Christopher D. Walker

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Contact Information

  • Email: cwalker66 AT math DOT ucr DOT edu
  • Office: Surge 264
  • Office Hours: Fall 2010 - TBA

Bio

I am currently a Ph.D. student in mathematics at UC Riverside. I received my Master's in mathematics from CSU - San Bernardino in 2006. I am also a mathematics instructor for Barstow College. I was previously a junior high and high school math teacher at Victor Valley Christian School, and in another life I studied  genetics at UNLV. In my free time I enjoy watching, playing, and coach all types of sports, especially soccer (I'm sorry to those outside the states, but I still can't bring myself to call it football). I am also a golf addict (I refer to it this way because it truly is as bad as a drug). 

Research

My Master's thesis "Freeness of Hopf Algebras" (under the guidance of Dr. Davida Fischman) focused on the ring theoretic properties of Hopf algebras and Hopf modules. In particular I looked at the Nichols-Zoeller Theorem and several of it generalizations. Here is the Abstract, or if you are more daring, The Complete Thesis.

My current interest is a continuation of this work in the fields of Category Theory and Quantum Groups. I am a student of Dr. John Baez. He is a mathematical physicist who specializes in  n-categories. For way more information you should visit his web site John Baez's Stuff  which contains (among a plethera of other things) lecture notes from his quantum gravity seminar and his (almost) weekly posting "This Week's Finds in Mathematical Physics".

Here are lecture notes and homework solutions (which I wrote) to a course in algebraic topology taught by Dr. Baez during Winter 2007 at UCR.

Papers

Here are my publications to date.

  • Christopher Walker, Hall Algebras as Hopf Objects, Preprint.

Talks

Here are slides for various talks I've given

Abstract - Linear algebra is a core idea in almost all areas of mathematics. In this talk we will look at a process called “groupoidification” which describes the basic structures of linear algebra in the language of groupoids. Groupoidification is the reverse of a systematic process called “degroupoidification”, which turns groupoids into vector spaces, and spans of groupoids into linear operators. Even though groupoidification itself is not a systematic process, we will still be able to find analogs of the main operations in Hilbert spaces including addition, scalar multiplication, and the inner product.

Abstract - In 1990 Ringel first proved that given any simply-laced Dynkin diagram, the Hall algebra of this diagram is isomorphic to the positive part of Uq(g), where g is the lie algebra associated to the same Dynkin diagram. Hall algebras turn out to be one of the most natural applications of the Baez/Dolan program of "groupoidification". In this talk we will describe the pieces of groupoidification necessary for this example, and then show how to apply the process to Hall algebras.

This is a longer version of the above talk.

Teaching Experience

I have served as a mathematics instructor at various levels since 2004. Here is a list of class I have taught as a post-secondary instructor.

I taught the following classes as a Teaching Assistant at UC Riverside

  • Math 8A - Intro to College Mathematics for the Sciences (Fall 2007, Spring 2008)
  • Math 8B - Intro to College Mathematics for the Sciences (Fall 2008, Fall 2009, Winter 2010)
  • Math 9A - First Year Calculus (Fall 2006)
  • Math 9B - First Year Claculus (Spring 2009, Spring 2010)
  • Math 9C - First Year Calculus (Winter 2009)
  • Math 10A - Calculus: Several Variables (Winter 2007)
  • Math 10B - Calculus: Several Variables (Winter 2007)
  • Math 22 - Business Calculus (Spring 2007)
  • Math 104 - Mathematics Education (Winter 2008)
  • Math 138A - Differential Geometry (Winter 2009)

I taught the following classes as a Primary Instructor at UC Riverside

  • Math 10A - Calculus: Several Variables (Summer 2007, Summer 2009)
  • Math 9B - First Year Calculus (Summer 2008, Summer 2010)

From the following list of classes, I have taught two each semester since 2006 as a Primary Instructor at Barstow College

  • Math 101 - Arithmetic
  • Math 50 - Introductory Algebra
  • Math 55 - Intermediate Algebra
  • Math 3 - College Algebra 

I taught the following class as a primary instructor for the Inland Counties Math Project. This is an organization designed to improve the level of mathematics instruction in Southern California by providing instruction to new high school math teachers. The class I taught is a prep class for the CSET I exam which all high school math teachers must pass to clear their credential.

  • CSET I: Algebra and Number Theory (Summer 2006)

See my Teaching Portfolio for teaching evaluations and comments.

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© 2010 Christopher D. Walker