PREVIOUSLY.......... |
| Seminar: Amicable Numbers |
| Speaker Name: Dr. Carl Pomerance (Department of Mathematics at Dartmouth College) |
| Date: Friday, 04/17/09 |
| Time: 1:00 p.m. - 2:00 p.m. |
| Room: 08-2355 |
Abstract: Sociable Numbers
Consider iterating the function which sends a natural number to the
sum of its proper divisors. A fixed point for this system, such as 6 or 28,is called perfect , while a number belonging to a cycle of length 2, such as 220 or 284, is called amicable . Known to Euclid and Pythagoras, some scholars have even found allusions to perfect and amicable numbers in the Old Testament. Sociable numbers are the natural generalization of perfect and amicable numbers to cycles of arbitrary length---they are mere youngsters, having been studied for only a century! This talk will describe the colorful history of the problem and report on some recent results on the distribution of sociable numbers within the natural numbers
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| Seminar: On sums of powers of primes |
| Speaker Name: Mr. Florian Luca (U.N.A.M.) |
| Date: Thursday, 03/26/09 |
| Time: 1:00 p.m. - 1:50 p.m. |
| Room: 08-2130 |
Abstract: All integers are divisible by the product of their primes factors. Some, like 30, are not prime
powers yet are also divisible by the sum of their prime factors. In this talk, we will take a
closer look at such integers as well as at integers satisfying related divisibility conditions.
For example, we will see that for every positive integer k there are in nitely many positive
integers n having more than two distinct prime factors and which are divisible by the sum
of their prime factors, by the sum of the squares of their prime factors, and so on up to the
sum of the kth powers of their prime factors. The proofs use variations of Vinogradov's
Three Primes Theorem.
Many of the results presented in the talk have been obtained jointly with Jean-Marie De
Koninck.
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| Seminar: “Instabilities at Astrophysical Fluid Interfaces: Flames, Winds, and Magnetic Fields” |
| Speaker Name: Jonathan Dursi (University of Toronto) |
| Date: Wednesday, 02/18/09 |
| Time: 12:00 p.m. - 12:50 p.m. |
| Room: 08-2130 |
Abstract: The problem of mixing between two fluids arises in many astrophysical systems, from the surfaces of stars to that of merging galaxy clusters; this mixing is often mediated by instabilities at the interface between the fluids. These interfacial instabilities can be still more interesting when the interfaces have their own dynamics, such as in the case of flames or detonations. In this talk I discuss recent work on instabilities at astrophysical fluid interfaces in a variety of contexts.
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| Seminar: TWO STRUCTURAL PROTEOMICS ALGORITHMS AND THEIR APPLICATIONS |
| Speaker Name: Dr. Vicente M. Reyes (RIT) |
| Date: Wednesday, 02/04/09 |
| Time: 1:00 p.m. - 1:50 p.m. |
| Room: 08-2130 |
Abstract:
Part 1. Representing Protein 3D Structures in Spherical Coordinates – Two Applications: 1. Detection of Invaginations and Protrusions as Potential Ligand Binding Sites on the Protein Surface; and 2. Separating the Protein Hydrophilic Outer Layer from the Hydrophobic Inner Core. Protein 3D structures have traditionally been represented in Cartesian coordinate systems with arbitrary origins. We investigated the utility of representing protein 3D structures in a spherical coordinate system in which the origin is the protein molecular centroid. We found that by binning ö and è, and then plotting the frequency distribution of maximum ñ in each ö-è bin, this representation allows the quantitative elucidation of protrusions and invaginations on the protein surface. Additionally, if the method is performed on a protein with and without bound ligand and the respective frequency distribution plots superimposed, an empirical rule for predicting ligand binding sites on the protein surface emerges. A second application of the spherical representation is the separation of the protein hydrophilic outer layer (HOL) from its hydrophobic inner core (HIC). This method is potentially important, as protein domains - the units of protein evolution - are defined in terms of their hydrophobic cores. In addition, active sites are usually constellations of hydrophilic residues within the HIC, while protein-protein interaction interfaces are usually patches of hydrophobic residues on the HOL.
