Dr. Zhilan Feng
Purdue University

will present

Evolutionary Implications of Influenza Medication Strategies

Tuesday, November 24, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Patients at risk for complications of influenza are commonly treated with antiviral medications, which however also could be used to control outbreaks. The adamantanes and neuraminidase inhibitors are active against influenza A, but avian influenza (H5N1) is resistant to oseltamivir and swine influenza (H1N1) to the adamantanes (but see postscript). To explore influenza medication strategies (pre-exposure or prophylaxis, post-exposure/pre-symptom onset, and treatment at successive clinical stages) that may affect evolution of resistance (select for resistant strains within or facilitate their spread between hosts), we elaborated a published transmission model and chose parameters from the literature. Then we derived the reproduction numbers of sensitive and resistant strains, peak and final sizes, and time to peak. Finally, we made these results accessible via user-friendly Mathematica notebooks. (Joint work with Rongsong Liu, Dashun Xu, Yiding Yang, and John Glasser)

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Professor Sergiy Koshkin
University of Houston-Downtown

will present

Gauge Theory of Faddeev-Skyrme Functionals

Friday, November 20, 2009, 3:30pm
Ungar Room 402

Refreshments at 3:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: We study geometric variational problems for a class of nonlinear sigma-models in quantum field theory. Mathematically, one needs to minimize an energy functional on homotopy classes of maps from closed 3-manifolds into compact homogeneous spaces G/H, similar to the case of harmonic maps. The minimizers are known as Hopfions and exhibit localized knot-like structure. Our main results include proving existence of Hopfions as finite energy Sobolev maps in each (generalized) homotopy class when the target space is a symmetric space. For more general spaces we obtain a weaker result on existence of minimizers in each 2-homotopy class.

Our approach is based on representing maps into G/H by equivalence classes of flat connections. The equivalence is given by gauge symmetry on pullbacks of G-->G/H bundles. We work out a gauge calculus for connections under this symmetry, and use it to eliminate non-compactness from the minimization problem by fixing the gauge.

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Dr. Alexander Engström
Miller Research Fellow
University of California, Berkeley

will present

Graph Theoretic Methods in Algebraic Statistics

Thursday, November 12, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: First I will review how methods from commutative algebra, for example Gröbner bases and toric ideals, can be used in statistics. Then I will describe two applications of graph theoretic methods in this context: My proof of Sturmfels and Sullivant's conjecture on cut ideals; and the ideals of graph homomorphisms introduced together with Patrik Noren.

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Dr. Daniel Ruberman
Brandeis University

will present

Slice Knots and the Alexander Polynomial

Thursday, November 5, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: A knot in the 3-sphere is slice if it bounds an embedded disk in the 4-ball. The disk may be topologically embedded, or we may require the stronger condition that it be smoothly embedded; the knot is said to be (respectively) topologically or smoothly slice. It has been known since the early 1980's that there are knots that are topologically slice, but not smoothly slice. These result from Freedman's proof that knots with trivial Alexander polynomial are topologically slice, combined with gauge-theory techniques originating with Donaldson. In joint work with C. Livingston and M. Hedden, we answer the natural question of whether Freedman's result is responsible for all topologically slice knots. We show that the group of topologically slice knots, modulo those with trivial Alexander polynomial, is infinitely generated. The proof uses Heegaard-Floer theory.

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Professor Xue-Zhi Li
Xinyang Normal University, P.R. China

will present

Coexistence of the Strains Induced by Super-infection and Mutation

Friday, October 16, 2009, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In this talk, I will present the research results on two two-strain epidemic models. One is an age-structured two-strain model with super-infection. For this model, the explicit expression of basic reproduction numbers and the invasion reproduction numbers corresponding to strain one and strain two are obtained. It is shown that the infection-free steady state is globally stable if the basic reproductive number R0 is below one. Existence of strain one and strain two exclusive equilibria is established. Conditions for local stability or instability of the exclusive equilibria of the strain one and strain two are established. Existence of coexistence equilibrium is also obtained under the condition that both invasion reproduction numbers are larger than one. Another is a two-strain epidemic model with single host population, it is assumed that strain 1 can mutate into strain 2. Also latent-stage progression age and mutation are incorporated into the model. Stability of equilibria (including the disease free equilibrium, dominance equilibria and the coexistence equilibrium) is investigated and it is found that they are locally stable under suitable and biological feasible constraints. Results indicate that the competition exclusion and coexistence of the two strains are possible depending on the mutation. Numerical simulations are also performed to illustrate these results.

