California Polytechnic State University

Colloquium Schedule

• Improving Mathematics Teaching: A Journey Beyond TIMSS Video
  James Stigler, UCLA
  
  Abstract
  Videos of classroom teaching collected as part of the Third International Mathematics and Science Study reveal that teaching is a cultural activity, varying more across cultures than within. It is learned implicitly; it is largely based on hidden cultural scripts; it is embedded in wider cultural beliefs and practices; and it is difficult to change. Given these facts, how can teaching be improved? In this presentation Professor Stigler will briefly describe most recent findings from the TIMSS Video Studies of mathematics and science teaching in seven countries, and discuss the implications of these findings for:
  • current debates about mathematics teaching and learning in schools, and
  • efforts to improve teaching through professional development.

 

• Detecting Inner Automorphisms of Right-Angled Coxeter Groups
  Anton Kaul, Mathematics Department, Cal Poly
  
  Abstract
  Group theoretic decision problems were originally formulated by Max Dehn (ca. 1912) in an effort to answer questions in topology. Since that time, decision problems have played a major role in the development of combinatorial and geometric group theory. One such problem is known as the generalized word problem or Magnus problem. Given a group G with generating set A and a subgroup H of G, a solution to the generalized word problem for H in G is an algorithm that takes as input a word w in the free group with basis A and decides whether w represents an element of H or not.
  
  Let W be a right-angled Coxeter group. In this talk I will describe an algorithm, developed jointly with Matthew White, that solves the generalized word problem for Inn(W) in Aut(W).

 

• Bioassay Data Analysis via Robust Nonlinear Regression
  Ryan Brown, Amgen
  
  Abstract
  Bioassays are types of in vitro experiments, typically used for measuring pharmacological characteristics of developmental substances. Such assays require analysis of high throughput screening (HTS) dose-response data. The traditional approach of Iterative Nonlinear Least Squares (INLS) is sensitive to outliers and therefore may produce inaccurate results. Often, outliers are manually removed from datasets and the regression is performed for a second time; such a methodology allows for subjective analysis, which may result in bias or inconsistency.
  
  To avoid subjectivity, more robust statistical techniques should be applied. We choose maximum likelihood estimation methods (M-estimates) as a means of performing robust nonlinear regression. In general, such robust methods have the advantage that all data points are taken into account, by progressively reducing the weighting of the outlying observations.
  Regarding analysis of data produced by HTS using M-estimates and robust INLS, the following topics are addressed:
  • What is the need for robust regression techniques
  • Contextual requirements
  • Choosing a data model
  • How to initialize the model
  • Robust nonlinear least squares using M-estimates
  • Constructing average data series from replicate data
  • Global fit using replicate data
  • Java implementation
  • Future concerns
  • Acknowledgements and conclusions

 

• A Nonlinear System Describing an Irreversible Process
  Weiqing Xie, Cal Poly Pomona
  
  Abstract
  http://math.calpoly.edu/xie.pdf

 

• Approximating the Norm of Composition Operators on the Dirichlet Space
  Marian Robbins, Mathematics Department, Cal Poly
  
  Abstract
  http://math.calpoly.edu/robbins.pdf

 

• California Currents of the Arctic Ocean
  Greg Holloway, Institute of Ocean Sciences, Sidney, BC, Canada
  
  Abstract
  The California Current, on eastern rim of subtropical gyre, is characterized by broad, shallow near-surface flow to the south overlying a narrow, deep Undercurrent to the north. Upwelling is prevalent. Similar circumstances are seen in the southern Beaufort Sea where surface flow is broadly westward over narrow, eastward undercurrent. Indeed such flow regimes are repeated throughout the world's oceans. Why? Classical mechanics, the basis for modern ocean dynamics, solves for fluids that are pushed and pulled, hence for what "pushes" any current. Statistical mechanics, treating the aggregate of innumerable "mechanical" interactions, reveals collective behavior beyond pushes and pulls. We consider California Current regimes (worldwide) from statistical mechanical perspective.

• How to Recognize Finiteness of Gorenstein Homological Dimensions
  Lars Winther Christensen, Department of Mathematics, University of Nebraska - Lincoln
  
  Abstract
  It is a maxim in ring theory that understanding a ring is tantamount to understanding its modules. One way of analyzing a given module is to approximate it by modules from a class that is already well-understood. This idea leads to the concept of homological dimensions. A classical example is approximation by free modules which leads to the concept of projective dimension. A module has finite homological dimension if an approximation can be achieved in finitely many steps, and experience shows that such modules have special properties. Hence, it becomes important to detect if a given module has finite homological dimension, possibly without explicitly constructing an approximation. Experience points to vanishing of (co)homology as a detection mechanism. For a family of dimensions, known as Gorenstein homological dimensions, such an alternative way to detect finiteness has long been sought. I will survey the background for this problem and describe a solution that works for the rings encountered in algebraic geometry.

