Department of Mathematics
Applied Mathematics Seminar, Fall 2014

Mondays 3:55 PM - 5:00 PM, LCB 222

September 19, Joint Stochastics/Applied Math/Math Biology Seminar, Note Time 3:00 - 4:00 pm, Room LCB 219
Speaker: Peter Bossaerts, Finance Department, University of Utah
Title: Human reaction to extreme events and its biological foundations
Abstract:The talk will discuss recent work on how humans react to extreme events. A deeper understanding of human reactions requires proper definition of an extreme event (linking it to the concept of an outlier in statistical analysis) and its nature (distinguishing between leptokurtic and platykurtic settings, and whether the outlier is transient or reflects more persistent changes). Evidently, the noradrenergic system in the human brain provides crucial support for tracking outliers, while signals in the anterior insula allow humans to distinguish between transient and fundamental outliers. Overall, human reaction to outliers that signal fundamental changes is better adapted than reaction to transient outliers. The latter type of outlier is ubiquitous in modern large-scale social institutions, however, such as financial markets, internet and air traffic.

September 22
Speaker: Tatyana Sorokina, Department of Mathematics, Towson University
Title: Dimension of splines and intrinsic supersmoothness
Abstract:The phenomenon, known as``supersmoothness" was first observed for bivariate splines and attributed to the polynomial nature of splines. Using only standard tools from multivatiate calculus it is easy to show that if we continuously glue two smooth functions along a curve with a ``corner", the resulting continuous function must be differentiable at the corner, as if to compensate for the singularity of the curve. Moreover, locally, this property characterizes non-smooth curves. We generalize this phenomenon to higher order derivatives. Additionally, we show how supersmoothness helps to find dimension of multivariate splines.
This talk is a part of the special session of CMDS13.

September 29
Speaker: Graeme Milton, Department of Mathematics, University of Utah
Title: The searchlight effect in hyperbolic media
Abstract:Hyperbolic media in which the dielectric tensor has both positive and negative eigenvalues have been shown to defeat the diff raction limit, and allow features at very small wavelengths to be resolved as demonstrated through hyperlenses. Even in quasistatics the underlying equation resembles a wave equation. Whereas a circular hole in a dielectric media has a simple dipolar field around it, we will see that a circular hole in an almost lossless hyperbolic media, has surrounding quasistatic fields which diverge along characteristic lines tangent to the hole, and which have finite total energy absorption along these lines, even as the loss in the media tends to zero. In a hyperbolic medium a dipole with small polarizability can dramatically influence the dipole moment of a distant polarizable dipole, if it is appropriately placed. We call this the searchlight e ffect, as the enhancement depends on the orientation of the line joining the polarizable dipoles and can be varied by changing the frequency. For some particular polarizabilities the enhancement can actually increase the further the polarizable dipoles are apart, like the way quarks interact more strongly the further they are apart.
Graeme Milton, R.C.McPhedran, A. Sihvola

October 6
Speaker: Maxence Cassier, Department of Mathematics, University of Utah
Title: Analysis of two time-dependent wave propagation phenomena: 1) Space-time focusing on unknown scatterers; 2) Limiting amplitude principle in a medium composed of a dielectric and a metamaterial.
Abstract:This talk consists of two independent parts related to my Ph.D research thema. In the first one, we are motivated by this challenging question: in a propagative medium which contains several unknown scatterers, how can one generate a wave that focuses selectively on one scatterer not only in space, but also in time? In other words, we look for a wave that "hits hard at the right spot". The technique proposed here is based on DORT method (French acronym for Decomposition of the Time Reversal Operator) which leads to space focusing properties in the frequency domain. The second part is devoted to a transmission problem between a dielectric and a metamaterial. The question we consider here is the following : does the limiting amplitude principle hold in such a medium? This principle defines the stationary regime as the large time asymptotic behavior of a system subject to a periodic excitation. An answer is proposed here in the case of an infinite two-layered medium composed of a dielectric and a particular metamaterial (Drude model).

October 20
Speaker: Andrejs Treibergs, Department of Mathematics, University of Utah
Title: Which Electric Fields are Realizable in Conducting Materials?
Abstract:The usual problem is that we are given the conductivity $\sigma$ and seek the electric field in the material, $\nabla u$, by solving the conductivity equation for the potential $$ \operatorname{div}(\sigma\nabla u) = 0. $$ We ask instead, given a field $\nabla u$, is it possible to find a conductivity scalar or matrix $\sigma$ to satisfy the conductivity equation? In other words, is the field is realizable? We show periodic fields are isotropically realizable by solving a first order PDE, although the conductivity may not be periodic. We can characterize fields that are isotropically realizable by a periodic conductivity. We also give conditions for periodic realizability by matrix conductivities.

This is joint work with Marc Briane and Graeme Milton.

October 27
Speaker: Elena Cherkaev, Department of Mathematics, University of Utah
Title: Spectral representation for composite materials in forward and inverse homogenization problems
Abstract:The spectral representation of the effective properties of composites is a Stieltjes analytic representation which relates the n-point correlation functions of the microstructure to the moments of the spectral measure of an operator depending on the geometry of composite. The talk discusses an inverse homogenization problem of deriving information about the microgeometry from known effective properties, the approach is based on reconstruction of the spectral measure. The spectral measure which contains all information about the microstructure, can be uniquely recovered from effective measurements known in an interval of frequency. In particular, the volume fractions of materials in the composite and an inclusion separation parameter, as well as the spectral gaps at the ends of the spectral interval, can be uniquely reconstructed. I will discuss identification of microstructural parameters from electromagnetic and viscoelastic effective measurements and show an extension to nonlinear composites.

November 3
Speaker: Braxton Osting, Department of Mathematics, University of Utah
Title: Geometric methods for graph partitioning
Abstract: Several geometric methods for graph partitioning have been introduced in the past few years, with wide applications in clustering, community detection, and image analysis. These methods, which I'll review, are built on graph-based analogues of total variation, motion by mean curvature, the Ginzburg-Landau functional, and the Merriman-Bence-Osher threshold dynamics. In this talk, I'll discuss a new graph partitioning method where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. The resulting eigenvalue optimization problem can be solved by a rearrangement algorithm, which we show to converge in a finite number of iterations to a local minimum of a relaxed objective function. The method compares well to state-of-the-art approaches when applied to clustering problems on graphs constructed from synthetic data, MNIST handwritten digits, and manifold discretizations. The model has a semi-supervised extension and provides natural representatives for the clusters as well.

November 10
Speaker: Varun Shankar, Department of Mathematics, University of Utah
Title: A Radial Basis Function (RBF)-based Leray Projection Method for the Incompressible Stokes and Navier-Stokes equations

November 17
Speaker: Benjamin Webb, Department of Mathematics, Brigham Young University
Title: TBA

November 24
Speaker: Dongbin Xiu, Department of Mathematics and Scientific Computing and Imaging (SCI) Institute, University of Utah
Title: TBA

December 1
Speaker: Andrej Cherkaev, Department of Mathematics, University of Utah
Title: TBA

December 8
Speaker: Ben Adcock, Department of Mathematics, Simon Fraser University
Title: TBA

Seminar organizer: Yekaterina Epshteyn (epshteyn (at)

Past lectures: Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Spring 2006, Fall 2005, Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003, Fall 2002, Spring 2002, Fall 2001, Spring 2001, Fall 2000, Spring 2000, Fall 1999, Spring 1999, Fall 1998, Spring 1998, Winter 1998, Fall 1997, Spring 1997, Winter 1997, Fall 1996, Spring 1996, Winter 1996, Fall 1995.

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