognize and Respond to Human Emotion, Department of Mathematics and Computer Science Colloquium, April 10, 2001.
• Keith Miller, University of Illinois-Springfield, Minimum Testing Standards for Commercial Software: Technical and Ethical Issues, Department of Mathematics and Computer Science Colloquium, April 5, 2001.
• Jane Hawkins, University of North Carolina, Smoothing Out the Rough Edges of Fractals, Leonard C. Sulski Memorial Lecture, March 29, 2001.
• Donald Gotterbarn, Professor, Computer and Information Sciences, East Tennessee State University, "Code Doesn't Count", Department of Mathematics and Computer Science Colloquium, March 15, 2001.
• Cem Kaner, J.D., Ph.D., Professor of Computer Science, Florida Institute of Technology, Legislation and Embedded Software: Fundamental Ambiguities in Law and Computer Science, Department of Mathematics and Computer Science Colloquium, March 12, 2001.

2000

• Richard Stallman, The Free Software Foundation, The Free Software Movement and GNU, Department of Mathematics and Computer Science Colloquium, December 6, 2000.
• Richard Freije, Corporate Attorney, Global Knowledge, The First Amendment, the Internet and the Regulation of Speech on Campus, Department of Mathematics and Computer Science Colloquium, November 30, 2000.
• Dan Kennedy, The Baylor School, Mathematical Paradoxes, Leonard C. Sulski Memorial Lecture, March 23, 2000.
• Fred Schneider, Cornell University, The Non-Technical Take on Computing System Trustworthiness, Department of Mathematics and Computer Science Colloquium, March 3, 2000.

1994-1999

• Tracy Camp, Colorado School of Mines, WANs to Worms to the Web: A History of the Internet, Department of Mathematics and Computer Science Colloquium, April 22, 1999.
• Lawrence Conlon, Washington University, Sighting the Infinite Loch Ness Monster in the 3-sphere, Leonard C. Sulski Memorial Lecture, April 15, 1999.

• Colin Adams, Williams College, Bus Tours of the Universe and Beyond, Leonard C. Sulski Memorial Lecture, April 16, 1998.

• Peter Bushell, University of Sussex, Prime Numbers: The Search for a Formula Giving Every Prime Number. A Story with a Happy Ending?, Leonard C. Sulski Memorial Lecture, April 9, 1997.

• Michael Rosen, Brown University, Historical Remarks on Fermat's Last Theorem, Leonard C. Sulski Memorial Lecture, April 18, 1996.

• Thomas Banchoff, Brown University, Visualizing Across Dimensions: From Flatland to Interactive Hypergraphics, Leonard C. Sulski Memorial Lecture, April 20, 1995.

• Robert Devaney, Boston University, The Fractal Geometry of the Mandelbrot Set, Leonard C. Sulski Memorial Lecture, April 14, 1994.