Seminars and Colloquia by Series

What is the Shortest Distance between Two Points? Well, Maybe That's Not the Right Question.

Series
Other Talks
Time
Friday, July 15, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Kaye Husbands Fealing, Chair and Professor – School of Public Policy, Georgia Tech
At a recent leadership training workshop, where chairs, deans and provosts engaged in "Vegas Rules" discussions about how to develop talent in staff and ourselves, I was asked the question-What was the thing that I enjoyed most during my childhood? Of course I responded: Solving math problems fast! But how does that relate to my research on pricing strategies in the automotive industry, technological aspirations in the developing-country context, earnings and employment differentials by race/ethnicity and gender in various market sectors, and return on investment in food safety research? The answers to this question will be the focus of this talk. The key takeaways will be that pathways meander, enjoy scientific explorations, and the quickest pathway to the crown of one's career is not necessarily the most fulfilling.

Limits to estimating the severity of emerging epidemics due to inherent noise

Series
Mathematical Biology Seminar
Time
Wednesday, July 6, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bradford Taylor – School of Biology, Georgia Tech

Please Note: When a disease outbreak occurs, mathematical models are used to estimate the potential severity of the epidemic. The average number of secondary infections resulting from the initial infection or reproduction number, R_0, quantifies this severity. R_0 is estimated from the models by leveraging observed case data and understanding of disease epidemiology. However, the leveraged data is not perfect. How confident should we be about measurements of R_0 given noisy data? I begin my talk by introducing techniques used to model epidemics. I show how to adapt standard models to specific diseases by using the 2014-2015 Ebola outbreak in West Africa as an example throughout the talk. Nest, I introduce the inverse problem: given real data tracking the infected population how does one estimate the severity of the outbreak. Through a novel method I show how to account for both inherent noise arising from discrete interactions between individuals (demographic stochasticity) and from uncertainty in epidemiological parameters. By applying this, I argue that the first estimates of R_0 during the Ebola outbreak were overconfident because demographic stochasticity was ignored. This talk will be accessible to undergraduates.

Algebraic models of gene regulatory networks

Series
Mathematical Biology Seminar
Time
Wednesday, June 29, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Elena Dimitrova – Clemson University
Progress in systems biology relies on the use of mathematical and statistical models for system level studies of biological processes. This talk will focus on discrete models of gene regulatory networks and the challenges they present, in particular data selection and model stability. Careful data selection is important for model identification since the process is sensitive to the amount and type of data used as input. We will discuss a criterion for deciding when a set of data points identifies an algebraic model with special minimality properties. Stability is another important requirement for models of gene regulatory networks. Canalizing functions, a particular class of Boolean functions, show stable dynamic behavior and are thus suitable for expressing gene regulatory relationships. However, in practice, relaxing the canalizing requirement on some variables is appropriate. We will present the class of partially nested canalizing functions and some of their properties and applications.

An Algebraic Introduction to Multiview Geometry and Tensors

Series
Algebra Seminar
Time
Monday, June 27, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Luke Oeding – Auburn University
In Multiview Geometry, a field of Computer Vision one is interested in reconstructing 3-dimensional scenes from 2-dimensional images. I will review the basic concepts in this area from an algebraic viewpoint, in particular I'll discuss epipolar geometry, fundamental matrices, and trifocal and quadrifocal tensors. I'll also highlight some in open problems about the algebraic geometry that arise.This will be an introductory talk, and only a background in basic linear algebra should be necessary to follow.

Some hyperbolic non-fillable manifolds

Series
Geometry Topology Seminar
Time
Thursday, June 23, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yajing Liu – UCLA
Existence of tight contact structures is a fundamental question of contact topology. Etnyre and Honda first gave the example which doesn't admit any tight structure. The existence of fillable tight structures is also a subtle question. Here we give some new examples of hyperbolic 3-manifolds which do not admit any fillable structures.

