Mathematics Colloquium Series
2011 – 2012
Unless otherwise noted below, the usual day/time for colloquia is Fridays, 2:30-3:30pm, Hall of Government, room 101
Contact: Svetlana Roudenko
roudenko@gwu.edu
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SPRING 2012 |
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Date |
Speaker |
Title & Abstract |
responsible person |
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April 27, Friday
Duques #651 |
Noser Singpurwalla Dept. of Stats GWU
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End of the semester Colloquium and Party (wine + cheese) - joint with Statistics Department Undergraduate and graduate students are encouraged to come to this expository talk Title: Subjective Probability: Its Axioms and Acrobatics (Expository Talk) Abstract: The meaning of probability has been enigmatic, even to the likes of Kolmogorov, and continues to be so. It is fallacious to claim that the law of large numbers provides a definitive interpretation. Whereas the founding fathers, Kardano, Pascal, Fermat, Bernoulli, de Moivre, Bayes, and Laplace, took probability for granted, the latter day writers, Venn, von Mises, Ramsey, Keynes, deFinetti, and Borel engaged in philosophical and rhetorical discussions about the meaning of probability. Entering into the arena were also physicists like Cox, Jeffreys, and Jaynes and philosophers like Carnap, Jeffrey, and Popper. Interpretation matters because the paradigm used to process information and act upon it, is determined by perspective. The modern view is that the only philosophically and logically defensible interpretation of probability is that probability is not unique, that it is personal, and therefore subjective. But to make subjective probability mathematically viable, one needs axioms of consistent behavior. The Kolmogorov axioms are a consequence of the behavioristic axioms. In this expository talk, I will review these more fundamental axioms and point out some of the underlying acrobatics that have led to debates and discussions. Besides mathematicians, statisticians, and decision theorists, the material here should be of interest to physical, biological, and social scientists, risk analysts, and those engaged in the art of “intelligence” (Googling, code breaking, hacking, and eavesdropping) |
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January 24, Tuesday 3:45pm Monroe 451 |
Natasa Pavlovic UT-Austin |
Special Colloquium Title: On the Gross-Pitaevskii hierarchies Abstract: The Gross-Pitaevskii (GP) hierarchy is an infinite system of coupled linear non-homogeneous PDEs, which appear in the derivation of the nonlinear Schrodinger equation (NLS). Inspired by the PDE techniques that have turned out to be useful on the level of the NLS, we realized that, in some instances we can introduce analogous techniques at the level of the GP. In this talk we will discuss some of those techniques which we use to study well-posedness for GP hierarchies. Time permitting, we will also discuss a new derivation of the defocusing cubic GP hierarchy in dimensions d=2,3, from an N-body Schrodinger equation describing a gas of interacting bosons in the GP scaling, in the limit N->infinity. In particular, we prove convergence of the corresponding BBGKY hierarchy to a GP hierarchy in the spaces introduced in our previous work on the well-posedness of the Cauchy problem for GP hierarchies, which are inspired by the solutions spaces based on space-time norms introduced by Klainerman and Machedon. We note that in d=3, this has been a well-known open problem in the field.
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Feb 3, 2:20pm |
Penn State |
Title: How to compute transition states/saddle points? Abstract: Exploring complex energy landscape is a challenging issue in many applications. Besides locating equilibrium states, it is often also important to identify transition states given by saddle points. Such problems have not been adequately studied in
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Feb 17, 2:20pm Gov 101 |
Andrew Pollington, |
Title: A question of Wolfgang Schmidt concerning two dimensional Diophantine approximation. Abstract: I will start with a short introduction to Diophantine approximation, how well can real numbers be approximated by rational numbers, and then go on to some recent results concerning higher dimensional questions. In the 1930's Littlewood conjectured that for every pair of real numbers (x,y) This conjecture is still open, although we now know, thanks to work of Einsiedler, Katok and Lindenstrauss, that the set of possible counter examples is a set of Hausdorff dimension 0. In any counter example to the conjecture there must be a constant $c>0$ so that for any pair of non negative real numbers (i,j), with i+j=1, We say that such a pair (x,y) belongs to Bad(i,j). It is relatively easy to show that for each possible pair (i,j) one has Bad(i,j) is non empty, and, in fact, has full Hausdorff dimension in the plane. The question that Schmidt asked in 1970 was to show that there are pairs which lie in both Bad(1/3,2/3) and in Bad(2/3,1/3). In this talk I will show that the intersection of any finite collection of Bad(i,,j) sets is non-empty. This is joint work with Dzmitry Badziahin, now at Durham University, and Sanju Velani at the University of York.
