| Date: | January 14 (Monday) |
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| Speaker: | Gary Walsh (CSE and University of Ottawa) |
| Title: | TBA |
| Date: | February 12, 2007 (Monday) |
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| Speaker: | Karen Chandler (Illinois) |
| Title: | Multiple conjectures and multible theorems on multiple points. |
| Abstract: | (to view the abstract, click here ) |
| Local host: | Karl Dilcher |
| Date: | March 5, 2007 (Monday) |
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| Speaker: | Neil Calkin (Clemson University) |
| Title: | Clemson's Research Experience for Undergraduates (REU) |
| Abstract: | I'll discuss Clemson's REU in mathematics, describing the program, our philosophies and implementation, and discuss some of the research projects undertaking, including parallel algorithms for computing (large) partition numbers, analyzing the Quadratic Sieve factorization algorithm, and discovering and proving new Ramanujan-type identities for restricted partition functions. This is joint work with Kevin James. |
| Local host: | Jon Borwein/Karl Dilcher |
| Date: | March 12, 2007 (Monday) |
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| Speaker: | Dan Goldston (San Jose State University) |
| Title: | Are there infinitely many twin primes? |
| Abstract: | This lecture given on April 6, 2006 at Cornell as the first lecture in the Chelluri Lecture Series in memory of Thyagaraju (Raju) Chelluri will be presented in our Colloquium Series as a DVD movie. To view the abstract and acquire more information on the Chelluri Lecture Series at Cornell, click here |
| Local organizers: | Alan Coley/Karl Dilcher |
| Date: | March 26, 2007 (Monday) |
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| Speaker: | Mikhail Kotchetov (Memorial University of Newfoundland) |
| Title: | Group gradings on simple Lie algebras |
| Abstract: | Group gradings on algebras, especially simple algebras, have been extensively studied since the 1960s. In particular, gradings on Lie algebras arise in the theory of symmetric spaces, Kac-Moody algebras, and Lie coloralgebras. In the context of simple Lie algebras, it suffices to consider only gradings by abelian groups (since the support of any grading generates an abelian group). V. Kac classified all gradings by cyclic groups on finite-dimensional simple Lie algebras in 1968. We will discuss recent progress in the classification of gradings on finite-dimensional simple Lie algebras by arbitrary abelian groups. |
| Local host: | Roman Smirnov |
| Date: | April 2, 2007 (Monday) |
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| Speaker: | Aaron Lauve (UQAM) |
| Title: | Questions concerning sums and products of matrices (with answers!) |
| Abstract: | If the greatness of a theorem is measured by its simplicity to state and the number of fields utilized to solve it, the resolution of Horn's Conjecture surely deserves Fermat-Wiles type billing. The problem: "given square matrices A,B and their eigenvalues, what do you know a priori about the eigenvalues of A+B?" The majority of my talk will be devoted to a gentle survey of the problem's history and surprising resolution---ultimately requiring a great deal more combinatorics than matrix analysis. In the waning minutes I address some variations on the theme, each also appealing to combinatorial gadgets to reach a solution: the Deligne-Simpson problem, a characteristic polynomial identity of Amitsur, and a work in progress. |
| Local hosts: | Kia Dalili/Sara Faridi |
| Date: | April 16, 2007 (Monday) |
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| Speaker: | Karl Dilcher (Dalhousie) |
| Title: | Euler, the master of us all |
| Abstract: | April 15 marks the 300th anniversary of the birth of Leonhard Euler, one of the greatest, most prolific, and most influential mathematicians in history. In this talk I will give a biographical sketch, and will try to put the various stages of Euler's life into a historical and academic perspective. I will say nothing, or very little, about Euler's mathematics. This will be left to a larger event, or events, being planned for later this year. |
| Local hosts: | S. Swaminathan |
| Date: | May 14, 2007 (Monday) |
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| Speaker: | John Cosgrave (St. Patrick's College, Dublin) |
| Title: | Gauss-4 primes: a (beautiful) new sequence of primes |