Part 2. Two Complementary Methods for Quantifying Ligand Binding Site Burial Depth In Proteins: 1. The 'Cutting Plane' Method; and 2. The 'Tangent Sphere' Method. Burial depth of active sites, binding sites and other biologically important protein local structures (‘functional sites’) is an important parameter as it is an indicator of protein flexibility manifested as conformational changes when the protein allows access to such functional sites by other molecules in the cell. Currently, however, there are no quantitative methods available to assess and compare ligand burial depth. Here we report two complementary, but not redundant, methods to quantify the depth of burial of ligand binding sites (LBS), namely, the ‘cutting plane’ (CP) and the ‘tangent sphere’ (TS) methods. The CP is the plane containing the LBS centroid (local centroid, LC) and normal to the line connecting the LC and the protein centroid (global centroid, GC). The TS has GC as center, GC-LC as radius, and is tangent to the CP at LC. The CP method depends on the percentage of protein atoms on CP's external side (opposite GC), while the TS method depends on the percentage of protein atoms inside TS. Neither method depends on protein size, and both may be extended to other protein functional sites such as amino acid modification sites (e.g., phosphorylation sites) and protein-protein interaction interfaces.
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| Seminar: Teaching, Learning, and Student Success |
| Speaker Name: Dr. Carol Marchetti (RIT SMS Faculty) |
| Date: Wednesday, 01/21/09 |
| Time: 2:00 p.m. - 1:50 p.m. |
| Room: 08-2130 |
Abstract: The SMS Teaching, Learning, and Student Success Taskforce (TLAST) was formed last spring to address concerns about retention at RIT. This group has been collecting data and researching a number of issues related to retention. We will present our findings on student success and on the effect of early alerts. Learn about our work-in-progress and give us your comments and suggestions. To be successful, we need you! We hope you'll join the conversation...
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| Seminar: Mathematical Crossword Puzzles (Puzzle 1. A Sort of Sudoku) |
| Speaker Name: Dr. Jonathan Farley (Johannes Kepler University, Linz) |
| Date: Monday, 01/05/09 |
| Time: 1:00 p.m. - 2:00 p.m. |
| Room: 08-2305 |
Abstract: Consider several left-justified rows of boxes stacked on top of one another, as in the game of Sudoku---only these rows may have different lengths (not just length 9) and may have different lengths than each other. Suppose the first row has $\lambda_1$ boxes, the second $\lambda_2$, and so on, where one may as well assume that $\lambda_1\ge\lambda_2\ge\cdots$. Such a picture is called a {\it Young diagram\/} of the {\it partition\/} $\lambda=(\lambda_1,\lambda_2,\dots)$. Starting from an empty diagram, can you fill in all the boxes with numbers, so that the numbers in row $i$ range from 1 to $\lambda_i$ and so that no number appears twice in a row or column? You can do it with the partition $\lambda=(5,3,3,2)$, but you can't for $(4,3,3,2)$. The Wide Partition Conjecture states precisely when a partition can be filled: when, for all subpartitions $\eta$ of $\lambda$, the conjugate of $\eta$ is less than or equal to $\eta$ in the dominance ordering.
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| Seminar: Mathematical Crossword Puzzles (Puzzle 1.5. Vaughan Pratt's $2,000 Crossword Puzzle) |
| Speaker Name: Dr. Jonathan Farley (Johannes Kepler University, Linz) |
| Date: Monday, 01/05/09 |
| Time: 1:00 p.m. - 2:00 p.m. |
| Room: 08-2305 |
Abstract: In January 2003, Stanford computer scientist Vaughan Pratt posed the following problem: Let $A$ be a set; call a function $f:A\to\{0,1\}$ a {\it word\/}. Let $D$ be a set (called a {\it dictionary\/}) of all words with the following properties: (1) $D$ contains the constant words; (2) for all distinct $a,b\in A$, there exists a word $f\in D$ such $f(a)=0$ and $f(b)=1$; (3) for every {\it crossword\/} $C$ (a function $C:A\times A\to\{0,1\}$) such that every row is a word in $D$ as well as every column (if one views $C$ as an $|A|\times|A|$ array of 0's and 1's), one has that the diagonal is a word in $D$. Pratt asked if the dictionary must necessarily contain all words, and offered a \$2,000 reward. Mark Aujus proved that the answer is yes if $A$ is at most countably infinite. As any such dictionary is closed under bitwise AND and OR, it is a distributive lattice. No knowledge of lattice theory will be needed to understand this talk, however.
