Seminars09
From CanisiusmathWiki
SEMINAR ANNOUNCEMENTS
6/19 (Fri.), 4:30 -- 5:30 p.m., OM 320.
Speaker: Jonathan Lopez (University of Rochester)
Title: Lie Algebras from Matrix Groups
Abstract: Lie algebras are algebraic objects that can be used to study geometric objects such as Lie groups and smooth manifolds. In this talk, we'll give a brief introduction to Lie algebras, and describe how to construct them from groups of matrices. In particular, we'll construct a Lie algebra that is generated by just three 2x2 matrices.
7/2 (Thur.), 4:00 -- 5:00 p.m., OM 320.
Speaker: Dominic Dotterrer (Stanford University)
Title: Expanders and Extremal Isoperimetry
Abstract: Can we build a better brain? The profuse existence of expander graphs is a useful geometric fact because it provides a class of counterexamples to (algorithmic) problems involving isoperimetric estimation. Examples include optimal brain tissue architecture as well as representing finite metric spaces as finite subsets of Euclidean space.
7/10 (Fri.), 4:00 -- 5:00 p.m., OM 320.
Speaker: Mike Janssen (University of Nebraska - Lincoln)
Title: What is Algebraic Geometry?
Abstract: Geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate. --- David Mumford
Algebraic geometry is a branch of mathematics which combines the techniques of abstract algebra (especially commutative algebra) with the language and problems of geometry. It has a wide range of applications in other branches of mathematics, including complex analysis, topology, and number theory. The purpose of this talk is to begin to answer the question posed in the title. We begin with a brief review of rings and ideals, and then develop the related geometric objects. Given time, we will end with a brief overview of some of the problems which have guided the development of algebraic geometry.
7/13 (Mon.), 4:00 -- 5:00 p.m., OM 110.
Speaker: Dr. Byungik Kahng (University of Minnesota - Morris)
Title: Redefining Chaos: On Devaney's Definition of Chaos for Discontinuous Dynamical Systems
Abstract: The term chaos had been used in various disciplines of engineering, social and natural sciences, as well as mathematics. However, making the precise mathematical definition of chaos or more precisely chaotic dynamical system, proved to be surprisingly difficult. Indeed, a considerable amount of literature had been devoted to this topic from early 1970s to mid 1990s. This topic is attracting some renewed attention these days, due in no small part to the introduction of the dynamical systems with singularities. The purpose of this talk is to provide a basic overview of the mathematical aspect of the chaotic dynamical systems, including some up-to-date development regarding the systems with singularities.
This talk is aimed at the general audience including upper-level undergraduate students. A good deal of attention will be paid to the visualization through the real-time computation. Time-permitting the applications of our examples in digital signal processing will also be discussed.
Key Words: Chaos, Devaney-chaos, Discontinuous dynamics, Singularity.
7/16 (Thurs.), 4:00 -- 5:00 p.m., OM 320.
Speaker: Dr. F. William Lawvere (Professor emeritus, University at Buffalo)
Title: Categorical Dynamics
7/17 (Fri.), 4:00 -- 5:00 p.m., OM 320.
Speaker: Ryan Grady (University of Notre Dame)
Title: A Mathematical Introduction to Quantum Field Theory
Abstract: In this talk we describe field theories based on the axioms of Atiyah and Segal. Motivated by physics, field theories have become a valuable mathematical topic. Recently, Lurie, Stolz, Teichner and others have used field theories to study higher category theory as well as generalized cohomology theories. This talk is meant to be a gentle introduction into these developments.
8/4 (Tue.), 4:00 -- 5:00 p.m., OM 320.
Speaker: Dr. Rolando Jimenez (Instituto de Matematicas UNAM, MEXICO)
Title: Fundamental Groups and Group Actions
Abstract: We introduce an invariant for group actions and show the relation with fundamental groups.
