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Contact Information
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.
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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
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Math 8A - Intro to College
Mathematics for the Sciences (Fall 2007, Spring 2008)
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Math 8B - Intro to College Mathematics for the
Sciences (Fall 2008, Fall 2009, Winter 2010)
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Math 9A - First Year Calculus (Fall 2006)
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Math 9B - First Year Claculus (Spring 2009, Spring
2010)
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Math 9C - First Year Calculus (Winter
2009)
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Math 10A - Calculus: Several Variables (Winter
2007)
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Math 10B - Calculus: Several Variables (Winter
2007)
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Math 22 - Business Calculus (Spring 2007)
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Math 104 - Mathematics Education (Winter 2008)
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Math 138A - Differential
Geometry (Winter 2009)
I taught the following classes as a Primary Instructor at
UC Riverside
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Math 10A - Calculus: Several Variables (Summer 2007, Summer
2009)
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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
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.
See my Teaching
Portfolio for teaching evaluations and
comments.
Professional Stuff
Random Stuff
Links
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arXiv.org - The free e-print for Mathematics
and Physics.

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