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| Seminar: “Control Methods for Ecological Systems” |
| Speaker Name: Ms. Julie Blackwood (University of California, Davis) |
| Date: Monday, 12/15/08 |
| Time: 12:00 p.m. - 1:00 p.m. |
| Room: 08-2130 |
Abstract: Part 1: The removal of invasive species is the first step toward restoring an ecosystem following invasion. We develop spatially-explicit, dynamic optimal control strategies for invasions of a large class of problems using linear-quadratic control. We assume adults are sedentary, and patches are connected via dispersal of offspring, as in the case of Spartina alterniflora. The control method allows linear dependence on species movement and removal, and quadratic dependence on associated ecological and economic costs. The ultimate goal is to develop a general framework of optimal management strategies that considers spatially-explicit dynamics.
Part 2: In recent decades, there has been evidence of coral reefs losing their resilience and consequently shifting to degraded macroalgal-dominated states. In the Caribbean, these shifts are largely a result of the mass mortality of Diadema antillarum, a sea urchin that dominated the grazing of coral reefs. However, by building on a previously developed model we show that it may be possible to reverse these phase shifts through hysteresis. In particular, we consider the impact of the over-fishing of parrotfish in the Caribbean.
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| Seminar: Crashing Symbolic Cymbals () Patterns and Mappings as seen and heard within a math/musical context |
| Speaker Name: Prof. JayAlan Jackson (RIT ) |
| Date: Wednesday, 12/10/08 |
| Time: 1:00 p.m. - 2:00 p.m. |
| Room: 08-2130 |
Abstract: This talk will present numerous sound examples that demonstrate pattens of symbols and mappings of symbols in both mathematical and musical domains.
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| Seminar: The Pros and Cons of Dark Matter and Modified Gravity |
| Speaker Name: Dr. Stacey McGaugh (University of Maryland) |
| Date: Friday, 12/05/08 |
| Time: 12:30 p.m. - 1:30 p.m. |
| Room: 78-2015 |
Abstract: There is overwhelming observational evidence for mass discrepancies in the unviverse. When we look at extragalactic systems, we see motions that are greater than can be accounted for by the action of gravity and the mass we see. The obvious and widely accepted inference is that there must be additional unseen mass, presumably in a novel type of particle. An alternative interpretation is that the equations governing the motions in such systems need to be generalized. I will discuss some of the pros
and cons of these ideas.
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| Seminar: A Brief Overview of the Rogers-Ramanujan Identities |
| Speaker Name: Dr. Elmer Young (RIT SMS Faculty) |
| Date: Wednesday, 11/12/08 |
| Time: 1:00 p.m. - 1:50 p.m. |
| Room: 08-2130 |
Abstract: The talk will include some background and a sketch of a proof of the Rogers-Ramanujan identity. It is based on the discussion in the number theory book by George Andrews.
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| Seminar: Enhancing Student Success In The Data Analysis Sequence Using Learner Centered Pedagogy And Best Practices Incorporating Instructional Technologies |
| Speaker Name: Dr. Yolande Tra and Dr. Bernadette Lanciauxs ( RIT SMS Faculty) |
| Date: Wednesday, 10/29/08 |
| Time: 1:00 p.m. - 1:50 p.m. |
| Room: 08-2130 |
Abstract: Not Available
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| Seminar: TBA |
| Speaker Name: Dr. Lee Lindblom (Caltech) |
| Date: Friday, 10/17/08 |
| Time: 12:00 p.m. - 1:00 p.m. |
| Room: 78-2015 |
Abstract: This talk will describe a variety of topics that arise in the generalized harmonic approach used by the Caltech/Cornell group to solve Einstein's equations: hyperbolicity, constraint damping, physical and constraint preserving boundary conditions, gauge drivers, etc.
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| Seminar: "Do Dogs Know Calculus?" |
| Speaker Name: Prof. Timothy Pennings (Hope College) |
| Date: Monday, 10/13/08 |
| Time: 1:00 p.m. - 2:00 p.m. |
| Room: 08-A300 |
Abstract: We will show that dogs - at least my dog, Elvis - knows calculus. That is,Elvis can find the optimal - fastest - route to a ball thrown into the water some distance down the beach.