 

• Wave propagations in the secondary forest succession
  Xiaojie Hou
  Department of Mathematical Sciences, University of Cincinnati
  
  Abstract
  The secondary forest succession is caused by the interaction between pioneer and climax tree species. Such interaction is modeled by a reaction diffusion system. The succession can be described by traveling wave solutions connecting the initial and final stage of the succession. Under some mild conditions, we show the existence, uniqueness, asymptotics and stability of the traveling wave solutions in the model system. The implications of the results are very interesting: the succession is wave-like; the wave has certain shape and maintains certain speed (existence); in the final stage of the succession, the rate that the pioneer tree species leaving the site is proportional to that of the climax tree species entering the site (asymptotics); the same wave can also be observed at other time and location (uniqueness except a shifting of origin); the succession is delicate, any big disturbance can disrupt the process (local stability in the exponentially weighted Banach spaces). Another interesting finding is the failure of the K-Selection due to the Allee effect in the climax tree species.

 

• Counting Descents with Specified Equivalences mod k
  Jeff Liese, University of California, San Diego
  
  Abstract

 

• Pattern Detection in Multivariate Time Series
  Charles Camp, Seattle University
  
  Abstract
  Multivariate time series consist of simultaneous measurements of multiple variables for observations taken at ordered moments in time, e.g., atmospheric temperature measured monthly at different spatial locations. Since many data records are both short (with respect to the time scales of interest) and noisy (in the sense that there are many processes which interact to create the data record), it is often difficult to extract information about the underlying processes creating the data. Techniques which simultaneously analyze the full multivariate data set offer a large improvement over techniques which analyze each time series independently since they have access to more information. However, since the time series of each variable are usually highly correlated, much of this additional information is redundant. There are two fundamental and related issues: Can we use the added information of a multivariate record to better isolate the underlying processes? Can we reduce the redundancy of information by reducing the dimensionality of the data set? In other words, can we find an underlying pattern which captures the fundamental behavior of the data? We will discuss some multivariate analysis techniques in the context of the interannual variability of the Earth's atmosphere.

 

• An Inverse Problem Arising in Cardiology
  Carl Toews, Institute for Mathematics and its Applications, University of Minnesota
  
  Abstract
  This talk is motivated by an inverse problem that arises in connection with a medical application. In order to treat atrial fibrilation, the electrical activity on the heart must be imaged and the cardiac wall mapped. This is done by inserting a probe whose position within the heart chamber needs to be known. One approach is to estimate this position by applying three orthogonal voltage potentials across the body, and for each potential collecting data corresponding to voltages at the probe. Were the fields linear, the probe position could be read directly from the voltage data, but the unknown conductivity of the medium surrounding the chamber induces nonlinear fields, and the problem becomes an inverse problem for which the objective is to simultaneously determine the probe position and the fields. The first half of the talk will be a tutorial introduction to the field of inverse problems, highlighting important concepts and techniques. It will dwell on several illuminating applications in both pure and applied mathematics. The second half takes a detailed look at our solution to the position registration problem within the framework of these ideas.

 

• On Correlation Polynomials and Subword Complexity
  Irina Gheorghiciuc
  
  Abstract

 

• Cells, Collisions, Curvature: An Introduction to Combinatorial Topology
  Jens Harlander, Wester Kentucky University
  
  Abstract
  In 1993 the Russian mathematician Anton Klyachko observed the following property which he described as "suitable for a school mathematics tournament":
  
  Given a tesselated 2-sphere, i.e. a subdivision of the surface of the ball into regions. Let a car drive around the boundary of each region in an anti-clockwise direction. The cars travel at arbitrary speed, never stop and visit each point on the boundary infinitely often. Then there must be at least two places on the sphere where complete crashes occur.
  
  He used this result to prove the Kervaire Conjecture for torsion-free groups (which had been open for 30 years). In my talk I will discuss Klyachko's Car Crash Lemma and other properties of the 2-sphere and give applications to combinatorial topology and group theory.

 

• Central Schemes for Shallow Water Flows along Channels with Irregular Geometry
  Jorge Balbas
  
  Abstract
  We present a new high-resolution, non-oscillatory semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme extends an existing central semi-discrete formulation for hyperbolic conservation laws and it enjoys two properties crucial for the accurate simulation of shallow water flows: it preserves the positivity of the water height, and it is well balanced, i.e., the source terms arising from the geometry of the channel are discretized so as to balance the non-linear hyperbolic fluxes --a condition necessary to correctly approximate steady-state solutions. Along with a detailed description of the scheme and its properties, we present several numerical experiments --including the approximation of exact equilibrium solutions-- that demonstrate the robustness --and simplicity-- of the numerical algorithm.

