Disclaimer: some of these notes are from informal seminars, and no reasonable person would claim the correctness of any statements made in these notes. These notes do not reflect the views of TCU, of the government of the United States of America, of the United Nations, or of any organized society of living creatures. Perusing these notes may be hazardous to your health, and we strongly advise that mathematicians with chronic health conditions look elsewhere for reading material.

• Diagonalization of Matrices of Continuous Functions (Efton Park, TCU)
• Deligne-Lusztig Representations (Loren Spice, TCU, incomplete)
• Unique Factorization and Class Groups (George Gilbert, TCU)
• Local Class Groups (Scott Nollet, TCU)
• Introduction to Fourier series (Ken Richardson, TCU)
• Groups of homotopy spheres, surgery, and the Kervaire invariant (incomplete, Greg Friedman, TCU)
• Elementary introduction to algebraic geometry (Scott Nollet, TCU)
• Introduction to the Ihara zeta function for graphs (Igor Prokhorenkov, TCU)
• Introduction to arithmetic quantum chaos (Igor Prokhorenkov, TCU)
• Orthogonal Polynomials (George Gilbert, TCU)
• A geometric glance at zeta functions, L-functions, and automorphic forms (incomplete, Ken Richardson, TCU)
• Functional Determinants (Igor Prokhorenkov, TCU)
• Zeta functions and L-functions (Qiao Zhang, TCU)
  Additional links:
  • Milne's notes on modular functions and modular forms.
  • Fairly elementary ways to get some minimal ranks for a couple families of curves:
    Elliptic Curves from Mordell to Diophantus and Back, by Ezra Brown and Bruce T. Myers, Amer. Math. Monthly 109 (2002), no. 7, 639–649.
• Introduction to Clifford algebras (Efton Park, TCU)
• The dictionary between commutative and noncommutative geometry (incomplete, Efton Park, TCU)
  Also: Efton's own notes.
• Quantum Field Theory Seminar (incomplete, Igor Prokhorenkov, Loren Spice, TCU)
• Novikov Additivity Seminar (incomplete, Greg Friedman, TCU)
• John Baez, UC Riverside, several lectures:
  
  • My favorite numbers:
    Five    Eight    Twenty-Four
  • Zooming out in time
  • Fundamental physics: where we stand today
• Operator Theory Approach to Chern-Weil Theory, Introduction to Smooth K-theory (Efton Park, TCU)
• Differential Form Approach to Intersection Homology (Greg Friedman, TCU)
• Introduction to the Eta Invariant (Ken Richardson, TCU)
• Chern Simons Theory (incomplete, Igor Prokhorenkov, TCU)
• Morse Theory (incomplete, Greg Friedman, TCU)
• The Noether-Lefschetz Theorem (Scott Nollet, TCU)
• Picard groups and class groups of algebraic varieties (Scott Nollet, TCU)
• Scissors Congruence (Efton Park, TCU)
• Birationality of etale maps via surgery (Scott Nollet, TCU)
• Holomorphic injectivity and the Hopf map (Scott Nollet, TCU)
• A new Kunneth theorem for intersection homology (Greg Friedman, TCU)
• Kirillov Orbit Method (not complete, Ruth Gornet, UTA)
• Geometric Quantization (not complete)
• Exotic Differentiable Structures (Greg Friedman, TCU)
• Kodaira Vanishing Theorem
• Lie Groups Seminar Notes
• Introduction to Spectral Sequences
• Mod k index theorem
• Introduction to Symplectic Manifolds
• Algebraic Consistent Quantum Theory (Mark Sinnett, St. John's College, Annapolis)
• Extending Poincare Duality to Manifold Homotopically Stratified Spaces (Greg Friedman, TCU)
• The covering spectrum (Ruth Gornet, UTA)
• Wave Trace Formulae (see Uribe notes)
  Wave Trace Invariants on Torus
• Introduction to Index Theory Notes
• What is a Dirac operator good for? (somewhat incomplete)
• Efton's lecture notes on determinants of Toeplitz operators
• Greg's lecture notes on sheaf theory
• Barbara's lecture notes on the Toda lattice
• Quillen K-theory notes