But what happens when Elvis is positioned in the water and
retrieves a ball that is also in the water? When should he swim
straight to the ball,and when should he swim in to the shore, run along the shore, and then swim back out to the ball? What is the bifurcation point for the change in optimal strategy? Does Elvis bifurcate? Does his fur bicate?
Dr. Elvis (he has an honorary doctorate degree) will be in the
building demonstrating that he's indeed the King of Calculus -
and much more than a hound dog.
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| Seminar: "Hypercompact Stellar Systems" |
| Speaker Name: Dr. David Merritt (RIT ) |
| Date: Friday, 10/03/08 |
| Time: 12:30 p.m. - 1:30 p.m. |
| Room: 78-2015 |
Abstract: Not Available
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| Seminar: AN INTRODUCTION TO AGENT-BASED MODELING |
| Speaker Name: Dr. Michael Long (RIT SMS Faculty) |
| Date: Wednesday, 10/01/08 |
| Time: 1:00 p.m. - 1:50 p.m. |
| Room: 08-2130 |
Abstract: Agent-Based Models use individual computer objects as players or agents.
Governed by a set of rules, these agents are turned loose in a computer generated landscape to perform their appointed task such a trading, segregating, spreading disease or minority opinions, reacting, creating mayhem, bank fraud, or any number of other laudable or mischievous endeavors. Their resultant behavior has a remarkable similarity to observed reality and can also lead to an understanding of emergent behavior.
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| Seminar: Nonlinear Waves In Discrete Equations |
| Speaker Name: Mr. Luis Cisneros (Post Doc at the University of Mexico) |
| Date: Friday, 09/26/08 |
| Time: 12:00 p.m. - 12:50 p.m. |
| Room: 08-2355 |
Abstract: We give a brief discussion on some linear and nonlinear continuous differential equations used in physics. We study the discrete counterpart of such models, that is, their space discretization. We mention the phenomelogical differences between continuous and discrete problems both in the linear and nonlinear regime. We give some results on two particular nonlinear discrete systems, the Sine-Gordon and the Toda equations.
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| Seminar: Modeling the dynamic organization of the IgE high affinity receptor |
| Speaker Name: Ms. Flor Espinoza (Doctoral candidate University of New Mexico. ) |
| Date: Friday, 09/26/08 |
| Time: 1:00 p.m. - 1:50 p.m. |
| Room: 08-2355 |
Abstract: It is well known the importance of both spatial and temporal organization in understanding how cells work. Our goal is to produce a phenomenological model that simultaneously captures the important features of the spatial organization of signaling molecules obtained by high resolution transmission electron microscopy (TEM) using nanogold-bead labeled reporter molecules on fixed patches of the cell membrane and the temporal features of motion of the same reporter molecules, now labeled with fluorescent quantum dots, moving in living cell membranes using fluorescence microscopy (FM).
The cell membrane is far too complex to model the motion from first principles using currently available tools. We therefore focus on phenomenological models, that is, models that reproduce the clustering phenomena in the static data and the motion seen in the dynamic data. We first develop models that ``appear to the eye' to be reasonable. We then use a powerful set of statistical tools to make a detailed comparison between the model and the data. In future work, we will attempt to use the phenomenological models to pinpoint the important aspects of the membrane organization that affect the motion of the receptor.
We focus on the FcepsilonRI (high affinity IgER) receptor that is expressed on circulating blood basophils and tissue mast cells and mediates allergic responses. Briefly, for the IgE receptor to create a signal, its alpha subunit first must bind to an IgE molecule with specificity for an allergen. In life, this specificity can be to cat dander, juniper, ragweed and many other environmental agents. The key feature of the allergen is that it must be at least bivalent. Most antigens are highly multivalent including common pollens and also the engineered laboratory allergen, DNPn-BSA (where n refers to the number of DNP molecules attached to a single molecule of bovine serum albumin, a common protein). The multivalency ensures that a single allergen will bind to two or more receptors, creating dimers or higher oligomers on the cell surface. Under moderate to strong stimulation, signaling complexes consist of from a few to a hundred or more receptor molecules in a cluster. It is clear that the clusters are dynamic, that is, non-crosslinked receptors and other membrane-associated molecules may enter a cluster and then leave in short periods of time.
