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Mathematics Colloquium Schedule
Date 5-15-2015 (2pm-3pm, F03-200A), Mark Dunster, CSUSD
Title: Old and New Approximations for Bessel Functions
Abstract: Bessel functions are functions of two variables, an argument and parameter (the so-called order). They satisfy a second order linear differential equation, and also can be defined explicitly by integral representations. They are arguably the most important of the special functions, and arise naturally in a multitude of physical and mathematical applications, including heat conduction, electrostatics, scalar and electromagnetic scattering, and hydrodynamics. Here we discuss uniform asymptotic approximations involving the simpler Airy functions, which themselves are well known and important special functions. We present some classical approximations for Bessel functions, as well as some new ones for their order derivatives. The talk is accessible to upper division and graduate students having knowledge of elementary differential equations.
Date 4-24-2015 (1:30pm-2:30pm, F03-200A), Heidi Furlong and Leslie Rodriguez, CSULB
Title:Alternating Volume, a Hyperbolic Invariant of Knots
Abstract: A knot is a loop in three-dimensional space. Alternating knots are a class of knots with useful geometric properties. Using methods originally due to Blair, we define the alternating volume of a knot to be the volume of an alternating link representation of that knot. We then extend results due to Lackenby to relate the alternating volume of a knot to the twist number of a knot.
Date 4-17-2015 (12pm-1pm, F03-200A), Dr. Charis Tsikkou, West Virginia University
Title:Analysis of 2+1 Diffusive-Dispersive PDE Arising in River Braiding
Abstract: In the context of a weakly nonlinear study of bar instabilities in a river carrying sediment carrying, P. Hall introduced an evolution equation for the deposited depth which is dispersive in one spatial direction, while being diffusive in the other. In this talk, we present local existence and uniqueness results using a contraction mapping argument in a Bourgain-type space. We also show that the energy and cumulative dissipation are globally controlled in time. This is joint work with Saleh Tanveer.
Date 3-27-2015 (12pm-1pm, F03-200A), Michaela (Puck) Rombach, UCLA
Title: Graph Representatives of Positroid Strata
Abstract: This talk will be very accessible (including to grad students) and will involve juggling. The positroid stratification, studied by many authors, is a coarsening of the matroid stratification of the Grassmannian. Each graph (with orientation and edge-ordering) gives a point in the Grassmannian; for a matroid stratum to contain such a point is a well-known forbidden minor condition on the matroid. We show that, by contrast, every positroid stratum contains a graphical representative; indeed, one can choose the graph to be planar. This is despite the fact that the matroid stratum dense in the positroid stratum does not typically contain such a representative (“positroids are not graphic matroids”). Joint work with Allen Knutson.
Date 3-13-2015 (12pm-1pm, F03-200A), Shiwen Zhang, Graduate Student, UCI
Title: Can one hear the shape of a drum?---An Introduction to spectral theory in math physics
Abstract: Mark Kac raised such a problem in an article in 1966. The mathematical concept behind this problem is spectrum. Spectrum is one of many examples how physics and mathematics are so closely related. In mathematics, spectrum has been developed into deep and wide concept which is very important in several branches. The study of spectrum indeed comes from the analysis of “detectable energy level” in physics, which could be viewed as a generalization of eigenvalue problem of finite dimensional matrix. This talk intends to give a brief introduction to spectral theory towards high grade undergraduate students as well as early graduate students who are interested in math physics and related topics. I would like to introduce the rough concepts of operator and spectrum, discuss what kind of problems we are interested in spectral theory and their relation to other branches. Then I'd like to talk about the spectrum of one kind of discrete Schrodinger operator.
