Santa Clara University

Mathematics and Computer Science department

SCU Mathematics/CS Colloquium Series

Spring 2011

Unless otherwise noted, talks will be at 3:50 PM, and there will be refreshments before each talk in O'Connor 31 at 3:40 PM.

Wednesday April 6, Joint Math/CS--Anthropology Talk, Kennedy Commons, TIME: 5-6 pm

Speaker: George Mohler, Santa Clara University

Title: The mathematics of crime hotspots

Abstract: Crime is not evenly distributed across space and time, as some neighborhoods in a city have a disproportionate number of criminal events. Theories for the spread of social disorder, such as the broken windows hypothesis and repeat victimization, offer partial explanations for how these "crime hotspots" form and persist. In this talk we show how mathematicians, alongside social scientists, have worked to fill in the gaps and build a quantitative theory for the emergence of hotspots starting from first principles of criminal behavior. This effort has led to new insights into some long standing questions: Why do some hotspots go away on their own, while others intensify? Why in some cases are policing efforts successful and in other cases hotspots are displaced to other parts of the city? This talk is aimed at a general audience and assumes no background in criminology or advanced mathematics.

Tuesday April 19, O'Connor 207

Speaker: Glenn Appleby, Santa Clara University

Title: It Seemed a Good Idea at the Time: Honeycombs and Products of Littlewood-Richardson Tableaux

Abstract: Tamsen McGinley and I work in the area of "algebraic combinatorics". We study relations between matrices over rings (an algebraic problem), and Littlewood-Richardson Tableaux (something in combinatorics). Littlewood-Richardson tableaux are sets of positive integers sorted in special arrays subject to a set of rules. Remarkably, finding even one such array is known to imply that a lot of other mathematical problems are solvable, and collections of such tableaux actually allow us to count all possible solutions. In previous work, Tamsen and I were able to build a solution to a matrix problem by using a Littlewood-Richardson tableaux as a blueprint. We also learned how to find a unique tableau associated to every solution to the matrix problem. So, last summer we thought: "Hey, it's actually easy to combine two solutions to the matrix problem and get one big solution. Maybe we can do this for tableaux! That means we should also be able to find two Littlewood-Richardson tableaux and combine them to get one big Littlewood-Richardson tableau (form their 'product')." We even thought it would be easy to come up with an algorithm that says how to do this. Well, like we said, it seemed a good idea at the time. Fortunately, the story has a happy ending, but it took some surprising twists and turns (literally) before it all worked out. As is often the case, the journey seems now to have been even more interesting than the destination.

Tuesday May 3, O'Connor 207

Speaker: Hongde Hu, CSU Monterey Bay

Title:Logical Methods in Graph Coloring

Abstract: This talk attempts to give a general notion of the totality in order to study the extremal problem and the coloring problem. We will discuss various total properties in Linear Logic and Graph Theory.
The presentation will be accessible to undergraduates, especially Mathematics and Computer Science majors.

Tuesday May 24, O'Connor 207

Speaker: Eric Babson, UC Davis

Title: Complexes with few triangles and random groups

Abstract: If every subcomplex of a two dimensional simplicial complex has too few triangles to be a torus then the complex has the topological type of some circles, spheres and projective planes. This topological fact arises in the study of random complexes and turns out to control the behavior of the fundamental group. The analogous situation in which the subcomplexes have too few edges to be a torus is not understood. This type of complex occurs in the study of clique complexes of random graphs and the analogous topological restriction would yield results about their fundamental groups.


If you have a disability and require a reasonable accommodation,
please call/email Rick Scott 408-554-4460/rscott at scu dot edu (or
use 1-800-735-2929 TTY—California Relay).

Abstracts of previous talks are available here.
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