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| Date/Time | Speaker | Title/Abstract |
|---|---|---|
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Thursday September 27, 2001 3:30 PM in ILB 370 |
John Cruthirds
University of South Alabama |
Mathematical Modeling of the Food Supply for Long-Term Space Missions |
| Abstract: The quantitative analysis of the food plan for long-term space missions is a crucial factor for the comparison of different food plans and for the evaluation of the food plan as part of the overall mission. Such analysis should include important factors such as nutrition, palatability, diet cycle length, and psychological issues related to food. This talk will describe the details of a mathematical model that has been developed which includes these four components. Additionally, an overview of the overall modeling problem for the type of closed system necessary for a possible trip to Mars will be given. The current model is compatible with the Equivalent System Mass (ESM) metric previously developed as the Advance Life Support (ALS) Research and Technology Metric that has been used to compare technology options in terms of their mass, volume, power, cooling and crew time requirements. Traditionally, the ESM metric evaluation of the food plan has not fully considered the important aspects of nutrition, palatability, diet cycle length, and the psychological benefits of including fresh food items in the diet. | ||
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Thursday October 4, 2001 3:30 PM in ILB 370 |
Lucian V. Boiculese
University of Medicine and Pharmacy "Gr.T.Popa" Iasi, Romania |
Medical Inference Using Neuro-Fuzzy Methods |
| Abstract: Neural networks and fuzzy systems were developed as a necessity to find new methods for solving medical, technical and economic problems. Fuzzy systems represent a tool for modeling intermediate grades of belonging that occur in almost all real situations. They have much in common with expert systems, as the inference is based on firing rules. This is a reason for which fuzzy systems are suitable for medical applications. Neural networks were developed based on the biological neuron potential. The aims of these systems are to simulate the brain function, and also to realize logic systems, that cope with problems of real life. One of the most important benefits of neural networks is the capacity of learning from examples. To help physicians in their services, intelligent systems that realize automatic classifications, control and even deduce the diagnosis must be realized. | ||
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Monday October 8, 2001 3:30 PM in ILB 370 |
Dan Nakano
University of Georgia |
Nilpotent matrices, support varieties and the Jantzen conjecture |
| Abstract: The variety of nilpotent matrices for a Lie algebra g has played an important role in studying the representation theory of g. In this talk I will show how support varieties (varieties associated to modules) for Weyl modules can be computed using conjugacy classes of nilpotent matrices. The results presented at the end of the talk verify a conjecture made by Jantzen in 1987. This is joint work with Brian Parshall and David Vella. | ||
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Thursday October 11, 2001 3:30 PM in ILB 370 |
Eric Loomis
Department of Philosophy, University of South Alabama |
Is the Logic of Arithmetic First- or Second-Order? |
| Abstract: The philosophers George Boolos and Stuart Shapiro have argued in recent years that second order logic is a better candidate for the logic that underlies Peano Arithmetic than is first-order logic, arguing that second-order logic possesses a number of advantages that outweigh the absence of a completeness proof for it. I will summarize this debate, and then argue that if the debate between first- and second-order advocates is taken to be one about the reasoning implicit in understanding elementary arithmetic, then the disjunction between these two alternatives constitutes a false dilemma. My talk will conclude with a proposal for providing a course in first-order metatheory at U.S.A. | ||
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Thursday October 18, 2001 3:30 PM in ILB 370 |
Igor Mineyev
University of South Alabama |
Hyperbolic groups, bounded cohomology, and the Baum-Connes conjecture |
| Abstract: First we will discuss hyperbolic groups introduced by M. Gromov, and some of their properties. We show that hyperbolic groups can be characterized by bounded cohomology. The main step in the proof is a combinatorial version of straightening that works for any hyperbolic group. As another application of those combinatorial techniques, we construct a nice metric on any hyperbolic group that allows proving the Baum-Connes conjecture for hyperbolic groups (this is a joint work with Guoliang Yu). In particular, this implies the Kadison-Kaplansky conjecture for torsion-free hyperbolic groups. | ||
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Thursday November 1, 2001 3:30 PM in ILB 370 |
Ding Jiu
University of Southern Mississippi, Hattiesburg, MS. |
Generalized inverses and perturbation theory of linear operators |
| Abstract: We introduce the concept of generalized inverses for matrices and bounded linear operators with some historical remarks. Then we generalize a classic perturbation theorem for invertible operators to arbitrary operators. If time permits, we'll present some new perturbation results for least squares problems. | ||
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Thursday November 8, 2001 3:30 PM in ILB 370 |
Dan Silver
University of South Alabama |
On Virtual Knots |
| Abstract:
In 1876 the Scottish physicist Peter Guthrie Tait published "On
Knots," the first
paper with the word knots in its title. Tait had no rigorous mathematical
tools as he began
the new subject, only keen intuition and the encouragement of some of the
greatest scientists
of the day, Lord Kelvin and James Clerk Maxwell. Today knot theory is a
sophisticated area
that draws on nearly every area of mathematics for its tools.