Log-Hilbert-Schmidt distance between covariance operators and their applications

Series
Applied and Computational Mathematics Seminar
Time
Wednesday, June 22, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dr. Ha Quang, Minh – Istituto Italiano di Tecnologia (Italy)
Symmetric positive definite (SPD) matrices play important roles in numerous areas of mathematics, statistics, and their applications in machine learning, optimization, computer vision, and related fields. Among the most important topics in the study of SPD matrices are the distances between them that can properly capture the geometry of the set of SPD matrices. Two of the most widely used distances are the affine-invariant distance and the Log-Euclidean distance, which are geodesic distances corresponding to two different Riemannian metrics on this set. In this talk, we present our recently developed concept of Log-Hilbert-Schmidt (Log-HS) distance between positive definite Hilbert-Schmidt operators on a Hilbert space.This is the generalization of the Log-Euclidean distance between SPD matrices to the infinite-dimensional setting. In the case of reproducing kernel Hilbert space (RKHS) covariance operators, we obtain closed form formulas for the Log-HS distance, expressed via Gram matrices. As a practical example, we demonstrate an application of the Log-HS distance to the problem of image classification in computer vision.

What states in which to (not) commit a crime

Series
Mathematical Biology Seminar
Time
Wednesday, June 22, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Emily Rogers – Georgia Tech
Although DNA forensic evidence is widely considered objective and infallible, a great deal of subjectivity and bias can still exist in its interpretation, especially concerning mixtures of DNA. The exact degree of variability across labs, however, is unknown, as DNA forensic examiners are primarily trained in-house, with protocols and quality control up to the discretion of each forensic laboratory. This talk uncovers the current state of forensic DNA mixture interpretation by analyzing the results of a groundbreaking DNA mixture interpretation study initiated by the Department of Defense's Defense Forensic Science Center (DFSC) in the summer of 2014. This talk will be accessible to undergraduates.

Macaulay dual spaces and local Hilbert function

Series
Algebra Seminar
Time
Monday, June 20, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Robert Krone – Queen's University
The Macaulay dual space offers information about a polynomial ideal localized at a point such as initial ideal and values of the Hilbertfunction, and can be computed with linear algebra. Unlike Gr\"obner basis methods, it is compatible with floating point arithmetic making it anatural fit for the toolbox of numerical algebraic geometry. I willpresent an algorithm using the Macaulay dual space for computing theregularity index of the local Hilbert function.

Diffusion-Based Metrics for Biological Network Analysis

Series
Mathematical Biology Seminar
Time
Thursday, June 16, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Lenore Cowen – Tufts University
In protein-protein interaction (PPI) networks, or more general protein-protein association networks, functional similarity is often inferred based on the some notion of proximity among proteins in a local neighborhood. In prior work, we have introduced diffusion state distance (DSD), a new metric based on a graph diffusion property, designed to capture more fine-grained notions of similarity from the neighborhood structure that we showed could improve the accuracy of network-based function-prediction algorithms. Boehnlein, Chin, Sinha and Liu have recently shown that a variant of the DSD metric has deep connections to Green's function, the normalized Laplacian, and the heat kernel of the graph. Because DSD is based on random walks, changing the probabilities of the underlying random walk gives a natural way to incorporate experimental error and noise (allowing us to place confidence weights on edges), incorporate biological knowledge in terms of known biological pathways, or weight subnetwork importance based on tissue-specific expression levels, or known disease processes. Our framework provides a mathematically natural way to integrate heterogeneous network data sources for classical function prediction and disease gene prioritization problems. This is joint work with Mengfei Cao, Hao Zhang, Jisoo Park, Noah Daniels, Mark Crovella and Ben Hescott.

Finding binomials in polynomial ideals

Series
Algebra Seminar
Time
Monday, June 13, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Anders Jensen – TU-Kaiserslautern / Aarhus University
Deciding if a polynomial ideal contains monomials is a problem which can be solved by standard Gr\"obner basis techniques. Deciding if a polynomial ideal contains binomials is more complicated. We show how the general case can be reduced to the case of a zero-dimensional ideals using projections and stable intersections in tropical geometry. In the case of rational coefficients the zero-dimensional problem can then be solved with Ge's algorithm relying on the LLL lattice basis reduction algorithm. In case binomials exists, one will be computed.This is joint work with Thomas Kahle and Lukas Katthän.

Pages