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Dr. Arnaldo Horta
Applied Research Mathematician
National Security Agency
Fort Meade, Maryland

will present

Inside the Puzzle Palace:
Careers in Mathematics and Computer Science at the National Security Agency

Thursday, October 8, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In this talk, I will discuss the role of mathematics and computer science at NSA and discuss hiring opportunities, including REUs (Research Experiences for Undergraduates) and programs for graduate students.

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Professor Mina Teicher
Bar-Ilan University
Director of Emmy Noether Research Institute
Chair of United States-Israel Binational Science Foundation
Vice President of ICMI (International Commission on Math Instruction)

will present

How Can Computational Neuroscience Help Us Understand How the Brain Works?

Tuesday, October 6, 2009, 5:00pm
Arts and Sciences Gallery at the Wesley Center
1210 Stanford Drive

Reception immediately following
All interested persons are welcome to attend.


Abstract: In this talk we will discuss what it means to understand the brain, will pose a conjecture and provide a proof, will discuss the advantages of MEG over EEG, and will also mention a few medical applications.

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James Keesling
Professor and Chair of Mathematics
University of Florida

in memory of Professor Edwin Duda
will present

Attractors in Dynamics

Friday, September 4, 2009, 5:00pm
Ungar Room 402

Reception immediately following in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Attractors have been an important focus in the study of dynamics. When a dynamical system maps a compact neighborhood into its interior, the limiting behavior in that neighborhood is an attractor. There are two ways that attractors are interesting. One is their geometric and topological structure. The other is the action of the dynamics on the attractor. The latter represents the long-term behavior of the system. Both of these are studied using inverse limits. The structure of hyperbolic attractors is quite well understood through the work of Bob Williams. However, non-hyperbolic attractors arise in applications and these are not so well understood. This talk will cover the general history of attractors and then concentrate on the most recent results on non-hyperbolic attractors.

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Prof. Frank Kutzschebauch
University of Bern, Switzerland

will present

Knotted Holomorphic Discs in C^2

Thursday, August 6, 2009, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In this joint work with Sebastian Baader and Erlend Fornaess Wold we solve problem 1.102 (B/C) of Kirby's list on "Problems in low dimensional Topology": We construct proper embeddings of \R^2 into \R^4 whose image is a topologically knotted minimal surface. The proof is a combination of facts from knot theory (due to Rudolph Lee and Stephan Orevkov) and complex analysis (due to Josip Globevnik).

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Dr. Salome Martinez
Universidad de Chile

will present

Asymptotic Behavior of an Inhomogeneous Linear Integro-differential Equation Modelling Dispersal

Tuesday, May 19, 2009, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: We will discuss the asymptotic behavior of a time dependent integro-differential equation modelling non-local dispersal in a inhomogeneous environment. In this equation, the space variable will be considered in bounded domains and in the whole space. The existence of steady state solutions is crucial to understand the long time behavior of the equation. We will establish their existence and profiles in some cases.

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Dr. Qing Nie
Center for Mathematical and Computational Biology
Department of Mathematics
Department of Biomedical Engineering
University of California, Irvine

will present

Systems Biology of Cell Signaling

Friday, April 24, 2009, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: The proper growth, development, and survival of an organism require extensive and accurate communication among the cells of the organism. Hence, cells sense and react to a wide variety of stimuli, which convey information such as nutrients, harmful insults, and the state of neighboring cells. Using a systems biology approach that integrates modeling and experimentation, we study two cell signaling systems: 1) robust sensing and signal transduction during mating of yeast cells, and 2) proliferative control of cell lineages in mammalian olfactory epithelium.