Several years ago Louis Kauffman introduced a new sort of knot which he termed "virtual." Virtual knots, which are purely combinatorial in nature, force us to rethink everything that we know about knots in general. Elementary open questions abound in this subject. Conjectures that at first seem so obvious turn out to be maddeningly just out of reach. We survey virtual knot theory and begin to understand how Peter Guthrie Tait felt. My soul's an amphicheiral knot Upon a liquid vortex wrought By Intellect in the Unseen residing, While thou dost like a convict sit With marlinspike untwisting it Only to find my knottiness abiding, Since all the tools for my untying In four-dimensioned space are lying, Where playful fancy intersperses Whole avenues of universes, Where Klein and Clifford fill the void With one unbounded, finite homoloid, Whereby the infinite is hopelessly destroyed. First stanza of poem by James Clerk Maxwell Students are encouraged to attend. |
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Thursday January 17, 2002 2 PM in ILB 370 Math/Stat Club Presentation |
Robert L. Taylor
Department of Statistics University of Georgia |
Graduate Work and Career Opportunities in Statistics |
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Thursday January 17, 2002 3:30 PM in ILB 370 |
Robert L. Taylor
Department of Statistics University of Georgia |
A Survey Talk on Limit Theorems for Negatively Dependent Random Variables |
| Abstract: Independence has been a common assumption for most of the basic results in probability and statistics as illustrated by the classical laws of large numbers and central limit theorems. Increasing attention has developed in recent years in obtaining more realistic and applicable models where alternatives to the assumption of independence are considered. Negative dependence is one alternative to the usual assumption of independence. This talk will be a survey of recent laws of large numbers and central limit theorems for negatively dependence random variables. The classical results for independent random variables will be used a template for comparisons of results for negatively dependent random variables, and examples will be provided to illustrate the differences in the results as well as the sharpness of the results. | ||
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Thursday February 28, 2002 3:30 PM in ILB 140 Reception following the presentation |
Karen Parshall
Professor of History and Mathematics University of Virginia |
The Mathematical Legacy of James Joseph Sylvester (1814 -1897) |
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Friday March 1, 2002 3:30 PM in ILB 370 |
Brian Parshall
Professor of Mathematics University of Virginia |
Attaching algebraic varieties to representations |
| Abstract: There are several natural ways in which an algebraic variety can be attached to a representation. These arise in the representation theory of Lie algebras, finite and algebraic groups, etc. Often the varieties themselves are natural and interesting, and representation theory can be used to study them. In some cases, the varieties are known in advance, while the appropiate representation theory remains to be studied. We will discuss some examples of this. (Part of this work represents joint work with Terrell Hodge.) | ||
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Saturday March 2, 2002 7:30 PM at the Ahavas Chesed Synagogue 705 Regents Way, Mobile Reception following the presentation |
Karen Parshall
Professor of History and Mathematics University of Virginia |
To Be a Jewish Mathematician: J.J. Sylvester in Victorian Britain and the United States |
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Thursday March 7, 2002 3:30 PM in ILB 370 |
Underwood Dudley
DePauw University |
Formulas for Primes |
| Abstract: Formulas are fascinating and so are primes, so formulas for primes should be fascination squared, or at least doubled. I will give a survey of the field and end with a moral message. Exactly one theorem will be proved. | ||
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Monday March 25, 2002 3:30 PM in ILB 370 |
Pantelimon Stanica
Auburn University at Montgomery |
Squarefree Catalan Numbers and Residues of Products of Factorials in Z_p |
| Abstract: Erdos conjectured that binomial{2n,n} is not squarefree for n>4. This was proved by Sarkozy (for sufficiently large n) and by Granville and Ramare for any n. We prove that the same is true for generalized Catalan numbers. In addition it is known that about p/e classes in Z_p are covered by factorials. What can be said about products of factorials. Will they cover all classes? We plan to give an answer to this question, as well. | ||
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Monday March 25, 2002 7:00 pm in ILB 405 Mobile Mathematics Circle Lecture Sponsored by the Alabama Space Consortium |
Pantelimon Stanica
Auburn University Montgomery |
"If everything else fails, generalize!" |
