Colloquium SeriesSpring 2015Unless otherwise noted, talks will be at 3:50 PM in O'Connor 207. Also, there will be refreshments before each talk in O'Connor 31 at 3:30 PM. Tuesday, 14 April Speaker: Elizabeth Gross, San Jose State University Title: Goodnessoffit testing for network models
Abstract: When using statistical models for network data, we would like to know the goodnessoffit of the model (i.e., how well the model fits the data). This question has proved particularly challenging even for relatively simple classes of network models, as it currently requires sampling graphs with the same sufficient statistics (e.g., number of edges, number of triangles, degree sequence, etc) as the observed network. In this talk, we will introduce statistical network models and present a method for goodnessoffit testing for loglinear network models that is rooted in computational algebraic geometry. We will demonstrate the approach on the HollandLeinhardt p_1 model for random directed graphs. This is joint work with Sonja Petrovic and Despina Stasi.
Tuesday, 28 April Speaker: Matthew Holmes, Undergraduate student at Santa Clara University Title: Enumerating Primitive Words and Images
Abstract: Primitive words are strings that are not repetitions of some simpler substrings. For example, the string 101010 is not primitive, while the string 10000 is. In this work, I will explain how to generalize this notion to rectangular images and prove a formula based on the Mobius function for counting the number of primitive images of dimensions (m x n) over an alphabet of size k. I will also discuss some upper and lower bounds for these formulas.
Tuesday, 5 May Speaker: Richard Scott, Santa Clara University Title: Cube complexes and generating functions Abstract: Some of your favorite geometric objects can actually be constructed by gluing together cubes of various dimensions along their faces. A very useful way to study the topology of such an object is to pass to an infinite version called the "universal cover"which retains the original local geometry. In this talk we will partition the (infinitely many) vertices in the universal cover in such a way that we can count them. The result of this count is a generating function, the likes of which which you may have encountered in a combinatorics class. After computing a couple of these, we will connect topological properties of the original geometric object to algebraic properties of this generating function. I promise at least six pictures, at least three colors, at least two theorems, and at most one proof.
Tuesday, 19 May Speaker: Jeff Calder, UC Berkeley Title: TBA
Abstract: TBA
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Abstracts of previous talks are available here.
