Lattice Boltzmann and Pseudo-Spectral methods for Decaying Turbulence

30 Years of Calderon's Problem
Abstract: In 1980 A. P. Calder\'on wrote a short paper entitled "On an inverse boundary value problem". In this seminal paper he initiated the mathematical study of the following inverse problem: Can one determine the electrical conductivity of a medium by making current and voltage measurements at the boundary of the medium? There has been substantial progress in understanding this inverse problem in the last 30 years or so. In this lecture we will survey some of the most important developments.

An Introduction to Geometric Quantization. Part II: Connections, Curvature, Hermitian Metrics

Homotopy Structures, Loops and String Topology
Abstract: We discuss how certain algebraic structures (like associative algebras) can be deformed up to homotopy. The natural examples come from topological examples like the loop space. String topology which was invented by Chas and Sullivan fits naturally into this realm of ideas, as we will explain.

Heat Kernel Estimates for the Fractional Laplacian

Metaplectic Whittaker Functions, Crystal Graphs, and Quantum Groups

Rank Functions for Simple C*-algebras

Weyman's Theorem

Twisted Euler Products
Abstract: Euler products are the foundation of the Langlands program and a great deal of modern number theory. In this talk I shall introduce twisted Euler products, a new construction, and explain how such twisted products arise. They offer hints of an unexpected connection to quantum groups. Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Elliptic Curves over Finite Fields

CANCELLED Associating Single Nucleotide Polymorphisms (SNPs) with Binary TraitsAssociation mapping uses statistical analyses to test for relationships between genomic markers that are called single nucleotide polymorphisms (SNPs) and traits. A statistically significant association between a SNP and a trait suggests that there exists a biological association between a nearby genomic region and the trait. This research focuses on the use of logistic regression to assess the additive, dominance, and epistatic effects when investigating associations between SNPs and binary traits, such as disease status. A very specific phenomenon, called quasi-separation of points (QSP), can arise in association mapping data, resulting in infinite maximum likelihood estimates (MLEs) of logistic regression parameters. One solution to this problem is to use Firth's MLE, which provides finite estimates in the presence of QSP. Two simulation studies are conducted to investigate the use of Firth's MLE in a QSP setting, as well as to assess the similarity between Firth's MLE and the traditional MLE when QSP is not present. Two published association mapping studies in humans are reanalyzed to demonstrate the implementation of Firth's MLE in real data settings. Balding DJ (2006) "A Tutorial on Statistical Methods for Population Association Studies," Nature Reviews Genetics 2006: Vol. 7 Iss. 10:781-791.Click here for a full schedule of BIOINFORMATICS SEMINARS, past and present.

Outline of BCHM's Approach

On the Geometry of Arc Spaces

Don't Miss The Forest For The TreesWe discuss why and how stochastic sequences are often changed into trees for applications and for theoretical analysis. In particular, we look at the relationships between patterns in sequences and subtrees. The methods for the analysis of trees and sequences usually include generating functions, singularity analysis, and several types of transforms. The analysis also usually requires a precise description of correlations (including autocorrelations) in sequences. The speaker will also give a very brief overview of his other research interests, and he will briefly trace his path to his current position at Purdue.

Differential Graded Algebras

Homology Operations in the Spectral Sequence of a Cosimplicial Space
Abstract: Given a cosimplicial space $X$, the spectral sequence of the title abuts to the mod 2 homology of $\operatorname{Tot}(X)$. If $X$ is a cosimplicial infinite loop space, then $\operatorname{Tot} (X)$ is an infinite loop space, so the target of the spectral sequence admits Araki-Kudo operations; our natural impulse is to lift these operations to the spectral sequence. This was accomplished by Jim Turner in 1998. We take a different approach and define, for any cosimplicial space $X$, external operations which land in the spectral sequence associated to $E C_2\times_{C_2} X \times X$. In the case when $X$ is a cosimplicial infinite loop space there is a cosimplicial map $E C_2\times_{C_2} X \times X \to X$ which induces the internal operations.

Dicritical Divisors and Quadratic Transformations, Part II
Abstract: The dicritical divisor coming out of integrable holonomie in dynamical systems which belong to the domain of real analysis gets miraculously married to the jacobian problem of algebraic geometry. This is a godsend for making inroads into the fortress jacobian. It also provides a sharp tool for studying local functions on algebraic as well as analytical surfaces. Although the jacobian problem is restricted to zero characteristic, it is amazing that the dicriticals, born out of real analysis, throw light on the theory of local rings of prime characteristic. We owe the real and complex theory of dicriticals to the pioneers like Artal, Cassou-Nogues, Eisenbud, Fourrier, Mattei, Moussu, Neumann, Norbury, and Rudolph. The algebraization of the dicriticals, as a tool for the jacobian problem and the mixed characteristic local ring theory, came out of Abhyankar's collaboration with Heinzer and Luengo in the Spring and Summer of 2009.The collaboration with Luengo falls in the category of what Zeilberger callsConcrete or Babylonian Mathematics in the pursuit of which he compares Abhyankarwith the physicist Feynman. The collaboration with Heinzer belongs to the category of what Glass calls Abstract Algebra in his description of Abhyankar's new book which, in its readablility, is declared by Glass to be comparable to Rawling's saga of Harry Potter. The abstract algebra of Heinzer includes the complete ideals of Zariski and Huneke as well as the Rees Rings and reductions of ideals introduced by Northcott and Rees. But it was certainly the collaboration with Luengo, who has a deep mastery of the Newton Polygon, which started off the rejuvenation process. This enabled Abhyankar to catch the spider in Sir Walter Scott's tangled web.This refers to the basic fact that the spider of the Marathi Poem ``EKA KOLIYANEEKADA APULE JALE BANDHIYELE UNCHA JAGI'' could not get back into the proverbial web which he had spun. Similarly, a point in the support of a power series which is not in its Newton Polygon cannot get into the Polygon even after quadratic transformations. Thus Sir Issac meets Sir Walter.At any rate Abhyankar continues to use the abstract complete ideals and the concrete spider to unravel the mysteries of the fireworks display coming out of special pencils in the neighborhood of a point of an algebraic or arithmetical surface. The proper transform of the pencil goes through a finite number of iterated quadratic transforms which constitute the sparks or stars of the display. Amongst them the dicriticals are the big stars.