| Abstract: The natural order in the human learning is from particular to general. However, in mathematics, often the general case is easier to solve than a particular one. The motivation behind this approach is rather simple: the particular case contains information which is not relevant, tempting the solver to give more importance to it, thereby making the proof difficult; also, the general case enables you to get in an area of mathematics, where better tools are available. In this talk, we will present various elementary problems that are easily solvable if one considers a generalization. | ||
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Thursday March 28, 2002 8AM - 5PM, ILB Room 370. |
Bryan Manly, D.Sc.
EcoSystem, Laramie, Wyoming |
A Workshop on Statistical Ecology |
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This is a workshop covering a variety of topics in the areas of ecology and environmental science at a level that is suitable for scientists with a good quantitative background working in these areas. Biometricians and statisticians should also find it of interest if they are not already familiar with the topics covered.
Workshop Contents 8:00 Registration and welcome 8:15 Introduction to the workshop 8:30 Module 1: Resource Selection by Animals. This will cover some of the most important aspects of this topic as approached through the estimation of resource selection functions. Estimation of these functions through the use of logistic regression and its generalizations will receive particular attention. 9:15 Break 9:30 Module 1, continued. 10:45 Break 11:00 Module 2: Some Methods for Estimating Animal Population Sizes. This will include a brief review of methods such as mark-recapture, line transect sampling, and stratified quadrat sampling. Special consideration will be given to the method of adaptive stratified sampling and its use for surveys involving estimating the size of several populations at the same time. 12:30 Lunch break 14:00 Module 3: Computer Intensive Methods. After briefly describing the methods of bootstrapping and randomization, some applications in ecology and environmental science will be described. 15:15 Break 15:30 Module 4: The Behrens-Fisher Problem and its Generalizations. In ecology and environmental science it is common for data to have highly non-normal distributions, with variances possibly differing for samples collected under different conditions. A randomization based approach to comparing sample mean values under these circumstances will be discussed, and also a testing scheme that results in one of the conclusions that (a) sample means differ significantly but not variances, (b) sample variances differ significantly but not means, (c) sample means and variances differ significantly, (d) sample means and variances do not differ significantly, or (e) sample means and/or variances differ significantly but it is not possible to say more than that. 17:00 End of workshop |
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Thursday April 4, 2002 3:30 PM in ILB 140 |
Dick Termes
Artist |
Special Presentation by the Artist |
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Monday April 8, 2002 7:00 pm in ILB 405 Mobile Mathematics Circle Lecture Sponsored by the Alabama Space Consortium |
Philip Kutzko
University of Iowa |
The Chinese Remainder Theorem: A modern look at some ancient Chinese mathematics. |
| Abstract:
Suppose that I tell you that I am thinking about a number between one and one hundred
and I also tell you that:
If you divide the number I am thinking about by 3, you get a remainder of 1. If you divide the number I am thinking about by 5, you get a remainder of 4. If you divide the number I am thinking about by 7, you get a remainder of 1. Can you tell me the number? What if I start with another number and again tell you the remainders when I divide by 3, 5 and 7? Can you figure out a method that will always enable you to find the number when I tell you the remainders? The solution to this problem, finding a number when you know the remainders you get when you divide by certain numbers, was known to the ancient Chinese, who used it to determine certain of their religious holidays. (Think about how you can predict when the next Friday the Thirteenth will occur.) In this talk, I am going to explain the way in which the Chinese went about solving this problem and I am also going to explain how the ideas they used can be applied to other problems that seem, at first, to have nothing to do with division and remainders. My hope is that you will see that doing math is only sometimes about thinking up new ideas -- sometimes it is about using old ideas in new and unexpected ways. |
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Thursday April 11, 2002 3:30 PM in ILB 370 |
George McNinch
University of Notre Dame |
Simple algebraic groups and reduction mod p |
| Abstract:
The compact Lie groups, or complex semisimple Lie groups,
have algebraic analogues which make sense (thanks to Chevalley) over
any field k. Examples include familiar linear groups, e.g. the group
SL(n,k) of n-by-n determinant one matrices with coefficients in k.
