From AIDS Wiki

Darin Christopher Brown

darincbrown@yahoo.com
U.S. Citizen

EDUCATION

• Ph.D., Mathematics, University of California, Santa Barbara (2004)

Research Area: Algebraic Number Theory

Dissertation Title: Lifting Properties of Prime Geodesics on Hyperbolic Surfaces

Dissertation Advisor: Professor Jeffrey Stopple

• M.A., Mathematics, University of California, Santa Barbara (2000)
• B.A., Mathematics, California State University, Stanislaus (1996)

Magna Cum Laude

EMPLOYMENT

Assistant Professor (August 2005 – August 2006)
Department of Mathematics; Eastern New Mexico University

I taught classes and participated in departmental and university activities. Lower-division classes typically had 30-40 students, while upper-division classes had about 10-15 students.

• College Algebra (Math 119; Fall 2005, Spring 2006)
• Calculus I (Math 124; Fall 2005)
• Calculus III (Math 202; Spring 2006)
• Ordinary Differential Equations (Math 351; Fall 2005)

Summer Session Instructor (Summer 1999, 2000, 2002, and 2003)
Department of Mathematics; University of California, Santa Barbara

I was the instructor of record for classes ranging in size from 20-30 students.

• Calculus with Applications 3 (Math 3C; Summer 1999)
• Vector Calculus (Math 5B; Summer 2003)
• Differential Equations and Fourier Series (Math 5C; Summer 2000)
• Transition to Higher Mathematics (Math 8; Summer 2002)

Teaching Assistant (September 1998 – June 2003)
Department of Mathematics; University of California, Santa Barbara

I led weekly discussion sections and assisted the instructor with the class.

• Calculus for the Social and Life Sciences 1 (Math 34A; Spring 2000)
• Calculus for the Social and Life Sciences 2 (Math 34B; Spring 2001)
• Calculus with Applications 2 (Math 3B; Fall 1998, Fall 2000, Fall 2001, Winter 2002, Winter 2003)
• Linear Algebra with Differential Equations (Math 5A; Fall 2002)
• Vector Calculus (Math 5B; Winter 1999)
• Differential Equations and Fourier Series (Math 5C; Fall 1999, Winter 2001, Spring 2003)
• Transition to Higher Mathematics (Math 8; Spring 1999)

Graduate Teaching Fellow (September 1996 – June 1997)
Department of Mathematics; University of Oregon

• College Algebra (Math 111; Fall 1996; about 50 students, instructor of record)
• Elements of Discrete Mathematics 2 (Math 232; Winter 1997, about 100 students, teaching assistant)

Tutoring and Grading
I have experience tutoring small groups of students at UCSB in both the departmental Mathlab and the Campus Learning Assistance Center, as well as at CSUS in the Campus Tutoring Center. I have privately tutored students in subjects ranging from high school algebra and geometry to upper-division classwork. I have also graded several classes, including calculus, linear algebra, and real analysis.

RESEARCH

I am interested in number theory in the broadest and most inclusive sense. My dissertation focused on the relationship between the algebraic behaviour of ideals in number fields and the geometric behaviour of geodesics on hyperbolic surfaces. In particular, I explored the relationship between the splitting behaviour of prime ideals in quadratic extension fields and the lifting behaviour of prime geodesics to covering surfaces. This relationship develops a notion of the Frobenius conjugacy class of a prime geodesic similar to the Frobenius conjugacy class of a prime ideal in number theory.

This striking similarity between algebra and geometry manifests itself in many other situations, including graph theory and dynamical systems. In each situation, there is a notion of a prime, a lifting behaviour, an asymptotic distribution result similar to the prime number theorem, some type of Galois and Frobenius structure, and some type of zeta function. All of these are related to each other in some fashion. My current research is aimed at exploring these different situations further and seeing if they can be situated in a general context. Some work which may prove useful in this direction includes the abstract analytic number theory of John Knopfmacher and the categorical Galois theory of Grothendieck.

For an interesting discussion of these ideas from a somewhat different viewpoint, see weeks 213, 215, 216, and 218 of John Baez's column This Week's Finds in Mathematical Physics.

Since mid-2005, I have devoted time to a cause I feel is of great immediate human and scientific importance — exposing the pseudoscience behind the HIV/AIDS paradigm and the crimes committed in its name. This effort has included uploading nearly 600 pages of documentation collected by Serge Lang. See also my AIDS Wiki article.

PUBLICATIONS

• Newly-rendered version of Peter Duesberg's 1992 Pharm & Thera monograph "AIDS Acquired by Drug Consumption and Other Non-contagious Risk Factors" (editor) (2007)
• “Serge Lang and the HIV Consensus”, letter to the editor of the Notices of the American Mathematical Society, co-signed by Mark Craddock, Rebecca Culshaw, Dan Fendel, and Hung-Hsi Wu (2006)
• Serge Lang Memorial HIV/AIDS Archive (curator) (2006)
• “Lifting Properties of Prime Geodesics”, accepted by the Rocky Mountain Journal of Mathematics (paper or TeX/PDF preprint available upon request) (accepted 2006)
• Lifting Properties of Prime Geodesics on Hyperbolic Surfaces, doctoral dissertation (2004)

PRESENTATIONS

• Introduction to Categories and Higher-dimensional Algebras — a talk delivered to the Graduate Student Seminar, University of California, Santa Barbara (Spring 2005)
• Quadratic Number Fields and Prime Geodesics — a talk delivered to the Graduate Student Seminar, University of California, Santa Barbara (Fall 2003)
• The Metrisation Problem in General Topology — a talk delivered to the Graduate Student Seminar, University of California, Santa Barbara (Fall 2000)
• Dirichlet's Theorem on Primes in Arithmetic Progression — a talk delivered to Ozlem Imamoglu's graduate number theory class, University of California, Santa Barbara (Spring 2000)
• Fractal Geometry and Fractal Dimension — a talk delivered to Tom Carter's cognitive studies class (general, non-mathematical audience), California State University, Stanislaus (Fall 1995)

REFERENCES

Available upon request.