Research

My research interests span a broad spectrum of mathematics generally classified as geometry, including

Feel free to download an overview of my research interests.

Reprints and preprints

  1. Harmonic Volume Can Be Computed As An Iterated Integral, by William M. Faucette, Canadian Mathematical Bulletin, vol. 35, no. 3, 1992
  2. Harmonic Volume, Symmetric Products, and the Abel-Jacobi Map, by William M. Faucette, Transactions of the American Mathematical Society, vol. 335, no. 1, January 1993
  3. Geometric Interpretation of the Reduction of the General Quartic by Galois Theory, by William M. Faucette, American Mathematical Monthly, vol. 103, no. 1, January 1996
  4. The Generalized Torelli Problem: Reconstructing a Curve and its Linear Series From its Canonical Map and Theta Geometry, by William M. Faucette, submitted
  5. Circling up the Wagons: Unifying Mathematics for the Calculus Student, by William M. Faucette, submitted
  6. Divisibility Rules for 7 and 13, by William M. Faucette, submitted
  7. How Not To Prove Fermat's Last Theorem, by William M. Faucette, submitted
  8. The Miracle Substitution: How and Why It Works, by William M. Faucette, submitted
  9. Trisecting an Angle . . . By Cheating, by William M. Faucette and Wendy C. Davidson, submitted
  10. Generalized Geometric Series, The Ratio Comparison Test and Raabe's Test, by William M. Faucette, accepted by The Pentagon
  11. Pascal's Theorem in Degenerate Cases, by William M. Faucette, submitted
  12. Around the Cubic Curve in Fifty Minutes, by William M. Faucette, completed
  13. A Poor Man's Derivation of the Double Angle Formula for Sine, by William M. Faucette, submitted
  14. Ceva's Therem and Its Applications, by William M. Faucette, completed
  15. The Nine Point Circle, by William M. Faucette, completed
  16. The Euler Line of a Triangle, by William M. Faucette, completed

Recent Presentations

  1. Math Makes the World(s) Go 'Round: A Mathematical Derivation of Kepler's Laws of Planetary Motion
  2. How Many Ways Can 945 be Written as the Difference of Squares: An Introduction to the Mathematical Way of Thinking


  3. Lectures on Public Key Cryptography
  4. Cryptography: Public Key vs. Private Key Cryptosystems
  5. Public Key Cryptography: The RSA Cryptosystem
  6. Public Key Cryptography: Elliptic Curve Cryptography


  7. Lectures on Hodge Theory
  8. Lecture 1: Calculus on Smooth Manifolds
  9. Lecture 2: The Hodge Theory of a Smooth, Oriented, Compact Riemannian Manifold
  10. Lecture 3: Complex Manifolds
  11. Lecture 4: Hermitian Linear Algebra
  12. Lecture 5: The Hodge Theory of Hermitian Manifolds
  13. Lecture 6: Kähler Manifolds
  14. Lecture 7: The Hard Lefschetz Theorem and the Hodge-Riemann Bilinear Relations
  15. Lecture 8: Mixed Hodge Structures


  16. Lectures on Multivariable Calculus
  17. Multivariable Differentiation
  18. The Inverse Function Theorem
  19. The Implicit Function Theorem