| Abstract: | In this talk (which will be understood by everyone - and that's a bet!) I introduce what I believe to be a new sequence of primes, one which I wish to call the Gauss-4 primes. Incidentally, every Fermat prime from 5 onwards is such a prime. You will not (yet) find that sequence in Sloane's well-known (and quite remarkable) On-Line Encyclopedia of Integer Sequences (check it out at www.research.att.com/~njas/sequences/). This sequence emerges in a most natural way from my recent wide-ranging work in connection with extending Gauss' generalisation of Wilson's theorem (if you don't already know what that is, then do not worry, for I shall explain it). The Gauss-4 primes begin: 5, 17 , 97, 193, 241 , 257, 641, 929, 3361 , 12289, 46817 , 65537, 114689, 120833, 285697, 345089, 652081, 786433, 1179649, 1908737, 3200257, 11118593, 27590657, 200578817, 2742091777, 8780414977, 10812547073, 12055618177 , ... The Gauss-4 primes occur at 'levels' (I shall explain what that means in my talk) 0, 4, 5, 6, 7, ... (5, by the way, is the only Gauss- level 0 prime, and there are none at levels 1, 2, 3), and I mention that the primes in bold are those at level 4 (now if you enter that subsequence in Sloane you will find that the first five do correspond to an entry... but then immediately diverge... there is much to be said about this...). The next several Gauss-4 level 4 primes - which could never have been found by direct systematic computation alone (since they involve massive factorial based modular reductions) - have 150, 229, 339, 401, 594, 806, 1088, 6404, 7645, 8517, 10038, 10051, 13230 and 14280 decimal digits, and are completely characterised by certain solutions of a single Fermat-Pell equation. The Gauss-4 primes 120833, 262337, 285697, 345089 (for example), do not appear in any sequence in Sloane's Encyclopedia. These primes have very beautiful properties, but, to find out what those properties are, you will have to attend... The background to my recent work is in the public domain, with my fortuitous discovery in December 2004 of what I have called 'Jacobi primes' (you will not find those in Sloane either). Andrew Granville played an invaluable part in connection with proofs. You might wish to read in advance of my Dalhousie colloquium talk, my February 2005 Jacobi-primes, Maple-based, Trinity College Dublin Student Mathematics Society talk at my web site. It is available in both Maple or html format at www.spd.dcu.ie/johnbcos/jacobi.htm. An extended version of this talk in the Maple format, can be downloaded here .(to view, download and save the file locally and then use Maple to open it.) |
| Local host: | Karl Dilcher |
| Date: | May 22, 2007 (Tuesday), 2:30PM-3:30PM, Colloquium Room (Chase 319) |
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| Speaker: | Erik D. Demaine (MIT) |
| Title: | Origami, Linkages, and Polyhedra: Folding with Algorithms |
| Abstract: | What forms of origami can be designed automatically by a computer? What shapes can result by folding a piece of paper flat and making one complete straight cut? What 3D surfaces can be cut open and unfolded into a flat piece of paper without overlap? When can a robot arm or protein be untangled or folded into a desired configuration? Geometric folding and unfolding is a branch of discrete and computational geometry that addresses these and many other intriguing questions. I will give a taste of the many discoveries that have been made in the past few years, as well as the several exciting problems that remain unsolved. Folding problems have applications throughout science and engineering, for example, to safer automobiles, space deployment, manufacturing, robotics, computer graphics, and protein folding. |
| Local host: | Karl Dilcher |
| Date: | August 13, 2007 (Monday), 11:00AM-12:00NOON, Colloquium Room (Chase 319) |
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| Speaker: | Peter Winkler (Dartmouth) |
| Title: | Where statistical physics meets graph theory |
| Abstract: | Statistical physicists and combinatorialists have discovered that they have many common objectives, at least after their terminologies have been matched. We will examine three statistical physics models which are particularly graphical, namely the hard-core model (a.k.a. random independent sets), percolation (random subgraphs), and branched polymers (random trees in space). |
| Local host: | Jeannettee Janssen |
| Date: | August 27, 2007 (Monday) |
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| Speaker: | Silvia Heubach (CSULA) |
| Title: | Avoidance of partially ordered patterns in compositions |
| Abstract: | Pattern avoidance has been primarily studied in permutations and words, but recently has been extended to compositions. In this talk we present generalizations of some of the results in the literature on pattern avoidance in permutations and words. In particular, we will be studying pattern avoidance of segmented partially ordered patterns (POPs) in compositions. We give a general result that expresses the generating function of the number of compositions that avoid a POP composed of two smaller patterns in terms of the generating functions for the smaller patterns. We apply this result to two specific types of POPs, namely shuffle patterns and multi-patterns and show equivalence for failies of patterns of each type. We close by giving a result for the maximum number of non-overlapping occurences of a POP in a composition. This is joint work with Sergey Kitaev (Reykjavik University) and Toufik Mansour (Haifa University). |
| Local host: | Roman Smirnov |
| Date: | September 13, 2007 (Thursday) |
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| Speaker: | Ross M. Richardson (Yianilos Labs and UCSD) |