Estimation for Nonparametric Mixture ModelsWe present an algorithm for estimation in finite mixture models where the observations are multivariate with conditionally independent coordinates but their distributions are otherwise completely unspecified. This algorithm is an extension and modification of the recent EM-like algorithm of Bordes, Chauveau, and Vandekerkhove (2007) for univariate mixture models with symmetric components, which we will also discuss. Unlike in the univariate case, the multivariate algorithm does not necessarily require an assumption on the component density functions for the model parameters to be identifiable. We explain what is known about identifiability, show why our algorithm is more appealing than other algorithms for this problem, and discuss some remaining open questions.Refreshments will be served at 4:00 PM in HAAS 111.

TBA

Quantum Decay Rates for Manifolds with Hyperbolic Ends
Abstract: Mathematically, quantum decay rates appear as imaginary parts of poles of the meromorphic continuation of Green's functions. As energy grows, decay rates are related to properties of geodesic flow and to the structure at infinity. For a cusp, infinity is "small", which typically slows decay. However, I will present a class of examples for which decay rates go to infinity with energy even in the presence of a cusp. This is part of a more general investigation of resonances on manifolds with hyperbolic ends.

TBA

Technology, Analysis, and Goals in the Ionomics of Arabidopsis(Part 1 of 3 lecture series)TBA

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Dicritical Divisors and Quadratic Transformations, Part III
Abstract: The dicritical divisor coming out of integrable holonomie in dynamical systems which belong to the domain of real analysis gets miraculously married to the jacobian problem of algebraic geometry. This is a godsend for making inroads into the fortress jacobian. It also provides a sharp tool for studying local functions on algebraic as well as analytical surfaces. Although the jacobian problem is restricted to zero characteristic, it is amazing that the dicriticals, born out of real analysis, throw light on the theory of local rings of prime characteristic. We owe the real and complex theory of dicriticals to the pioneers like Artal, Cassou-Nogues, Eisenbud, Fourrier, Mattei, Moussu, Neumann, Norbury, and Rudolph. The algebraization of the dicriticals, as a tool for the jacobian problem and the mixed characteristic local ring theory, came out of Abhyankar's collaboration with Heinzer and Luengo in the Spring and Summer of 2009.The collaboration with Luengo falls in the category of what Zeilberger callsConcrete or Babylonian Mathematics in the pursuit of which he compares Abhyankarwith the physicist Feynman. The collaboration with Heinzer belongs to the category of what Glass calls Abstract Algebra in his description of Abhyankar's new book which, in its readablility, is declared by Glass to be comparable to Rawling's saga of Harry Potter. The abstract algebra of Heinzer includes the complete ideals of Zariski and Huneke as well as the Rees Rings and reductions of ideals introduced by Northcott and Rees. But it was certainly the collaboration with Luengo, who has a deep mastery of the Newton Polygon, which started off the rejuvenation process. This enabled Abhyankar to catch the spider in Sir Walter Scott's tangled web.This refers to the basic fact that the spider of the Marathi Poem ``EKA KOLIYANEEKADA APULE JALE BANDHIYELE UNCHA JAGI'' could not get back into the proverbial web which he had spun. Similarly, a point in the support of a power series which is not in its Newton Polygon cannot get into the Polygon even after quadratic transformations. Thus Sir Issac meets Sir Walter.At any rate Abhyankar continues to use the abstract complete ideals and the concrete spider to unravel the mysteries of the fireworks display coming out of special pencils in the neighborhood of a point of an algebraic or arithmetical surface. The proper transform of the pencil goes through a finite number of iterated quadratic transforms which constitute the sparks or stars of the display. Amongst them the dicriticals are the big stars.

Refreshments will be served at 4:00 PM in HAAS 111.

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Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Technology, Analysis, and Goals in the Ionomics of Arabidopsis(Part 2 of 3 lecture series)TBA

Spatial Statistics in Environmental and Atmospheric Sciences

Refreshments will be served at 4:00 PM in HAAS 111.

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Technology, Analysis, and Goals in the Ionomics of Arabidopsis(Part 3 of 3 lecture series)TBA

Accurate asset price modeling and related statistical problems under microstructure noise

Refreshments will be served at 4:00 PM in HAAS 111.

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Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

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