A strong reason for studying FcepsilonRI is that the static organization of the receptors has been studied extensively, while the dynamics have been more recently studied using quantum-dot particle tracking techniques on the extracellular part of the receptor. However, the data sets have not been integrated for a comprehensive dynamic model of spatiotemporal organization of the membrane during signal initiation. Our models will help to accomplish this.
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| Seminar: How Black Holes Get Together |
| Speaker Name: Dr. Cole Miller (University of Maryland) |
| Date: Friday, 09/19/08 |
| Time: 12:00 p.m. - 12:50 p.m. |
| Room: 78-2015 |
Abstract: From the standpoint of fundamental physics, black holes with
the same spin parameter are the same regardless of their mass.
Astrophysically, however, the environments of black holes do
depend on their mass, hence so do the properties of mergers
between black holes. I will discuss the likely properties
of mergers as a function of mass, with particular emphasis on
eccentricities and spins. I will also present several currently
open questions about the astrophysics of black hole coalescence.
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| Seminar: Dynamics and Morphologies of a Dewetting Ultrathin Solid Film (Colloquium) |
| Speaker Name: Dr. Mikhail Khenner (SUNY Buffalo) |
| Date: Thursday, 05/22/08 |
| Time: 2:00 p.m. - 2:50 p.m. |
| Room: 08-2130 |
Abstract: Dewetting of lattice-matched ultrathin solid films such as the sub-10 nm Si film on the SiO2 substrate was recently observed in experiments at temperatures around 800 C. The cause for film dewetting is a long-range, attractive film-substrate interaction (also called wetting interaction) which amplifies perturbations of the planar film surface and makes the film height decrease locally until the surface touches the substrate, resulting in the formation of an array of islands (quantum dots). At this most general level of description, dewetting of solid films is similar to well-studied dewetting of liquid films, the only difference is the nature of the mass transport, i.e. the thermally activated surface diffusion of adatoms in the former case vs. the fluid flow in the latter case. There are, however, two determinative reasons of as to why the dynamics of dewetting in these systems is qualitatively different. One reason is the nonzero (and generally, strong) anisotropy of the solid film surface energy (tension) which is not present in liquids. This anisotropy causes faceting of the surface which opposes the tendency to dewet. Another reason is "geometrical," meaning that a planar surface of the as-deposited solid film may feature local defects of arbitrary shape protruding arbitrarily deep into the film (i.e., the pinholes). Since the attractive substrate potential decreases with the film height, its influence is stronger on deep pinholes, which therefore dewet faster.
In this talk I will describe new, PDE-based models for studying the dynamics of a pinhole for the varying initial depth of a pinhole and the strengths of the potential and the surface energy anisotropy. Results of the simulations demonstrate how the corresponding parameters may lead to complete or partial dewetting of the film.
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| Seminar: Types of linear chaos: a geometric approach (Colloquium) |
| Speaker Name: Dr. Gabriel Prajitura (SUNY Brockport) |
| Date: Friday, 05/09/08 |
| Time: 1:00 p.m. - 1:50 p.m. |
| Room: 08-2130 |
Abstract: We will discuss about hypercyclic linear operators in Hilbert spaces and will provide several descriptions of the geometric behavior of orbits.
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| Seminar: Multiple Intelligences & the College Mathematics Classroom (Conversations in Mathematics) |
| Speaker Name: Dr. Carol Marchetti (RIT School of Mathematical Sciences) |
| Date: Wednesday, 05/07/08 |
| Time: 1:00 p.m. - 1:50 p.m. |
| Room: 08-2130 |
Abstract: Howard Gardner introduced the theory of Multiple Intelligences in 1983. Since then, many teachers have expanded their teaching tools through this theory. The Teaching for Understanding Project, based at the Harvard Graduate School of Education, provides a framework for planning and teaching that is well-suited for multiple intelligence theory. An introduction to Multiple Intelligences and the Teaching for Understanding framework will be provided. Come listen, bring your own ideas, and share in the discussion on how multiple intelligences could be implemented in a college mathematics classroom.