 

• Composition Operators on Spaces of Analytic Functions
  Christopher Hammond, Connecticut College (visiting Cal Poly)
  
  Abstract
  This talk will provide an introductory survey of the study of composition operators acting on Hilbert spaces of analytic functions. We will begin with the relevant definitions and consider the motivation for studying such operators. We will discuss a number of problems that have attracted attention in recent years, including ones relating to the spectrum, adjoint, and norm of a composition operator, as well as the component structure of spaces of composition operators.

• Adjoints of Certain Composition Operators
  Jennifer Moorhouse, Colgate University
  
  Abstract

   

• What is an Angle in Higher Dimensions?
  Sinai Robins, Temple University
  
  Abstract
  We first introduce the notion of an angle in higher dimensions, and then ask how these higher dimensional angles are related to each other. To answer this question, we introduce combinatorial-type theta functions, with respect to a polyhedral cone in R^d. As a consequence of some asymptotics, we retrieve new types of identities for solid angles of polyhedral domains that come from a simple polytope.
  
  These results extend the well-known Gram relations for solid angles of polytopes, from the 1860's.

 

• Fair Division Problems: Cake-Cutting and Convexity
  Ted Hill, Emeritus Professor, Georgia Tech
  Research Scholar in Residence, Cal Poly
  
  Abstract
  The general subject of this talk will be the question of whether an object (such as a cake or piece of land) can be divided among a number of people so that each receives a portion he considers a fair share, according to his own values. (Formally, there are n measures on the same object - a measurable space - and a typical goal is to find a partition of the object into n pieces so that the minimum value of the i-th measure on the i-th piece is as large as possible.) Classical problems such as Steinhaus' "Cake-cutting Algorithm" and "Ham Sandwich Problem", Neyman and Pearson's "Bisection Problem", and Fisher's "Problem of the Nile" will be mentioned, and several recent results and open problems concerning Lyapounov's Convexity Theorem will be discussed, along with applications to disarmament, dividing inheritances, and selection of college deans or department chairs.

 

• The Median is the Message, or
  Where's the Hub?
  Kent Morrison, Chair, Mathematics Department, Cal Poly
  
  Abstract
  The original shipping strategy of FedEx is to fly all packages to a hub location during the afternoon and evening, sort them there, and then fly them to their destinations during the night for delivery the next day. This talk deals with the problem of finding the optimal hub. The mathematical problem is this: given a random sender and receiver, what is the location of the hub that minimize the expected distance from the sender to the receiver via the hub? Along the way we will compare FedEx's choice to the optimal solution and examine the Census Bureau's definition of the U.S. population center.

 

• Discrete and Combinatorial Mathematics for Preservice Teachers - A Non-Traditional Approach
  Richard Grassl, School of Mathematical Sciences, University of Northern Colorado
  
  Abstract
  Discrete and combinatorial mathematics is receiving increased attention in teacher preparation programs. Given the rapidly changing needs of our secondary educators, it is incumbent upon those of us responsible for preparing these teachers to stay current in reform efforts and to incorporate successful teaching into preservice teacher undergraduate courses such as discrete mathematics. This presentation will focus on several strands: The method of content delivery, how content can be "spiraled through the curriculum", the advantages of using technology, connections (especially to calculus), data collection-conjecturing-proving, multiple representations (geometric interpretations of combinatorial identities), integration of problem solving and proof techniques, and challenging problems. Specific examples will illustrate use of cooperative groups, voicing, visual approaches, and dovetailing content with methods.

• Spectral Dominance and Commuting Chains
  Ilya Spitkovsky, College of William and Mary, Williamsburg, Virginia
  
  Abstract
  A positive semi-definite (PSD) operator A "spectrally dominates" a PSD operator B if A^t-B^t is PSD for all t > 0. We (i) give a new characterization of spectral dominance in finite dimensions in terms of a monotonic chain of intermediate, pairwise commuting operators and (ii) determine for which pairs {A;B} spectral dominance persists under the taking of arbitrary compressions. Earlier results about spectral dominance are proven (in finite dimensions) in new ways, and several corollary observations are made.
  
  This is a joint work with Charlie Johnson and Bich Hoai, started during the REU program at William and Mary in the summer of 2006 (and is accessible for undergraduates).

CP Home • CP Find It

Get Adobe Reader • Microsoft Viewers

Credits

Last Update: mm/dd/yyyy

Department of Mathematics
California Polytechnic State University
San Luis Obispo, CA 93407-0403
805.756.2206
math@calpoly.edu