Santa Clara University

Mathematics and Computer Science department

Colloquium Series

Fall 2015

Unless otherwise noted, talks will be at 3:50 PM in O'Connor 104.  Also, there will be refreshments before each talk in O'Connor 31 at 3:40 PM.


Tuesday, 13 October

Speaker:  Abraham Martin del Campo, Centro de Investigacion en Matematicas (CIMAT)

Title:  Euclidean Distance via Monodromy and Numerical Algebraic Geometry

Abstract:  Many models in statistics and engineering can be represented as the set of real solutions to systems of multivariate polynomial equations with real coefficients. In practice, model observations are often noisy and may not satisfy all the equations. In such situations, one usually try to find the point in the model that is closest to the noisy sample.

I will present an algorithm that uses tools from Numerical Algebraic Geometry to find the critical points of a distance function. This talkis based on a joint work with Jose Rodriguez. I will introduce some basics on Numerical Algebraic Geometry and Monodromy, to explain the main features of our algorithm.


  Tuesday, 20 October

Speaker:  Abel Rodriguez, UC Santa Cruz

Title:  What are politicians thinking?  spatial voting models and revealed preference models


Abstract:  The use of quantitative methods has transformed the way social scientists approach problems. In the particular case of political science, scaling methods based on spatial voting models have become an indispensable tool in describing preferences and testing specific theories of legislative or judicial behavior. The first part of this talk provides an overview of spatial voting models and presents some recent developments in handling abstentions and testing hypotheses about changes in revealed preferences. In addition to discussing the theoretical underpinnings of these methodologies, we provide illustrations using roll call votes from different sessions of the US Senate.


  Tuesday, 27 October

Speaker:  Matthew Johnston, San Jose State University

Title:  Extinction and Persistence in Discrete Chemical Reaction Networks

Abstract:  Well-mixed biochemical reaction networks are commonly modeled as either a deterministic system of ordinary differential equations, which tracks continuous molecular concentrations, or as a stochastic continuous-time Markov chain, which tracks discrete molecular counts. Recent work has focused on describing the class of systems for which the long-term behaviors of these two modeling frameworks do not agree---in particular, when an extinction event may occur in the stochastic model but not in the deterministic model. New results will be described."





Tuesday, 3 November

Speaker:  Aparna Higgins, University of Dayton

Title:  Demonic Graphs and Undergraduate Research

*** A Pi Mu Epsilon Sponsored Event

*** Pizza starts at 4:30 in O'Connor 206 and talk starts at 4:40 in same room. 


Abstract:    Working with undergraduates on mathematical research has
been one of the most satisfying aspects of my professional life.  This
talk will highlight some of the beautiful and interesting research
done by my former undergraduate students on line graphs and pebbling
on graphs. We will consider line graphs, some pioneering results in
pebbling graphs, and pebbling numbers of line graphs. This work has
inspired other students to investigate questions in these areas, and
it has contributed to my research as well.



Tuesday, 17 November

Speaker:  Jose Rodriguez, University of Chicago

Title:  Numerically computing Galois groups with Bertini.m2


Abstract:  Galois groups are an important part of number theory and algebraic geometry.
To a parameterized system of polynomial equations one can
associate a Galois group whenever the system has k (finitely many)
nonsingular solutions generically. The Galois group of a parameterized system is a subgroup of the symmetric group on k symbols. Using random monodromy loops it has been shown how to compute the Galois group when it is the full symmetric group.
In this talk, we show how to compute Galois groups that are not the full symmetric group.
We conclude with an implementation using Bertini.m2, an interface to the numerical algebraic geometry software Bertini through Macaulay2.
This is joint work with Jonathan Hauenstein and Frank Sottile.





Tuesday, TBA

Speaker:  Jordan Schettler, San Jose State University

Title:  TBA

*** A Pi Mu Epsilon Sponsored Event





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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