Mathematics Colloquium Schedule

Fall 2014


More coming ...


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.