Date 3-6-2015 (12pm-1pm, F03-200A), Dr. Scott McCalla, Montana State University
Title: Crimes with Undergraduates
Abstract:In this talk, I will discuss two undergraduate research projects on modeling crime. The first part of the talk will concentrate on extending a model for burglary hotspot formation. Most animals, including humans, are known to make large changes in area when foraging for resources. Our extension assumes criminals will do the same when looking for possible targets to burgle. The second part will concentrate on understanding seasonal variations in crime rates. Many law enforcement personal believe simple statements like "when the temperature heats up, so does my job". We examine this ideology by extracting seasonal variations in crime rates from noisy data in the Los Angeles and Houston metropolitan areas, and then modeling this data with a stochastic differential equation.
Date 2-27-2015 (12pm-1pm, F03-200A), Paul Fish, Wolfram Technologies in Education and Research
Title: Mathematica 10 & Wolfram Alpha Pro
Abstract:This talk illustrates capabilities in Mathematica 10 and other Wolfram technologies that are directly applicable for use in teaching and research on campus.
Date 2-20-2015 (2:30pm-3:30pm, F03-200A), Casey Kelleher, UCI
Title: The Differential Geometry of the Maxwell Equations
Abstract:The Maxwell equations are a family of partial differential equations which describe the interactions of electric and magnetic fields and constitute the foundations of electromagnetic theory. While students often are introduced to this family in the physics classroom setting, these equations are seldom seen in a predominately geometric light. Approaching the Maxwell equations from this perspective is an ideal way to lay down and bolster an understanding of foundational Riemannian geometric topics, (e.g. vector fields, connections, curvature). I will both explore this viewpoint while emphasizing the underlying physical intuition.
Date 12-5-2014 (12pm-1pm, F03-200A), Dr. Konstantina Trivisa, University of Maryland
Title: A Nonlinear Model for Tumor Growth: Global in time weak solutions
Abstract:We investigate the dynamics of a class of tumor growth models known as mixed models. The key characteristic of these type of tumor growth models is that the different populations of cells are continuously present everywhere in the tumor at all times. In this work we focus on the evolution of tumor growth in the presence of proliferating, quiescent and extra cellular cells as well as a nutrient. The system is given by a multi-phase flow model and the tumor is described as a growing continuum such as both the domain as well as its boundary evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion and viscosity in the weak formulation.
Date 11-14-2014 (12pm-1pm, F03-200A), Dr. Scott Crass, CSULB
Title: Dynamics of a soccer ball
Abstract: Exploiting the symmetry of the regular icosahedron, Peter Doyle and Curt McMullen constructed a solution to the quintic equation. Their algorithm relied on the dynamics of a certain icosahedrally-symmetric map for which one of the icosahedron's special orbits consists of superattracting periodic points. In this talk, we'll consider the question of whether there are maps with icosahedral symmetry with superattracting periodic points at a 60-point orbit. The investigation leads to the discovery of two maps whose superattracting sets are configurations of points that are respectively related to a soccer ball and a companion structure. It happens that a generic 60-point attractor provides for the extraction of all five of a quintic's roots.
Date 11-7-2014 (12pm-1pm, F03-200A), Dr. Mehrdad Aliasgari, CSULB
Title: Secure Computation and its Applications
Abstract: Cryptography is often described as the science of securing information in transit. However, with recent developments in computing, there is a need to provide data security in new settings. Cloud storage and cloud computing are examples of new security challenges. Secure Multiparty Computation (SMC) is when parties wish to jointly compute a function on their private input while maintaining privacy of their inputs. In this talk, we focus on cryptographic techniques that enable us to achieve security in SMC and we discuss some of their applications.
Date 10-17-2014 (12pm-1pm, F03-200A), Dr. Diane Hoffoss, University of San Diego
Title: How Wide is a 3-Manifold?
Abstract: In this talk, we will discuss some interesting ways to define the width of a 3-manifold, and we'll consider what relationships (if any!) these various definitions might have with one another.
