Seminars and Colloquia by Series

Latent voter model on Locally Tree Like Random graphs

Series
IMPACT Distinguished Lecture
Time
Friday, March 17, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rick Durett – Duke University –
In the latent voter model, which models the spread of a technology through a social network, individuals who have just changed their choice have a latent period, which is exponential with rate λ during which they will not buy a new device. We study site and edge versions of this model on random graphs generated by a configuration model in which the degrees d(x) have 3 ≤ d(x) ≤ M. We show that if the number of vertices n → ∞ and log n << λn << n then the latent voter model has a quasi-stationary state in which each opinion has probability ≈ 1/2 and persists in this state for a time that is ≥ nm for any m <∞. Thus, even a very small latent period drastically changes the behavior of the voter model.

Spatial Evolutionary Games

Series
IMPACT Distinguished Lecture
Time
Thursday, March 16, 2017 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rick Durrett – Duke University –
The use of evolutionary game theory biology dates to work of Maynard-Smith who used it to explain why most fights between animals were of the limited war type. Nowak and collaborators have shown that a spatial distribution of players can explain the existence of altruism, which would die out in a homogeneously mixing population. For the last twenty years, evolutionary games have been used to model cancer. In applications to ecology and cancer, the system is not homogeneously mixing so it is important to understand how space changes the outcome of these games. Over the last several years we have developed a theory for understanding the behavior of evolutionary games in the weak selection limit. We will illustrate this theory by discussing a number of examples. The most recent work was done in collaboration with a high school student so the talk should be accessible to a broad audience.

Genome-scale estimation of the Tree of Life

Series
IMPACT Distinguished Lecture
Time
Monday, October 17, 2016 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tandy Warnow – The University of Illinois at Urbana-Champaign
Estimating the Tree of Life is one of the grand computational challenges in Science, and has applications to many areas of science and biomedical research. Despite intensive research over the last several decades, many problems remain inadequately solved. In this talk I will discuss species tree estimation from genome-scale datasets. I will describe the current state of the art for these problems, what is understood about these problems from a mathematical perspective, and identify some of the open problems in this area where mathematical research, drawing from graph theory, combinatorial optimization, and probability and statistics, is needed. This talk will be accessible to mathematicians, computer scientists, probabilists and statisticians, and does not require any knowledge of biology. (Refreshments will be served after the talk.)

Geometric graph-based methods for high dimensional data

Series
IMPACT Distinguished Lecture
Time
Thursday, March 17, 2016 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Andrea Bertozzi – UCLA –
We present new methods for segmentation of large datasets with graph based structure. The method combines ideas from classical nonlinear PDE-based image segmentation with fast and accessible linear algebra methods for computing information about the spectrum of the graph Laplacian. The goal of the algorithms is to solve semi-supervised and unsupervised graph cut optimization problems. I will present results for image processing applications such as image labeling and hyperspectral video segmentation, and results from machine learning and community detection in social networks, including modularity optimization posed as a graph total variation minimization problem.

Seismic inverse problems

Series
IMPACT Distinguished Lecture
Time
Tuesday, October 27, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor Maarten de Hoop – Rice University –
We give a brief analysis of the oscillations of the earth and then extract the system of equations describing acousto-elastic, seismic waves. Processes in Earth's interior are encoded in the coefficients of this system, which also parametrize its structure and material properties. We introduce the seismic inverse problem with its different aspects including a dual time-frequency point of view. Central in the analysis is the formulation as an inverse boundary value problem with the Dirichlet-to-Neumann map or Neumann-to-Dirichlet map as the data. We discuss various conditional Lipschitz stability estimates for this problem for coefficients containing discontinuities, and with partial boundary data, which involves the introduction of an unstructured tetrahedral mesh. Quantitative estimates of the stability constants play acritical role in analyzing convergence for iterative reconstruction schemes, making use of Hausdorff warping and leading to a multilevel approach requiring hierarchical, multi-scale compression. We present computational experiments on the regional and geophysical exploration scales. We conclude with some results pertaining to the high-frequency inverse boundary value or geometric inverse problems, again, in the presence of discontinuities.