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Eberly College of Science Mathematics Department

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August 1st, 2013 (10:00am - 12:00pm)
Seminar: Ph.D. Thesis Defense
Title: "Dolbeault dga of a formal neighborhood"
Speaker: Shilin Yu, Adviser: Nigel Higson, Penn State
Location: MB106

We will define a differential graded algebra (dga) for the formal neighborhood of a closed embedding of complex manifolds, which plays the role of Dolbeault complex in complex geometry. Using this dga, we obtain a dg-categorical description of the category of coherent sheaves over the formal neighborhood following Jonathan Block and generalize a result by Kapranov on diagonal embeddings.

August 26th, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Basics of Isogeometric Analysis and Computational Fluid—Structure Interaction
Speaker: Yuri Bazilevs, University of California, San Diego
Location: MB114
Abstract: http://ristretto.ucsd.edu/~bazily/Site/Home.html

In this presentation I will cover the basics of Isogeometric Analysis (IGA), a new computational technology that aims at integrating engineering design and analysis. I will also present background material on computational fluid—structure interaction (FSI). The presentation is aimed at covering the basic concepts in these areas prior to the Colloquium presentation.

August 26th, 2013 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Computational Fluid—Structure Interaction: Methods and Applications
Speaker: Yuri Bazilevs, University of California, San Diego
Location: MB106
Abstract: http://ristretto.ucsd.edu/~bazily/Site/Home.html

A framework for computational fluid—structure interaction based on the Arbitrary Lagrangian—Eulerian formulation is presented. The fluid—structure interface discretization is assumed to be nonmatching allowing for the coupling of standard finite-element and isogeometric discretizations for the fluid and structural mechanics parts, respectively. FSI coupling strategies and their implementation in the high-performance parallel computing environment are discussed. Simulations of engineering systems at vastly different spatial scales, including cardiovascular medical devices, surface ships, and wind turbines are presented, and the corresponding computational challenges are addressed.

August 27th, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Organizational meeting
Speaker: Stephen G. Simpson, Pennsylvania State University
Location: MB315
August 27th, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Groupoid crossed-modules and cohomology
Speaker: Jean-Louis Tu, Universite de Lorraine, Metz
Location: MB106

It is well-known that bundle gerbes on a manifold, possibly endowed with an action of a Lie group, can be defined in terms of central extensions of Lie groupoids, which are classified by a second cohomology group. In this talk, we will explain the analogue for bundle 2-gerbes, and see how the language of groupoids can conveniently explain the existence of a product in equivariant twisted K-theory.

August 27th, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Ergodicity of irrational billiards, I
Speaker: Giovanni Forni, University of Maryland
Location: MB216
August 29th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Ordinary reductions and F-singularities
Speaker: Karl Schwede, Penn State
Location: MB106

I will discuss recent work of Bhargav Bhatt, myself and Shunsuke Takagi relating several open problems. First: whether a smooth complex variety is ordinary after reduction to characteristic $p > 0$ for infinitely many $p$. Second: that multiplier ideals reduce to test ideals for infinitely many $p$ (regardless of coefficients). Finally, whether complex varieties with Du Bois singularities have $F$-injective singularities after reduction to infinitely many $p > 0$.

August 29th, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: What is noncommutative geometry?
Speaker: John Roe, Penn State University
Location: MB106
August 29th, 2013 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: A model for cortical spreading depression with neurovascular coupling
Speaker: Robert Miura, New Jersey Institute of Technology
Location: MB114

Cortical spreading depression (CSD) is a slowly propagating wave of ionic and metabolic disturbances in cortical brain tissue. In addition to massive cellular depolarization, CSD involves significant changes in tissue perfusion and metabolism. CSD has been linked to migraine with aura, which affects about 30% of all people who suffer from migraine. The triggers for this disease are mainly undiagnosed. To devise rational treatments of migraine with aura, we need to learn much more about the brain and about CSD. CSD was discovered almost 70 years ago by A.A.P. Leão, a Brazilian physiologist during his PhD research on epilepsy at the Harvard Medical School. CSD is characterized by nonlinear chemical waves that propagate at very slow speeds, on the order of mm/min, in the cortex of different brain structures in various experimental animals, and occurs in humans. CSD waves generate massive changes in extracellular ion concentrations. In this talk, I will review some of the characteristics of CSD wave propagation and describe some of the mechanisms that are believed to be important for CSD. We develop a new mathematical model for CSD consisting of coupled nonlinear ODEs and PDEs that describe ionic diffusion and cellular membrane potentials. We account for the sodium-potassium ATPase, responsible for cellular polarization and recovery from CSD, which operates at a rate that is dependent on local oxygen concentration. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree. Our model replicates the qualitative and quantitative behavior of CSD found in experimental studies and elucidates the effect of oxygen deprivation on CSD recovery. Our key findings are that during CSD, the metabolic activity of the cortex exceeds the normal physiological limits placed on oxygen delivery and changes in perfusion alter the intensity and duration of the event. The combination of experimentation and modeling should accelerate our understanding of how these mechanisms conspire to form CSD.

August 29th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

August 30th, 2013 (12:00pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport
Speaker: Bin Zheng, Pacific Northwest National Laboratory
Location: MB315

We have developed efficient numerical algorithms for solving 3D steady-state Poisson-Nernst-Planck (PNP) equations with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by a finite difference scheme and solved iteratively using the Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Then, the algebraic multigrid method is applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed, which reduces computational complexity from $O(N^2)$ to $O(N\log N)$, where $N$ is the number of grid points. Integrals involving the Dirac delta function are evaluated directly by coordinate transformation, which yields more accurate results compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for lithium-ion (Li-ion) batteries are shown to be in good agreement with the experimental data and the results from previous studies.