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| Seminar: Fractal-based Methods in Imaging and Analysis (Colloquium) |
| Speaker Name: Dr. Herb Kunze (University of Guelph) |
| Date: Wednesday, 04/30/08 |
| Time: 12:00 p.m. - 12:50 p.m. |
| Room: 08-2130 |
Abstract: Both the philosophy and the basic concepts of fractal analysis have led to the development of various ideas in (i) the production of fascinating and marvelously colored images, (ii) the representation and processing of digital pictures, and (iii) a remarkable collection of frameworks for the solution of a wide array of inverse problems in differential equations (ordinary, partial, delay, random, stochastic).
In this talk, we first embark on a quick stroll through some basic concepts, ending with the fundamental idea that a hyperbolic iterated function system (IFS) has a unique fixed point. More leisurely, we talk about the recently developed extensions of such ideas to iterated multi-function systems (IMSs), and we also discuss "color stealing." The latter idea is a novel way of using the connected dynamics of two different IFSs to produce interesting colored images, with applications to computer graphics and gaming, information hiding and image encryption.
Next, we talk about the basic framework of fractal imaging. While the original goal of fractal imaging was image compression, we discuss ideas related to image watermarking, denoising, recovery, and prospects for edge detection algorithms.
Finally, we will see how related ideas have led to the development of frameworks for the solution of inverse problems in differential equations. A few topics of current interest and activity are highlighted.
Throughout the talk, we will use computer programs, images, and animations to illustrate the results.
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| Seminar: Riemannian Flag Manifolds with Homogeneous Geodesics (Colloquium) |
| Speaker Name: Dr. Andreas Arvanitoyeorgos (University of Patras, Greece) |
| Date: Wednesday, 04/23/08 |
| Time: 12:00 p.m. - 12:50 p.m. |
| Room: 08-2130 |
Abstract: A geodesic in a Riemannian homogeneous manifold (M=G/K, g) is called a homogeneous geodesic if it is an orbit of a one-parameter subgroup of the Lie group G. In this joint work with D.V. Alekseevsky we investigate G-invariant metrics with homogeneous geodesics (i.e. such that all geodesics are homogeneous) when M=G/K is a flag manifold, that is an adjoint orbit of a compact semisimple Lie group G. We use an important invariant of a flag manifold M=G/K, its T-root system, to give a simple necessary condition that M admits a non-standard G-invariant metric with homogeneous geodesics. Hence, the problem reduces substantially to the study of a short list of prospective flag manifolds.
A common feature of these spaces is that their isotropy representation has two irreducible components. We prove that among all flag manifolds M=G.H of a simple Lie group G, only the manifold SO(m +1)/U(m) of complex structures in R(2m+2) and the complex projective space Sp(m)/U(1).Sp(m-1) admit a non-naturally reductive invariant metric with homogeneous geodesics. In all other cases the only G-invariant metric with homogeneous geodesics is the metric which is homothetic to the standard metric (i.e. the metric associated to the negative of the Killing form of the Lie algebra of G). We also find explicitly homogeneous geodesics in some examples of flag manifolds.
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| Seminar: Total Variation Minimization and Graph-cuts (Colloquium) |
| Speaker Name: Dr. Jerome Darbon (UCLA) |
| Date: Thursday, 04/10/08 |
| Time: 12:00 p.m. - 12:50 p.m. |
| Room: 08-1154 |
Abstract: The minimization of the variation with convex data fidelity terms is considered both from a continuous and a discrete point of view. I'll briefly review existing minimization algorithms, and in particular the best one which is the parametric maximum-flow. Then I'll show how one can use it to efficiently perform crystalline mean curvature flow, solve deconvolution and compressive sensing problems via TV minimizations.
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| Seminar: How Can I Say that A "Toy Model" Reminds Me of My Observations? A Dynamical Systems Perspective of Modeling (Colloquium) |
| Speaker Name: Dr. Erik Bolt (Clarkson University) |
| Date: Wednesday, 04/09/08 |
| Time: 12:00 p.m. - 12:50 p.m. |
| Room: 08-2130 |
Abstract: We address a fundamental modeling issue in science as related to the field of dynamical systems: when is a model of a physical system a "good" representation? Conjugacy provides a means to define if two systems are dynamically equivalent; it is the central equivalence relationship in the field of dynamical systems. However, it cannot cope with systems which are not dynamically identical. What then to do with the common scientific practice of modeling, whereby we build heuristic and phenomenological models which "remind" us of the true system?