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Dr. Jianshe Yu
Guangzhou University

will present

The Minimal Period Problems for the Classical Forced Pendulum Equation

Wednesday, April 22, 2009, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In the talk I will discuss the periodicity of solutions to the classical forced pendulum equation y'' + A siny = f(t) where A= g/l is the ratio of the gravity constant and the pendulum length, and f(t) is an external periodic force with a minimal period T. The major concern is to characterize conditions on A and f under which the equation admits periodic solutions with a prescribed minimal period pT, where p>1 is an integer. I will show how the new approach, based on the critical point theory and an original decomposition technique, leads to the existence of such solutions without requiring p to be a prime as imposed in most previous approaches. In addition, I will present the first non-existence result of such solutions which indicates that long pendulum has a natural resistance to oscillate periodically.

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Dr. Michael Zieve
Institute for Advanced Study, Princeton

will present

Polynomial Mappings

Friday, April 17, 2009, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: I will present properties of polynomials mappings and generalizations. I will first describe all polynomials f and g for which there is a complex number c such that the orbits {c, f(c), f(f (c)), ...} and {c, g(c), g(g(c)), ...} have infinite intersection. I will also discuss a common generalization of this result and Mordell's conjecture (Faltings' theorem). After this I will move to polynomial mappings over finite fields, with connections to curves having large automorphism groups and instances of a positive characteristic analogue of Riemann's existence theorem.

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Dr. Leon Takhtajan
SUNY at Stony Brook

will present

Eisenstein-Maass Series and Chern Forms on Moduli Spaces of Curves and Parabolic Bundles

Thursday, April 2, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: We will review construction of natural Hermitian metrics on the tautological line bundles over the moduli spaces of curves and parabolic bundles. Corresponding Chern forms are expressed through the Eisenstein-Maass series and appear as cuspidal defect in local index theorem for families with non-compact fibers.

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Professor Greg Pearlstein
Michigan State University

will present

The Zero Locus of an Admissible Normal Function

Monday, March 30, 2009, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: I will discuss recent work with Patrick Brosnan on proving that the zero locus of an admissible normal function on a smooth complex algebraic variety S is algebraic over the complex numbers.

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Dr. Dung Le
Department of Mathematics
University of Texas at San Antonio

will present

Global Existence and Regularity of Weak Solutions to Large Cross Diffusion Systems via Nonlinear Heat Approximation Methods

Friday, March 27, 2009, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Nonlinear elliptic/parabolic partial differential systems have been used to model real life phenomena. Regularity theory of solutions to these systems plays a fundamental role in the mathematical and rigorous study of these models. A priori estimates for Holder norms of solutions will provide global existence, compactness property etc. for the flow of solutions in order to carry out further investigations on the dynamics of the solutions. I will introduce a so called nonlinear heat approximation technique to derive a priori estimates for Holder norms of bounded or unbounded weak solutions. The theory can apply to large nonlinear systems in applications such as a generalized version of the Shigesada-Kawasaki-Teramoto models. In this model, the number of interacting species and the dimension of the domain can be arbitrary. If time permits, I will also talk about the generalized versions of our method for fully nonlinear systems with degeneracy/singularity such as p-Laplacian or porous media type systems.

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Dr. Jianhong Wu
Canada Research Chair
MITACS Centre for Disease Modeling at York University

will present

Optimal Timing and Delay of the Use of Antiviral Drugs in Pandemic Influenza:
Mathematical Challenges for Policymakers

Thursday, March 26, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: The use of antiviral drugs has been recognized as the primary public health strategy for mitigating the severity of a new influenza pandemic strain. However, the success of this strategy requires the prompt onset of therapy within 48 hours of the appearance of clinical symptoms, and the evolution of highly transmissible drug-resistant viral mutants can become a critical limitation to the use of these drugs. A comprehensive mitigation plan must consider the optimal timing of antiviral drugs within individual hosts and at the population level, in the presence of other non-medical intervention measures and in anticipation of an imperfect vaccine at a late stage of the pandemic. These policy issues have suggested the use of some compartmental and structured models and led to intensive efforts in modelling and analysis of the disease transmission dynamics. On the other hand, model-based and mathematical analysis-suggested policy recommendations have imposed significant challenge to the policymakers for practical implementation. This talk gives a summary of a Canadian (MITACS) team's efforts in this interface between modellers and policymakers for an evolving pandemic influenza preparedness plan.