Date 10-10-2014 (11:15am-12:15pm, F03-200A), Dr. Dominique Zosso, UCLA
Title: Variational image segmentation with dynamic artifact detection and bias correction
Abstract: Region-based image segmentation has essentially been solved by the famous Chan-Vese model. However, this model fails when images are affected by artifacts (scars, scratches, outliers) and illumination bias that outweigh the actual image contrast. Here, we introduce a new model for segmenting such damaged images: First, we introduce a dynamic artifact class X which prevents intensity outliers from skewing the segmentation. Second, in Retinex-fashion, we decompose the image into a flattened piecewise-constant structural, and a smooth bias part, I=B+S. The CV-segmentation terms are then only acting on the structure part, and only in regions not identified as artifact. We devise an efficient alternate direction minimization scheme involving averaging for S, thresholding for X, time-split MBO-like threshold dynamics for the perimeter TV-term, and spectral solutions for the bias B.
Date 10-3-2014 (12noon-1pm, F03-200A), Dr. Blake Hunter, Claremont McKenna College
Title: Topic Point Processes
Abstract: The widespread use of social media has created a need for automated extraction of useful information making detection of trends. This is essential to gain knowledge from the vastly diverse massive volume of data. This talk explores topic modeling and self-exciting time series models applied to social media microblog data. We use topic modeling and compressed sensing to discover prevalent topics and latent thematic word associations with in topics. Modeling tweet topics over time as temporal or spatial-temporal Hawkes process allows identification of self-exciting topics and reveals relationships between topics. This talk looks at applications to Twitter microblogs, text mining, image processing and content based search.
Date 9-26-2014 (3pm-4pm, F03-200A), Dr. Matt Rathbun, CSUF
Title: Knots, Fiber Surfaces, and the Building Blocks of Life
Abstract: DNA encodes the instructions used in the development and functioning of all living organisms. The DNA molecule, however, often becomes knotted, linked, and generally entangled during normal biological processes like replication and recombination. The subject of Knot Theory, correspondingly, can inform our understanding of these processes. I will introduce Knot Theory, and some of the myriad of tools that mathematicians use to understand knots and links. In particular, I will focus on a special class of link called fibered links. I will explain some recent results, joint with Dorothy Buck, Kai Ishihara, and Koya Shimokawa, about transformations from one fibered link to another, and explain how these results are relevant to microbiology.
Date 9-19-2014 (12pm-1pm, F03-200A), Dr. Ryan Compton , HRL
Title: Geotagging One Hundred Million Twitter Accounts with Total Variation Minimization
Abstract: Geographically annotated social media is extremely valuable for modern information retrieval. However, when researchers can only access publicly-visible data, one quickly finds that social media users rarely publish location information. In this work, we provide a method which can geolocate the overwhelming majority of active Twitter users, independent of their location sharing preferences, using only publicly-visible Twitter data.
Our method infers an unknown user's location by examining their friend's locations. We frame the geotagging problem as an optimization over a social network with a total variation-based objective and provide a scalable and distributed algorithm for its solution. Furthermore, we show how a robust estimate of the geographic dispersion of each user's ego network can be used as a per-user accuracy measure, allowing us to discard poor location inferences and control the overall error of our approach.
Leave-many-out evaluation shows that our method is able to infer location for 101,846,236 Twitter users at a median error of 6.33 km, allowing us to geotag over 80% of public tweets.
Date 9-12-2014 (12pm-1pm, F03-200A), Professor Ko Honda, UCLA
Title: An invitation to Floer homology
Abstract: This is a gentle introduction to Floer homology. ``Floer homology'' is a generic term for various homology theories of knots, 3- and 4-dimensional manifolds (aka spaces), symplectic manifolds, contact manifolds, etc., and has had an enormous impact in geometry/topology since its introduction by Floer more than twenty years ago. In this talk we start with a baby version of this theory called Morse homology, which gives a way to distinguish topological spaces (e.g., a sphere from the surface of a donut). We then build our way up to more recent theories such as contact homology and embedded contact homology.