We develop mathematical technology to decide when dynamics of a toy model are like dynamics of the physical system, since the concept of conjugacy is too rigid for such cases. When applied to non-conjugate dynamical systems, we show that a fixed point iteration scheme yields a limit point, that is a function we call a "commuter" --- a non-homeomorphic change of coordinates translating between dissimilar systems. This translation is natural to the concepts of dynamical systems in that it matches systems within the language of their orbit structures. We introduce methods to compare nonequivalent systems by quantifying how much the commuter function fails to be a homeomorphism, an approach that better respects the dynamics than the traditional comparisons based on normed linear spaces. Our discussion addresses a fundamental issue --- how does one make principled statements of the degree to which a "toy model" might be representative of a more complicated system. We highlight our methods with a lower-ordered model of a "noisy" logistic map and also a simplified model of a Lorenz system such that the usual one-dimensional map model is not exactly justified in the traditional sense.
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| Seminar: Computing Pi (Colloquium) |
| Speaker Name: David and Gregory Chudnovsky (Polytechnic University of New York) |
| Date: Wednesday, 04/09/08 |
| Time: 2:30 p.m. - 3:30 p.m. |
| Room: 08-1300 |
Abstract: "The Chudnovsky brothers have held records, at different times, for computing Pi to the largest number of places, including two billion digits in the early 1990s on a supercomputer they built (dubbed 'm-zero') in their apartment in Manhattan. In 1987, the Chudnovsky brothers developed the algorithm that they used to break several Pi computation records. Today, this algorithm is used by Mathematica to calculate Pi."
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| Seminar: Applications of Knot Theory to Biology, Chemistry and Physics (Colloquium) |
| Speaker Name: Dr. Joel Zablow (RIT School of Mathematical Sciences) |
| Date: Wednesday, 04/02/08 |
| Time: 12:00 p.m. - 12:50 p.m. |
| Room: 08-2130 |
Abstract: We will go over some of the ideas discussed in the AMS short course this past January, on applications of knot theory, to biology, chemistry and physics. After some generalities on knots, we look at applications, particularly to the notion of chirality of molecules in chemistry, and toward a mathematical understanding of DNA and its properties, and some techniques in use. Finally, we look at connections between knot polynomials and certain models in statistical mechanics, by way of some graph theory. TBA
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| Seminar: Developing materials for on-line courses (Conversations in Mathematics) |
| Speaker Name: Dr. Richard Fasse (RIT On-line Learning) |
| Date: Wednesday, 03/26/08 |
| Time: 1:00 p.m. - 1:50 p.m. |
| Room: 08-2130 |
Abstract: Not available
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| Seminar: TBA (Colloquium) |
| Speaker Name: Dr. Herb Kunze (University of Guelph) |
| Date: Friday, 02/29/08 |
| Time: 12:00 p.m. - 12:50 p.m. |
| Room: -TBA |
Abstract: TBA
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| Seminar: Exploring black holes using gravitational waves (CCRG Invited Speaker) |
| Speaker Name: Dr. Badri Krishnan (Albert Einstein Institut) |
| Date: Wednesday, 02/29/08 |
| Time: 11:00 a.m. - 11:50 a.m. |
| Room: 78-2015 |
Abstract: Not available
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| Seminar: Compact object binaries: stellar and binary evolution in the gravitational wave era (CCRG Invited Speaker) |
| Speaker Name: Dr. Bart Willems (Northwestern University) |
| Date: Friday, 02/22/08 |
| Time: 10:00 a.m. - 10:50 a.m. |
| Room: 08-2015 |
Abstract: The construction and planning of ground- and space-based laser interferometers has led to a massive surge of interest in sources of gravitational wave radiation during the past decade. Direct detection of these ripples in space-time will provide unprecedented tests of Einsteins theory of general relativity and open a brand new window on the universe unhindered by the main obstacles affecting electromagnetic radiation. Among the rich set of anticipated gravitational wave sources, binary star systems made up of compact remnants of stellar evolution are expected to be the most numerous class of gravitationally radiating objects. In this colloquium, I will look into the future and discuss the physics that will become accessible with the launch of the Laser Interferometer Space Antenna (LISA), the most ambitious gravitational wave observatory planned to date. I will particularly focus on binary star systems consisting of one or two white dwarfs, the evolutionary endpoints of more than 90% of the stars in the galaxy (including the Sun). Recent theoretical advances and observations by the Spitzer infrared space telescope show that the formation of circumbinary disks during mass-transfer episodes between the binary components can drastically affect the binary evolution, potentially resolving longstanding problems and raising questions about neutron star and black hole binary formation. I will also show the unique opportunity offered by globular clusters and LISA to unveil white dwarf physics with LISA inaccessible through electromagnetic observation.
