Xander Faber       Department of Mathematics       Office: 610 Mathematics       Email: xander@math.columbia.edu Shortly I will be moving to my new position as a Postdotoral Fellow with the Centre de Recherches Mathématiques and the Institut des Sciences Mathématiques in Montreal, Quebec.

(Photo by Jeff Mozzochi)

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Current Teaching:

• Summer 2008 - College Algebra
Course begins May 26, Monday - Thursday, 12:30-2:55pm

Previous Teaching:

• Summer 2007 - College Algebra
• Fall 2006 - Undergraduate Seminar: Arithmetic and algebraic geometry over finite fields
• Fall 2006 - Undergraduate Seminar: Random Walks and Circuit Theory
• Summer 2006 - Calculus 1
• Fall 2005 - Algebraic Number Theory Homework Information
• Fall 2005 - Calculus IV Homework Solutions
• Summer 2005 - College Algebra
• Fall 2004 - Undergraduate Seminar: The Inverse Galois Problem
• Fall 2004 - Undergraduate Seminar: Analytic and Geometric Number Theory
• Summer 2004 - Calculus II

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Research:

My research interests fall into several disparate fields of mathematics. Lately I've been interested in
arithmetic geometry, algebraic dynamical systems, metric graphs, and nonarchimedean geometry.
All of my research is motivated strongly by number theory or geometry in some way.

• Uniform Bounds on Pre-Images under Quadratic Dynamical Systems
  with Benjamin Hutz, Patrick Ingram, Rafe Jones, Michelle Manes, Thomas J. Tucker, and Michael E. Zieve.
  Submitted. Last updated 5.4.2008. (arXiv:0805.0441)


• The Geometric Bogomolov Conjecture for Small Genus Curves
  Submitted. Last updated 3.6.2008.
  This paper is part II of my PhD thesis. The arXiv edition (arXiv:0803.0855) contains
  reproductions of the Mathematica code used for the computations and the
  Mathematica Notebooks in which those computations were run.


• Equidistribution of Dynamically Small Subvarieties over the Function Field of a Curve
  Submitted. Last updated 5.23.2008.
  This paper is part I of my PhD thesis. (arXiv:0801.4811v2)


• On the Finite Field Kakeya Problem in Two Dimensions
  Journal of Number Theory. 124 (2007), 248-257.


• Spectral Convergence of the Discrete Laplacian on Models of a Metrized Graph
  New York Journal of Mathematics. 12 (2006), 97-121.
  
  
• Metrized Graphs, Electrical Networks, and Fourier Analysis
  with Matt Baker. (arXiv: math.CO/0407428)
  This is the unpublished original version of the next paper. It contains a section on Fourier analysis.
  
  
• Metrized Graphs, Laplacian Operators, and Electrical Networks
  with Matthew Baker.
  Quantum Graphs and Their Applications. Papers from the Joint Summer Research Conference
  held at Snowbird, Utah, June 18-June 24, 2005. Edited by Gregory Berkolaiko, Robert Carlson,
  Stephen A. Fulling, and Peter Kuchment. Contemporary Mathematics, v. 415,
  American Mathematical Society, Providence, RI 2006.
  This is a shorter incarnation of the above paper.
  
  
• Upper Bounds for Ropelength as a function of Crossing Number
  with Jason Cantarella and Chad A. Mullikin.
  Topology and its Applications 135 (2003), no. 1-3, p. 253-264.
  

All of the above papers are the intellectual property of X.W.C. Faber,
with copyrights held by the authors or the journals in which they appear.

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Places I go sometimes when I'm thinking about math:

• Outside (Photo by X. Faber)
• New York Joint Number Theory Seminar --- Columbia, CUNY and NYU
• Algebraic Geometry Seminar at Columbia University
• Columbia Discrete Math Seminar
• Collaborative Number Theory Seminar at the CUNY Graduate Center

Places I've gone in the past while thinking about math:

• Shou-Wu Zhang's page. He was my PhD thesis advisor at Columbia University.
• MSRI Okay, so that's just a photo I took from beside MSRI. The actual site is here. (Photo by X. Faber)
• Jordan Ellenberg's Blog
• Terence Tao's Blog
• The graveyard where Carl Friedrich Gauss is buried. (Photo by X. Faber)
• Ravi Vakil's Suggestions for New Graduate Students. This is a nice collection of pearls of wisdom for a graduate student
  just starting down the yellow brick road of research. Vakil is at Stanford, so don't take it literally when he says,
  "Occasionally go to Berkeley when you hear about something particularly interesting."
• How many protons are in the universe? This is an amusing calculation due to Jeffrey Copeland & Jeffrey Haemer.
• MR Collaboration Distance. This is like the oracle of Bacon, but it uses the Mathematics Reviews Database. For instance,
  it shows I have Erdős number 4.

Places I go sometimes when I'm not thinking about math:

• Alana's blog! I do some guest blogging on here from time to time too.
• My Awesome Wedding Pictures We ran away to Scotland and got married in a 12th century abbey.
• footbag.org. The gateway to the most fun sport I've ever found. I've actually competed at the professional level!
• xkcd A webcomic of romance, sarcasm, math, and language.
• The Oracle of Bacon. The definitive tool for winning "Six degrees of separation."

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