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Dr. John Shareshian
Washington University

will present

Intervals in Subgroup Lattices of Finite Groups

Tuesday, March 24, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: The following question, which arose from a problem in universal algebra, remains open: Is it true that for every finite lattice L, there exist a finite group G and a subgroup H of G such that the interval [H,G] of subgroups of G that contain H is isomorphic with L?

The answer to this question seems likely to be "no". I will discuss the history of this problem and recent approaches. Much of this talk will be expository, but I will discuss a recent joint paper with M. Aschbacher.

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Professor Alexander Volberg
Michigan State University
Salem Prize Recipient

will present

Buffon Needle and Buffon Noodle Probability

Friday, March 13, 2009, 3:00pm
Ungar Room 402

Refreshments at 2:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In 1733 Georges-Louis Leclerc, count de Buffon, asked the question about the probability of intersecting a line of a grid by a needle dropped randomly on the grid. In 1898 Painlevé asked for the geometric description of the sets that are removable singularities of bounded holomorphic functions. In 1930's Besicovitch built a theory of 1-rectifiable sets. At the end of the XXth century all these 3 topics turned out to be intimately related and by the beginning of XXIst century a certain unified theory did emerge. It is still not completely finished, but I will present the nowdays state of the knowledge.

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Dr. Sheree Arpin
Framingham State University

will present

Modeling Frequency-dependent Selection in a Population of Fish

Friday, February 27, 2009, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: We present discrete-time models for a population of predatory cichlid fish known to exhibit frequency-dependent selection. We construct the models by incorporating both population genetic and population dynamic processes. We show the models predict a temporal phenotypic oscillation in mouth-handedness, which coincides with field data and is driven by the defense mechanism of the prey species. Furthermore, our analysis indicates a previously unknown and, perhaps, unexpected feature of the oscillation. We will discuss the different routes to destabilizing a 1:1 phenotypic ratio and their biological implications.

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Professor Patrick Clarke
University of Pennsylvania

will present

Categorical T-duality

Wednesday, February 25, 2009, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: We give a categorical formulation of T-duality by considering homological mirror symmetry as an equivalence of A_\infty categories. Our results produce a mirror algebro-geometric object to an A_\infty category when it admits a certain type of degeneration. We will also discuss how this formulation can be used to solve problems including:
     - finding the mirror of a symplectic manifold
     - giving an explanation of multiple mirror phenomena
     - giving an A_\infty enrichment of Orlov's B-brane category for Landau-Ginzburg models.

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Prof. Frank Kutzschebauch
Universit?t Bern

will present

A Solution to the Gromov-Vaserstein Problem

Thursday, February 19, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Any matrix in $Sl_n (\C)$ can (due to the Gauss elimination process) be written as a product of elementary matrices. If instead of the complex numbers (a field) the entries in the matrix are elements of a ring, this becomes a delicate question. In particular the rings of maps from a space $X \to \C$ are interesting cases. A deep result of Suslin gives an affirmative answer for the polynomial ring in $m$ variables in case the size of the matrix ($n$) is greater $2$. In the topological category the problem was solved by Thurston and Vaserstein. For holomorphic functions on $\C^m$ the problem was posed by Gromov in the 1980's. We report on a complete solution of Gromov's problem. A main tool is the Oka-Grauert-Gromov-h-principle in Complex Analysis. This is joint work with Bj?rn Ivarsson.