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| Seminar: Osteoporosis: A Mathematical Perspective (Colloquium) |
| Speaker Name: Dr. Antonio Cabal (Merck Research Laboratories) |
| Date: Wednesday, 02/20/08 |
| Time: 12:00 p.m. - 12:50 p.m. |
| Room: 08-2130 |
Abstract: Osteoporosis is a common age related chronic disorder of the skeleton that constitutes a considerable public health problem. Some estimates of the number of Americans affected by osteoporosis are as high as 15 million, and another 30 million are thought to have osteopenia, a precursor condition describing the disease. The purpose of my talk is to present an overview of osteoporosis. I will give you a quick tour of the bone remodeling process and of the fundamental elements involve in determining bone strength in vivo. The take home message of the talk will be for the audience to understand why mathematics is playing an increasingly relevant role in the research, diagnosis, and monitoring of osteoporosis.
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| Seminar: Random Scattering in Industrial Mathematics (Colloquium) |
| Speaker Name: Dr. Peter Castro (SMS Advisory Board) |
| Date: Wednesday, 01/30/08 |
| Time: 12:00 p.m. - 12:50 p.m. |
| Room: -TBA |
Abstract: Light scatter in random media is an old, vexing problem. I will present a model of light scatter developed in an industrial context, illustrating both theoretical and numerical aspects of modeling in industry.
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| Seminar: The Butterfly Effect: An Interesting Motivation to Curve Sketching (Conversations in Mathemtatics) |
| Speaker Name: Dr. Alejandro Engel (RIT School of Mathematical Sciences) |
| Date: Wednesday, 01/30/08 |
| Time: 1:00 p.m. - 1:50 p.m. |
| Room: 08-2154 |
Abstract: Enticing students with an illustration that relates to their non-academic life is a sure way to get their attention and have them make an extra effort to understand the material that one wants to present. The Butterfly Effect is a cult movie that most students have enjoyed and for them to see the root of the idea is very appealing, so this title and the (mathematical) history of it is a good motivator. The fact that a minute change in a parameter can derive in a large change in the behavior of the function will be illustrated in terms of sketching rational functions.
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| Seminar: What To Do When Associativity Fails (Curiosity Seminar) |
| Speaker Name: Dr. Manny Lopez (RIT School of Mathematical Sciences) |
| Date: Wednesday, 01/23/08 |
| Time: 2:00 p.m. - 2:50 p.m. |
| Room: 08-2130 |
Abstract: The traditional approach to dealing with lack of associativity will be presented using the Moufang Equalities as an example. This approach has produced some very respectable algebraic constructs. However, this won't stop us from trying to find fault in it. We'll propose a different point of view in dealing with a non-associative structure and offer a possible way to implement a solution according to this point of view. The implementation is in terms of Category Theory to be applicable in a variety of mathematical contexts.
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| Seminar: The Final Spin of Black Hole Binaries (CCRG invited speaker) |
| Speaker Name: Dr. Erik Schnetter (LSU & AEI) |
| Date: Friday, 01/18/08 |
| Time: 2:00 p.m. - 2:50 p.m. |
| Room: 78-2230 |
Abstract: The evolution from the initial to the final state of a generic binary black hole system can be viewed as black box, with just a few input and output parameters such as masses and spins. Combining a series of numerical simulations and certain reasonable assumptions, I derive accurate analytic expressions describing the final state after the merger process, for the common case of aligned spins and non- eccentric orbits. These results required a substantial amount of large-scale numerical calculations, and I will also give an overview over the current state and future directions of our computational infrastructure which made this work possible.
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