Especially interesting is the case where k is a finite field: according to the classification theorem, the resulting "finite Lie type groups", together with the alternating groups and a handful of sporadic groups, account for all of the non-abelian finite simple groups. To study a finite group of Lie type G(k), it is often useful to regard it as the group of k-rational points of an algebraic group G over an algebraic closure of k; such algebraic groups are the "algebro geometric" analogue of Lie groups. The talk will discuss some results concerning conjugacy classes and subgroups of a simple algebraic group G. Many results which are valid for complex semisimple Lie groups remain valid for G; for example (with mild restrictions on the characteristic) the classification of nilpotent orbits in the Lie algebra is independent of the field. We will focus on results in characteristic p>0 which are deduced from corresponding results for complex Lie groups by "reduction mod p". |
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Monday April 22, 2002 3:30 PM in ILB 370 |
Eddie Cheng
Department of Mathematics Oakland University |
Time-Stamped Graphs and Their Associated Influence Digraphs |
| Abstract: Consider the research collaboration (multi)graph C, in which the vertices are mathematicians (or other researchers), and there is an undirected edge joining two mathematicians for each joint paper they have published, with or without other coauthors. Thus, for instance, there are 20 edges between Paul Erdös and Ernst Straus, based on their numerous collaborations from 1953 to 1983; and there are three edges joining Straus and Albert Einstein shows these joint articles in the mid-1940s. There is no edge, however, between Erdös and Einstein. If we make the simplifying assumption that the interaction between researchers takes place instantaneously, say at the moment a paper is finished, then we can assign a time-stamp to each edge. From this we see that Einstein may have influenced the thinking of Erdös, since Straus already bore the former's imprint when he worked with the latter, but not conversely. Therefore, if we construct the associated influence digraph CI on the same vertex set as C, then we would find arcs from Einstein, Straus, and Erdös to each of the others except for the arc (Erdös, Einstein). Of course, it is possible that Erös influenced Einstein through some longer time-increasing string of collaborations, but we know of none. More formally, a time-stamped graph is an undirected graph with a real number on each edge. Vertex u influences vertex v if there is a non-decreasing path from u to v. The associated influence digraph of a time-stamped graph is the directed graph that records the influences. Among other results, we present for what n and t there exists a time-stamped graph whose associated influence digraph has n vertices and t arcs. We also investigate the minimum number of vertices a graph can have so that a given digraph is an induced subgraph of its associated influence digraph. A number of other questions are also explored. (Joint work with Marc J. Lipman and Jerrold W. Grossman.) | ||
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Monday April 22, 2002 7:00 PM in ILB 370 Mobile Mathematics Circle Lecture Sponsored by the Alabama Space Consortium |
Eddie Cheng
Department of Mathematics Oakland University |
Be Greedy |
| Abstract: Many operational problems such as scheduling problems require the manager to look for optimal solutions (MORE services, LESS money.) These types of problems are usually very difficult. For example, the airline industries spend a lot of money to find better schedules in order to improve the bottom line. However a simple procedure called greedy algorithm will give an optimal solution for certain special optimization problems. For other problems, it may give us a good solution (but not the best). In this talk, we will look at examples of these types of problems. | ||
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Department of Mathematics and Statistics |
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