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Feb 24, 2:30pm |
Konstantina Trivisa, |
Title: On a Fluid-Particle Interaction Model Abstract: Fluid–particle interactions arise in many practical applications in biotechnology, medicine, combustion and atmospheric sciences. Aerosols and sprays can be modeled by fluid–particle type interactions in which bubbles of suspended substances are seen as solid particles. In this talk I will present results on the global-in-time existence and asymptotic analysis of a fluid–particle interaction model in the so-called bubbling regime. The system under investigation describes the evolution of particles dispersed in a viscous compressible fluid and is expressed through the conservation of fluid mass, the balance of momentum and the balance of particle density often referred as the Smoluchowski equation. The coupling between the dispersed and dense phases is obtained through the drag forces that the fluid and the particles exert mutually by the action–reaction principle. |
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March 2, 11am |
Title: Noise Attenuation and Robustness in Cell Signaling and Patterning Abstract: Noises and stochastic effects usually exist in every biological system due to many intrinsic and extrinsic factors. In this talk, I will discuss strategies and principles for noise attenuation and robustness to genetic or/and environmental perturbations in cell signaling and embryonic patterning. In one case, I will introduce a critical quantity that dictates capability of attenuating temporal noises in feedback systems. In another case, I will show that noises in signal transduction actually enable reduction of stochastic effects in spatial patterns. In addition, I will present several new experimental data in yeast cells and zebrafish embryo that support our modeling and computational predictions.
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April 3
1957 E St. Room # 111 |
Louis H. Kauffman, University of Illinois at Chicago |
"Distinguished First of April Talk" Title: The Four Color Theorem Abstract: In this talk the speaker will perform a proof of the Four Color Theorem due to G. Spencer-Brown. This proof is based on diagrammatic reformulations of the problem, coupled with a transcendental logical principle that states that an entity is identical with what it is not. A second proof, due to the speaker, based on legerdemain, will also be presented. Methods of infinite descent are welcome, but proof by intimidation will be used only as a last resort. The talk will be self contained and it will contain itself. The only prerequisite for this talk is an understanding of the consequences of the existence of coequalizers in the category of categories (see ref [2], p. 44-49). References
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J.Przytycki |
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FALL 2011 |
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Date |
Speaker |
Title & Abstract |
responsible person |
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October 6, Thursday 4--5pm Funger #210 |
Zhanghan Wang Microsoft Station Q |
Jointly with Applied Math Seminar and Quantum Computing Seminar Title: Topological Quantum Computation Abstract: Quantum computing models have the potential to perform tasks such as factoring integers and simulating quantum physics exponentially faster than any known classical algorithms, thus revolutionizing information science. But the construction of a large-scale quantum computer is still in its infancy due to the decoherence of quantumness. One promising way to defeat decoherence is via topology. I will give an introduction to this approach to building a large-scale quantum computer, as pursued at Microsoft Station Q (http://stationq.ucsb.edu/), and discuss the mathematical and scientific challenges. Dr. Zhenghan Wang is a senior researcher at Station Q, Microsoft Research located on UC Santa Barbara campus, and an adjunct professor of UC Santa Barbara Math Dept. Before joining Microsoft, he was on the faulty of Indiana University from 1996-2007. His main interests are quantum topology, theoretical models of topological phases of matter, and their application to quantum computing. |
Y.Rong and X.Ren |
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Oct 10, Monday 4--5pm Monroe #353 |
John Oprea, Cleveland State University |
Note: the talk will be "hands-on" and geared towards undergrad students. Title: Mathematics and Soap Films Abstract: Why do one-celled creatures take the shapes they do? Why were spiral staircases preferred in old architecture? More and more, in biology as well as other sciences, the notion of "shape" is becoming important. Mathematicians have ways of measuring shape and of determining shape through optimization. This fits well with Nature's penchant for economy, so it isn't surprising (in retrospect) that soap films, which arise from surface tension's ability to shrink surface area, are a kind of analog computer for the mathematics of minimizing surface area. This talk, which will be aimed at undergraduate science majors, will consist of soap film demonstrations and a bit of the mathematics and physics which explain soap film principles in science. Since audience participation is required for soap film experiments, attendees are encouraged