Dr. Pengzi Miao
School of Mathematical Sciences
Monash University

will present

Critical Metrics for the Volume Functional on Compact Manifolds with Boundary

Thursday, February 4, 2010, 5:00pm
Ungar Room 402

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


Abstract: It is known that, on closed manifolds, Einstein metrics of negative scalar curvature are critical points of the usual volume functional constrained to the space of metrics of constant scalar curvature. In this talk, I will discuss how this variational characterization of Einstein metrics can be localized to compact manifolds with boundary. I will derive the critical point equation and focus on geometric properties of its solutions. In particular, if a solution has zero scalar curvature and the boundary of the manifold can be isometrically embedded into the Euclidean space as a convex hypersurface, I will show that the volume of such a critical metric is always greater than or equal to the Euclidean volume enclosed by the image of the isometric embedding, and two volumes are the same if and only if the critical metric is isometric to the Euclidean metric on a round ball. I will also give a classification of all conformally flat critical metrics. This is joint work with Luen-Fai Tam.

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Dr. Brian J. Weber
RTG/Simons Center Postdoc
Stony Brook University

will present

Einstein Metrics, the Bach Tensor, and Metric Degenerations

Monday, February 1, 2010, 5:00pm
Ungar Room 402

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


Abstract: One might search for "canonical metrics," such as Einstein metrics, on a manifold by trying to prove the convergence of a sequence of metrics that minimize some functional, although such a direct approach usually fails. In this talk we present an indirect approach which has been successful in some cases. A local obstruction to finding an Einstein metric in a conformal class is the non-vanishing of the Bach tensor, defined to be the gradient of the Weyl curvature functional $\int |W|^2$. On a Kaehler manifold there are no other obstructions, and any Bach-flat Kaehler metric is locally conformally Einsteinian. Additionally, the conformal factor is geometrically interesting and sometimes controllable. This talk will describe the results of a 2008 paper with X. Chen and C. LeBrun, where circumstances under which a Kaehler manifold is Bach-flat were established, and where it was shown that these conditions hold for a certain Kaehler metric on $CP^2 # 2\overline CP^2$ with non-zero conformal factor, establishing for the first time an Einstein metric on $CP^2 # 2\overline 2CP^2$.

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Dr. Hans Boden
McMaster University

will present

Metabelian SL(n,C) Representations of Knot Groups

Thursday, January 28, 2010, 5:00pm
Ungar Room 402

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


Abstract: In this talk, which represents joint work with Stefan Friedl, we will present a classification of irreducible metabelian SL(n,C) representations of knots groups. Under a mild hypothesis, we prove that such representations factor through a finite group, hence they are all conjugate to unitary representations, and we give a simple formula for the number of conjugacy classes. For knots with nontrivial Alexander polynomial, we discuss an existence result for irreducible metabelian representations. Given a knot group, its SL(n,C) character variety admits a natural action by the cyclic group of order n, and we show how to identify the fixed points of this action with characters of metabelian representations. If time permits, we will describe conditions under which such points are simple points in the character variety using a deformation argument of Abdelghani, Heusener, and Jebali.

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Dr. Brett L. Kotschwar
C.L.E. Moore Instructor
Massachusetts Institute of Technology

will present

Backwards Uniqueness for the Ricci Flow and the Non-expansion of the Isometry Group

Monday, January 25, 2010, 5:00pm
Ungar Room 402

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


Abstract: One of the fundamental properties of the Ricci flow -- an evolution equation for Riemannian metrics -- is that of isometry preservation, namely, that an isometry of the initial metric remains an isometry of the solution, at least as long as the curvature remains bounded. In this talk, I will take up the complementary problem of isometry development under the flow. While the solution may acquire new isometries in the limit, one does not expect the flow to sponsor their generation within the lifetime of the solution. The impossibility of such a phenomenon is equivalent to a backwards uniqueness (or unique-continuation) property for the equation: two solutions which agree at some non-initial time must agree identically at all previous times. I will discuss recent work which establishes this property for complete solutions of bounded curvature, and prohibits, additionally, a solution from becoming Einstein or self-similar in finite time.

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Dr. Stephen Gourley
University of Surrey, UK

will present

Impulsive Delay Equation Models for the Control of Vector-borne Diseases

Friday, January 15, 2010, 4:00pm
Ungar Room 402

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


Abstract: Delay equation models for the control of a vector-borne disease such as West Nile virus will be presented. The models make it possible to compare the effectiveness of larvicides and adulticides in controlling mosquito populations. The models take the form of autonomous delay differential equations with impulses (if the adult insects are culled) or a system of nonautonomous delay differential equations where the time-varying coefficients are determined by the culling times and rates (in the case where the insect larvae are culled). Sufficient conditions can be derived which ensure eradication of the disease. Eradication of vector-borne diseases is possible by culling the vector at either the immature or the mature phase. Very infrequent culling can actually lead to the mean insect population being increased rather than decreased.

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Professor Philippe LeFloch
University of Paris 6 and CNRS

will present

Einstein Spacetimes with Bounded Curvature

Thursday, December 10, 2009, 4:30pm
Ungar Room 402

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


Abstract: I will present recent results on Einstein spacetimes of general relativity when the curvature is solely assumed to be bounded and no assumption on its derivatives is made. One such result, in a joint work with B.-L. Chen, concerns the optimal regularity of pointed spacetimes in which, by definition, an "observer" has been specified. Under geometric bounds on the curvature and injectivity radius near the observer, there exist a CMC (constant mean curvature) foliation as well as CMC--harmonic coordinates, which are defined in geodesic balls with definite size depending only on the assumed bounds, so that the components of the Lorentzian metric has optimal regularity in these coordinates. The proof combines geometric estimates (Jacobi field, comparison theorems) and quantitative estimates for nonlinear elliptic equations with low regularity.

---

CANCELLED

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.

---

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).

---

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.