| Title: | Sharp Concentration of Random Polytopes |
| Abstract: | In 1964 R\'enyi and Sulanke instigated the study of the convex hull of $n$ random points chosen in a convex set $K$. In particular, they studied the expectation of certain \emph{functionals} of this random polytope, e.g. the number of vertices or the volume. We will discuss a method for analyzing higher moment questions based on sharp concentration (martingale) techniques for this and other random polytope models. This work is joint with Van Vu (Rutgers) and Lei Wu (Bosch Research). |
| Local host: | Jeannettee Janssen |
| Date: | September 17, 2007 (Monday) |
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| Speaker: | Dorette Pronk (Dalhousie) |
| Title: | Orbifold Bredon Cohomology |
| Abstract: | Orbifolds are defined in terms of atlases with charts, just like manifolds, except that an orbifold is locally the quotient of Euclidean space by the action of a finite group of isometries. Although orbifolds are defined in terms of group actions on spaces, up till now not much of the theory of equivariant algebraic topology has been applied to them. Equivariant algebraic topology considers invariants of $G$-spaces for a fixed Lie group $G$. Orbifolds are generally only defined by local group actions, and an orbifold is called representable or reduced if it can be described in terms of a global Lie group action on a manifold. But even then, the orbifold does not uniquely determine the manifold and the group acting on it. So if we want to define an orbifold version of (equivariant) Bredon cohomology, we need to show that it does not depend on the representation of the orbifold as a quotient of a manifold by a Lie group action. In this talk I will show how a representation of orbifolds in terms of Lie groupoids helps us to describe the maps between representable orbifolds as a kind of equivariant maps and gives us a description of the relation between different representations as global quotients in terms of Morita equivalence. We use this then to define a notion of Bredon cohomology which is an orbifold invariant. This is joint work with Laura Scull from UBC. |
| Local host: | Roman Smirnov |
| Date: | November 5, 2007 (Monday) |
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| Speaker: | Martin Mathieu (Queen's University at Belfast) |
| Title: | Spectral characterizations of Jordan homomorphisms |
| Abstract: | There are many reasons to study Jordan homomorphisms of associative algebras. One of them comes from the relevance of the Jordan structure in Quantum Mechanics, as observed by Jordan, von Neumann and Wigner in 1934. In fact, the question whether it is possible to recognize a Jordan homomorphism through spectral theory is related to the basic question of reconstruction of a mathematical model from given observational data. Although contributions to this problem go as far back as work by Frobenius at the end of the 19th century, it was Kaplansky who, in 1970, draw the attention to this problem. Since then, many advances were made but the general situation still evades solution. We shall provide a survey on what is, and what is not yet, known in this area which is a nice mix of Algebra, Functional and Complex Analysis. |
| Local host: | Karl Dilcher |
| Date: | November 19, 2007 (Monday) |
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| Speaker: | Amal Amleh (St. Mary's) |
| Title: | On Second-Order Rational Difference Equations |
| Abstract: | A summary of recent and new results on the global character of solutions of a second-order rational difference equation will be presented. The primary interest is in the boundedness nature of solutions, the global stability of the equilibrium points, the periodic character of the equation, and with convergence to periodic solutions including periodic trichotomies. Some open problems and conjectures will be given. |
| Local hosts: | Karl Dilcher/Roman Smirnov |
| Date: | November 26, 2007 (Monday) |
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| Speaker: | Pawel Pralat (Dalhousie) |
| Title: | Cleaning $d$-regular graphs with brushes |
| Abstract: | A model for cleaning a graph with brushes was recently introduced. We consider the minimum number of brushes needed to clean $d$-regular graphs in this model, focusing on the asymptotic number for random $d$-regular graphs. We use a degree-greedy algorithm to clean a random $d$-regular graph on $n$ vertices (with $dn$ even) and analyze it using the differential equations method to find the (asymptotic) number of brushes needed to clean a random $d$-regular graph using this algorithm (for fixed $d$). We further show that for any $d$-regular graph on $n$ vertices at most $n(d+1)/4$ brushes suffice, and prove that for fixed large $d$, the minimum number of brushes needed to clean a random $d$-regular graph on $n$ vertices is asymptotically almost surely $\frac{n}{4}(d+o(d))$. This is a joint work with N. Alon, M.-E. Messinger, R.J. Nowakowski, and N. Wormald. |
| Local hosts: | Roman Smirnov |