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Dr. Larry Shepp
Rutgers University

will present

Managing Diabetes Using Mathematics and Statistics to Help in the Design of an Artificial Pancreas

Friday, February 6, 2009, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Closed-loop control of diabetes automates insulin delivery by an implanted insulin pump, using an algorithm which bases its decisions on continuous readings of blood sugar levels. The algorithm is effective if it lowers A1C, the percent of hemoglobin molecules (a proxy for collagen) which have been glycated, i.e., have absorbed a molecule of sugar, because damage occurs to a cell when its collagen is glycated. Red blood cells contain hemoglobin molecules and have a mean lifetime of 120 days. Thus a blood sample can be used to obtain a new measurement of A1C every 120 days. We derive a formula for A1C by a direct mathematical method (which seems to give physical and medical insight) based directly on blood sugar levels, without the need for a blood sample. The new formula is useful in many ways, despite the fact that the data shows that it is less accurate in particular people (apparently the "slow glycaters"); though the formula is close to simply averaging the blood glucose level. One application is particularly useful: we have found a way to "impute" the blood glucose levels that would have been obtained under closed loop control from the blood glucose levels that were actually recorded for each of 136 patients who wore both a pump and a continuous glucose monitor and who were under open loop control, i.e. the decision to infuse insulin was made by a human being. The imputation is key and is not on a path by path basis but only holds, "on the average". Once we have the imputed levels we can apply the above formula to obtain what would have been the A1C value if the closed loop algorithm were used instead of the open-loop algorithm. In every one of the 136 cases a lower A1C is obtained. This indicates that closed loop control should benefit insulin-dependent diabetics, especially those who are not diligent in their management.

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Dr. Chris Brooks
Mississippi State University

will present

Using Network Models to Predict Disease Dynamics

Friday, January 30, 2009, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: One of the most difficult challenges in controlling the spread of infectious diseases is understanding which hosts in the population are responsible for the greatest number of new infections. The classic example is "Typhoid Mary" Mallon who, as a housekeeper and cook in New York, caused almost 50 cases of Typhoid Fever in the early 20th century. Understanding the contribution of these individuals can be critically important to developing effective control of infectious disease outbreaks. In the past decade or so theoreticians have begun to use network models to account for this kind of host-to-host variation when predicting the rates and routes of disease spread. I will discuss approaches to fitting network models to spatial data and present an analysis of pathogen transmission data from my own work on anther smut transmission among a population of fire pink (Silene virginica). These models provide accurate prediction of the dynamics of infection 1-2 years in advance and may be useful in understanding the role of spatiotemporal variation on the persistence of many host-pathogen systems.

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Dr. Andrei Okounkov
Princeton University

will present

Noncommutative Geometry of Random Surfaces

Tuesday, January 27, 2009 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.

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Dr. Xiuxiong Chen
University of Wisconsin

will present

Space of Ricci Flows

Thursday, January 8, 2009, 4:00pm
Ungar Room 506

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In this talk, we present our recent work on the moduli spaces of non-collapsed Ricci flows with bounded L^{n\over 2} norm energy and the scalar curvature bound. We obtain a weak compactness theorem for these flows under Cheeger-Gromov topology. It goes back to renowned work on the moduli space of einstein metrics with energy bound in early 1990s. The basic techniques are bubble analysis and contradiction arguments of Perelman's style. It has important applications in kahler Ricci flow. This is a joint work with my former student Bing Wang.

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Dr. Drew Armstrong
University of Minnesota

will present

Coxeter Combinatorics

Monday, December 15, 2008, 4:00pm
Ungar Room 402

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In 1935 Coxeter classified all of the finite groups generated by reflections. Today we call these groups finite Coxeter groups; the motivating example is the symmetric group S_n, in which the transposition (i,j) is thought of as a reflection in the hyperplane x_i=x_j. It turns out that many classical combinatorial objects can be defined in terms of the symmetric group in such a way that their definition extends uniformly to all finite Coxeter groups. This leads to a beautiful mixture of algebra and combinatorics. I will describe several classical concepts that extend in this way, including: sorting algorithms, catalan numbers, noncrossing partitions, and polygon triangulations.

