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.
 Ken Richardson (TCU, 1032024ff): Foliations, Metrics, and Mean Curvature
See updated notes here.
 Efton Park (TCU, 9122024ff): Traces, Determinants, and Toeplitz Operators
See updated notes here.
 Zhaoting Wei (George) (TAMU Commerce, 8/22/24 ff):
GrothendieckRiemannRoch theorem, superconnections,
and index theorem
See updated slides here.
See a related joint paper with Bismut and Shen here.
 Greg Friedman (TCU, 4/1,15/24): Can you make a Möbius band?
 Scott Nollet (TCU, 1/29???): Smoothing theorems in algebraic geometry
Notes from this lecture series
 Loren Spice (TCU, 11/611/27): The rolling ball and G_2
Go here to get the relevant paper by Baez and Huerta on the arxiv.
Go here to see a video related to the "coin paradox".
 Efton Park (TCU, 10/310/23): Polynomial Covering Maps
Notes from Lectures
 Ken Richardson (TCU, 8/28/239/25/23): Intro to the geometry of
contact and Sasaki manifolds
Notes from Lectures
 Scott Nollet (TCU, 4/3/23): Moduli of distributions
 Greg Friedman (TCU, 2/20/23): Geometric homology and cohomology
 José Carrión (TCU, 11/11,18/22, 12/2/22): Classifying amenable operator algebras
 Ignat Soroko (UNT, 11/4/22): Divergence in Coxeter groups
 Efton Park (TCU, 10/28/22): Unitary equivalence of normal matrices over topological spaces
 Ken Richardson (TCU, October, 2022): Lectures on formality, starting from basic principles:

Lie Groups
(Link to Borcherds' 2012 notes, discussion in seminar led by Loren Spice)

Lie Groups
(Link to Borcherds' 2012 notes, discussion in seminar led by Loren Spice)

Traces and Determinants
(Efton Park, TCU)

Geometric invariants of manifolds with
boundary and symmetry
(Ken Richardson, TCU)

Quantum Motion on Manifolds
(Fred Xavier, TCU)

Introduction to Singular
Riemannian Foliations, including recent results and open problems
(Ken Richardson, TCU)

Smooth Projective Surfaces
(Scott Nollet, TCU)

Moduli Spaces of Curves
(Scott Nollet, TCU)

Injectivity of local diffeomorphism and the
global asymptotic stability problem
(Luis Fernando Mello,
Universidade Federal de Itajubá, Brazil)

Darbouxian Umbilic Points on
Smooth Surfaces in R^{3}
(Luis Fernando Mello,
Universidade Federal de Itajubá, Brazil)

Polynomial vector fields in R^{3} having a
quadric of revolution as an invariant
algebraic surface
(Luis Fernando Mello,
Universidade Federal de Itajubá, Brazil)

On Central Configurations of the
nBody Problem
(Luis Fernando Mello,
Universidade Federal de Itajubá, Brazil)
 Coarse Geometry: Lecture 1,
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Lecture 6
Lecture 7
Lecture 8
Lecture 9
(Efton Park, TCU)
 Amenable Groups
(José Carrión, TCU)
 Index Theory and Quantum Field Theory  the Chiral Anomoly
(Christian Bär, Universität Potsdam)
 Toeplitz Operators
(Efton Park, TCU)
 The 27 lines on the smooth cubic in complex projective 3space
(Scott Nollet, TCU)
 The Kodaira Embedding Theorem
(Scott Nollet, TCU)
 Introduction to the Work of Miriam Mirzakhani
(Ken Richardson, TCU)
 The Selberg trace
formula of compact Riemann surfaces
(Igor Prokhorenkov, TCU)
 SubRiemannian geometry
(Ken Richardson, TCU)
 The
Twin Prime Conjecture
(Qiao Zhang, TCU)
 Unitary Equivalence of Normal Matrices over Compact Hausdorff Spaces
(Efton Park, TCU)
 Unbounded operators on Hilbert space
(Efton Park, TCU)
 Witten's proof of the Morse Inequalities
(Igor Prokhorenkov, TCU)
 An entertaining proof using invertible cobordism and
an infinite process trick
(Greg Friedman, TCU)
 Diagonalization of Matrices of Continuous Functions
(Efton Park, TCU)
 DeligneLusztig 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, Lfunctions, and
automorphic forms
(incomplete, Ken Richardson, TCU)
 Functional Determinants
(Igor Prokhorenkov, TCU)
 Zeta functions and Lfunctions
(Qiao Zhang, TCU)
Additional links:
 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:

Operator Theory Approach to ChernWeil Theory, Introduction
to Smooth Ktheory (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 NoetherLefschetz 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 Ktheory notes