not to wear their best attire! John Oprea received his Ph.D. in 1982 from Ohio State University and has been at Cleveland State University since 1985. His interests lie in both algebraic topology and differential geometry and he has written extensively in these areas. His books include: Differential Geometry and its Applications (MAA Classroom Resources 2007), The Mathematics of Soap Films (AMS Student Math Library 2000), Symplectic Manifolds with no Kaehler Structure (with A. Tralle, Springer Lecture Notes 1997), Lusternik- Schnirelmann Category (with O. Cornea, G. Lupton and D. Tanre, AMS Monographs 2003) and his most recent, Algebraic Models in Geometry (with Y. Felix and D. Tanre, Oxford U Press 2008). Oprea was awarded the Lester R. Ford award from the Mathematical Association of America in 1996 for his American Mathematical Monthly paper Geometry and the Foucault Pendulum. In 2008, he was named as the Cleveland State College of Science Outstanding Researcher and received the University Distinguished Faculty Award for Research. He is currently an associate editor for the Journal of Geometry and Symmetry in Physics. |
F.Baginski |
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Oct 31, Monday 4--5pm Monroe #353 |
William "Bus" Jaco, Regents Professor and Grayce B. Kerr Professor, Oklahoma State University |
Title:Minimal triangulations for infinite families of 3--manifolds Abstract: A notion of complexity for a 3--manifold is the minimal number of tetrahedra necessary for a (pseudo) triangulation of the manifold. We shall present results giving for the first time the complexities of several infinite families of 3--manifolds. In particular, we have that the complexity of the product of a closed orientable surface of genus g with an interval, is 10g - 4. Furthermore, while the minimal triangulations of these manifolds are not unique, they all have the form of an inflation of a cone over a minimal triangulation of the surface S. This case is surprisingly simple in comparison to other infinite families for which we have determined the complexity. (Joint Work with J.Johnson, H Rubinstein, and S. Tillmann). |
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Nov 7, Monday 4--5pm Monroe #353 |
Temple University |
Title:An Optimal Metrization Theorem for Topological Groupoids Abstract: Metrization theorems (i.e. the question whether a certain topology is induced by a metric) play a basic role in many areas of mathematics including topology, functional analysis, analysis on spaces of homogeneous type, partial differential equations. In this talk I will discuss a sharp general metrization theorem in the setting of abstract groupoids (groupoids have been introduced by Brandt in the 1920's as a generalization of groups which also include arbitrary sets). This theorem contains as particular cases several basic metrization results such as the Alexandroff- Urysohn metrization theorem in Topology, the Aoki-Rolewicz metrization theorem in topology, and the Macias-Segovia metrization theorem in Harmonic Analysis. (Refreshments will be served at 3:30pm in the main math office) |
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Nov 21, Monday 4--5pm Monroe #353 |
University of Illinois |
Title: Averaging over Rectangles in Euclidean Spaces |
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Dec 2, Friday 1pm Rome #352 |
Adam Levine Brandeis University |
Jointly with the opening of the conference Knots in Washington Title: Combinatorial Spanning Tree Models for Knot Homologies Abstract: It is well-known that the Alexander and Jones polynomials of a knot can be computed as sums of monomials corresponding to spanning trees of the Tait graph of a diagram for the knot. In this talk, I describe recent progress on extending this approach to the knot homology theories that categorize these polynomials. Specifically, Baldwin and I have constructed a complex whose generators correspond to spanning trees, whose homology is isomorphic to the knot Floer homology of the knot, and whose differential can be described completely explicitly. Roberts used a similar approach to construct a spanning tree complex for Khovanov homology. The similarities between these two constructions suggest a possible strategy for relating the two theories. |
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Dec 5, Monday 4--5pm Monroe #353 |
U.S. Naval Academy |
Title: Generalizations of the linking number Abstract: The linking number was introduced by Gauss, who expressed it as an integral which measures the number of times two circles wrap around one another in three-dimensional space. Since that time many equivalent definitions have been proposed. I will propose an alternative viewpoint which has two benefits: (1) It gives a general definition of linking of arbitrary manifolds in an arbitrary manifold, and (2) It suggests that the linking number is really a "relative" invariant; that is, it depends on certain choices. I will also briefly discuss Milnor's higher-order invariants, which show, for example, how the Borromean rings and its generalizations are linked. Using a similar relative perspective I will argue that Milnor's invariants are "multi-relative", and can also be generalized to linking of arbitrary manifolds in higher-dimensional Euclidean space. |
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