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Lun-Yi Tsai
Visual Artist and "Mathemacher"

will present

Processes and Representations

Wednesday, December 3, 2008, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Named "Math Maker of the Week," August 25th, 2008 during Germany's Year of Mathematics, mathematicaly trained artist Lun-Yi Tsai makes creative connections between mathematics and art, demonstrating that the inner beauty of mathematics can be reflected in visual images. In this talk, he will discuss how he came to use math in his art, his process of making art, his collaborations with mathematicians, and his latest abstract paintings that were recently exhibited in Berlin (lunyitsai.com).

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Dr. Robert D. Holt
Arthur R. Marshall, Jr. Chair in Ecology
University of Florida

will present

Reflections on the Interface of Food Web Ecology and Island Biogeography

Friday, November 14, 2008, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.

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Dr. Maoan Han
The Institute of Mathematics
Shanghai Normal University

will present

Limit Cycle Bifurcations by Perturbing a Cuspidal Loop in a Hamiltonian System

Monday, November 3, 2008, 4:30pm
Ungar Room 402

Refreshments at 4:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In this talk, we first study the analytical property of the first Melnikov function for general Hamiltonian systems exhibiting a cuspidal loop and obtain its expansion at the Hamiltonian value corresponding to the loop and the expresions of the first coefficients of the expansion. Then by using the expresions of these coefficients we give some conditions for the perturbed system to have 4, 5 or 6 limit cycles in a neighborhood of the loop. As an application of our main results, we consider some polynomial Lienard systems and find 4, 5 or 6 limit cycles.

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Dr. V. Shukurov
Johns Hopkins University

will present

Termination in the Minimal Model Program of Algebraic Varieties

Wednesday, October 22, 2008, 4:00pm
Ungar Room 506

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Birational classification of algebraic varieties is intimately related with many fundamental problems of mathematics arising in theory of functions and integration, arithmetic and mathematical physics. Classification of algebraic curves and Riemann surfaces is one of remarkable achievements in mathematics of XIXth century. Classification of algebraic surfaces was completed by Enriques in the mid-XXth century. The Minimal Model Program, also known as the Mori program and being a higher dimensional analog of the Enriques classification, was set in works by Mori, Reid, Shokurov and Kawamata, and accomplished by Mori for dimension 3 in 1988. Its log generalization was suggested by the speaker.

The talk gives a current state of the log Minimal Model Program. An algorithm to construct a log minimal model will be discussed. The main open problem is termination of the algorithm. For any log pair up to dimension 4, weak termination and existence of final models was established. For the log pairs of general type, weak termination and existence of log minimal models was announced in any dimension.

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Professor Mikio Furuta
University of Tokyo

will present

Polarization and Localization

Thursday, October 16, 2008, 4:00pm
Ungar Room 506

Refreshments at 3:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In the passage from classical mechanics to quantum mechanics, one expects that the quantum states of a quantum system correspond to the Bohr--Sommerfeld fibers which are defined using a real polarization. A mathematical formulation of this expectation leads to a comparison problem for geometric quantizations obtained using real polarization and Kahler polarization. I will explain an approach to this comparison via introducing a localization technique for the Riemann--Roch number of a spin^c manifold with a torus fibration. (Joint work with Takahiko Yoshida and Hajime Fujita)

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Dr. Dorothy Buck
Imperial College London

will present

The Topology of DNA-Protein Interactions

Wednesday, October 1, 2008, 3:30pm
Ungar Room 402

Refreshments at 3:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: The central axis of the famous DNA double helix is often topologically constrained or even circular. The topology of this axis can influence which proteins interact with the underlying DNA. Subsequently, in all cells there are proteins whose primary function is to change the DNA axis topology -- for example converting a torus link into an unknot. Additionally, there are several protein families that change the axis topology as a by-product of their interaction with DNA.

This talk will describe typical DNA conformations, and the families of proteins that change these conformations. I'll present a few examples illustrating how Dehn surgery methods have been useful in understanding certain DNA-protein interactions, and discuss the most common topological techniques used to attack these problems.