WSU Vancouver Mathematics and Statistics Seminar
 WSU Vancouver Mathematics and Statistics Seminar (Fall 2017) Welcome to the WSU Vancouver Seminar in Mathematics and Statistics! The Seminar meets on Wednesdays at 1:10-2 PM in VUB 107 . This is the building marked "N" in the campus map, where all Math/Stat faculty have offices. The seminar is open to the public, and here is some information for visitors. Students could sign up for Math 592 (titled Seminar in Analysis) for 1 credit. Talks will be given by external speakers, as well as by WSUV faculty and students. Contact the organizer Bala Krishnamoorthy if you want to invite a speaker, or to give a talk.
Date Speaker Topic Slides
Aug 23 Intro, coordination
Aug 31 Jari Vauhkonen, Luke Finland A generic Markov model for climate change impacts on forest carbon dynamics
(Thursday, Aug 31, 4:10-5 PM)

Forests and forestry are expected to play an important role in the mitigation of climate change. Forests are carbon sinks and stocks while forest products can be used to replace fossil based raw materials and energy. The impacts of climate change on forest carbon dynamics when different management strategies are applied are less studied.

In this presentation, first I'll revisit my previous research topics and explain how a three-dimensional canopy model can be derived from sparse-density airborne LiDAR data applying computational geometry and topology. Second, I'll present our recent work on projecting forest dynamics with an area-based matrix model.

Sep  6 Steven Klee, Seattle U. Counting faces on simplicial complexes: V-E+F and beyond

A graph is a combinatorial object that is built out of vertices and edges. More generally, a simplicial complex is a combinatorial object that is built out of vertices, edges, triangles, tetrahedra, and their higher-dimensional cousins. The most natural combinatorial statistics to collect on a simplicial complex are its face numbers, which count the number of vertices, edges, and higher-dimensional faces in the complex.

This talk will give a survey on face numbers of simplicial complexes, beginning with planar graphs and moving on to graphs on other surfaces, such as tori or projective planes. From there, we will study spheres and manifolds of higher dimensions. We will undertake two main questions in this talk: First, what is the relationship between the face numbers of a simplicial complex and its underlying geometric structure? Second, how can we infer extra combinatorial information from properties of the underlying graph of a simplicial complex, such as graph connectivity or graph colorability?

Sep 13 Nathaniel Saul, WSUV From Reeb Graph to Mapper: An Introduction to Topological Data Analysis

With the rise of computers has come an era of big data. Many traditional methods of exploratory data analysis fail to extract any useful insights from the growing mountains of bytes. In this light, researchers have begun to look deep into the world of pure mathematics for new tools that could be applicable. By making the simple assumption that data has an underlying shape, the world of algebraic topology becomes a ripe field of theory and methods for extracting insights.

In this talk, we will detail the Reeb graph, a useful object for capturing topologically important aspects of a shape. We will then talk about another object called the Mapper, which has been shown to be a particularly useful construction for exploring high dimensional point cloud data.

Concepts of this talk will be presented at an undergraduate level and will be of interest to anyone that likes pretty visualizations of big data.

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Sep 20 Srijanie Dey, WSUV Energy Propagation in Deep Convolutional Neural Networks

When you are asking Google to translate words from one language to another, or receiving recommendations for products from Amazon or movies from NetFlix, or asking Siri for directions, you are most likely asking for some magic using Neural Networks. The field of artificial intelligence has reached impressive heights with the advent of the neural networks.

In this talk, we discuss a specific type of neural network called the Convolutional Neural Network (CNN), and see the mathematics behind it. We will talk about feature extraction, the operation that allows CNNs to do what they do. Here, features are considered as "energy". We analyze ways to make energy propagation more efficient, thus leading to energy conservation, and in turn leading to better feature extraction. This talk is based on the preprint with the same title available on arXiv (1704.03636).

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Sep 27 no seminar
Oct  4 Bala Krishnamoorthy On optimal transport problems scribe
Oct 11 no seminar
Oct 18 no seminar
Oct 25 Olga Rumyantseva, WSUV Lotka model and von Foerster model

Lotka model is a continuous-time model that tracks a female population's birth rate. von Foerster model is a model in which the dynamics of one-sex population is described by an age distribution function. Two basic assumptions are made about the population. These prescribe how individuals are removed from and introduced into the population. If the derived equations can be solved for the age distribution function, then the dynamics of the population can be predicted.

Nov  1 Bryn Keller, Intel Labs Deep learning, deep waters, topology, and drones: a year at Intel Labs

What does a researcher at Intel Labs work on? The answer might surprise you! We'll take a journey through such diverse topics as topological data analysis, drones, neuroscience, machine learning, and humpback whales.

Nov  8 John Lind, Reed College Fixed point theory and the free loop space

Many questions in mathematics can be encoded into a fixed point problem: given a self-map $$f : X \to X$$ of a geometric object $$X$$, which points satisfy $$f(x) = x$$? For example, the Brouwer fixed point theorem asserts that any self-map of a disk must have a fixed point. The Lefschetz fixed point theorem gives a partial answer to the fixed point problem when $$X$$ is a topological space, and its generalizations in geometric analysis, algebraic geometry, and number theory inspired many fundamental achievements of the twentieth century. After surveying these results, I will describe current work that uses algebraic K-theory and the free loop space to give a stronger answer to the fixed point problem in the original topological setting.