Math

Expositions, research notes and papers, mostly in homotopy theory and arithmetic geometry.

82 posts

  1. Using Automorphism Groups of Curves to Control the Slopes of their Jacobians MathAlgebraic & arithmetic geometryNumber theory
  2. Cut and Paste Invariants and Duality: A Motivating Example Via zeta(-1), zeta(2) and SL_2Z MathAlgebraic & arithmetic geometryNumber theory
  3. The Bernoulli Numbers Come from a Shift Operator MathNumber theoryCombinatorics & puzzles
  4. Half Haunted: The 1/2 in Harish-Chandra via the Fourier Transform MathGeometric representation theoryAlgebra & representation theory
  5. Half Haunted: Relating the 1/2's in Duflo and Harish-Chandra MathGeometric representation theoryAlgebra & representation theory
  6. Stop Staring and Compute! Automorphism Groups of Rational Curves MathAlgebraic & arithmetic geometryAlgebra & representation theory
  7. Hecke orbits and Homotopy MathHomotopy theoryFormal groupsNumber theory
  8. Honda, Taira, On the Formal Structure of the Jacobian Variety of the Fermat Curve over a (p)-adic Integer Ring MathFormal groupsAlgebraic & arithmetic geometryNumber theory
  9. Overview of the Classic Theory of p-Divisible groups MathFormal groupsAlgebraic & arithmetic geometryNumber theory
  10. Fiber Bundles of Formal Disks MathAlgebraic & arithmetic geometryGeometry & topology
  11. Automorphisms of the Jacobian MathAlgebraic & arithmetic geometryProgramming & tools
  12. Geometry For Prime Addicts MathAlgebraic & arithmetic geometryNumber theory
  13. The Height of a Formal Group Law in terms of the Symmetry of the Underlying CM Abelian Variety MathFormal groupsAlgebraic & arithmetic geometryNumber theory
  14. Calculating the Period Matrix of a Shiga Curve, \(y^3 = x^4-1\). MathAlgebraic & arithmetic geometryProgramming & tools
  15. Models of Formal Group Laws of Every Height MathFormal groupsAlgebraic & arithmetic geometryNumber theory
  16. Calculating the homotopy groups of tmf at the prime 2 MathHomotopy theory
  17. Umbral Calculus Derivation of the Bernoulli numbers MathNumber theoryCombinatorics & puzzles
  18. How do I construct the Tits-Freudenthal magic square? MathAlgebra & representation theory
  19. What does an algebraic integer have to be? MathNumber theory
  20. Newspaper Ad: Looking for a Variety MathFormal groupsAlgebraic & arithmetic geometry
  21. How do I explicitly write an ODE as a linear ODE + a nonlinear ODE? MathAnalysis & calculusPhysics
  22. Spectrum of a Ring and Spectrum of a Linear Operator MathAlgebraic & arithmetic geometryAlgebra & representation theory
  23. What is the “universal enveloping algebra” of a formal group law? MathFormal groupsAlgebra & representation theory
  24. Classification of Conic Sections MathGeometry & topology
  25. A quick comparison of Lie algebras and formal group laws MathFormal groupsAlgebra & representation theoryGeometric representation theory
  26. The Cup Product of the Klein Bottle mod 2 MathHomotopy theoryGeometry & topology
  27. A question on primes MathAlgebraic & arithmetic geometryNumber theory
  28. Chromatic Coppersmith Theory MathHomotopy theoryFormal groups
  29. A Short Post on a Problem of Euler MathNumber theory
  30. On Detiling Polynomials: A Generalization of the Euler MacLaurin Formula MathNumber theoryAnalysis & calculusCombinatorics & puzzles
  31. A Quick Note on a Geometric Definition of (v_n) MathHomotopy theoryAlgebra & representation theory
  32. What is the orientation of a ring? MathHomotopy theoryNumber theory
  33. Group Contractions for Elliptic Curves MathFormal groupsAlgebraic & arithmetic geometry
  34. Complex Analysis: Poles, Residues, and Child’s Drawings MathAnalysis & calculusAlgebraic & arithmetic geometry
  35. What is the difference between homotopy and coherent homotopy? MathHomotopy theoryAlgebra & representation theory
  36. Thoughts on Fractional Cohomology MathHomotopy theoryAlgebra & representation theory
  37. Dirichlet Series and Homology Theories MathNumber theoryHomotopy theoryAnalysis & calculus
  38. A First Look at an Equivariant Elliptic Cohomology MathHomotopy theoryFormal groups
  39. Spf (E*[[x]]): Your walk through a flower garden MathFormal groupsAlgebraic & arithmetic geometry
  40. A Second Glimpse of Spectra MathHomotopy theoryGeometry & topology
  41. Bordism with singularities construction of elliptic homology MathHomotopy theoryAlgebra & representation theory
  42. Elliptic Curve Formal Group Laws: Philosophy and Derivation MathFormal groupsAlgebraic & arithmetic geometry
  43. What does the sphere spectrum have to do with formal group laws? MathHomotopy theoryFormal groups
  44. Landweber-Ravenel-Stong Construction Flowchart MathHomotopy theoryFormal groups
  45. The Landweber exact-functor theorem MathHomotopy theoryFormal groups
  46. Die Philosophie der formalen Gruppengesetzen der elliptischen Kurve MathFormal groupsAlgebraic & arithmetic geometry
  47. What is an elliptic curve? MathAlgebraic & arithmetic geometryNumber theory
  48. Group Law on the (Punctured) Affine Line MathAlgebraic & arithmetic geometryAlgebra & representation theory
  49. (Pic(X)) vs. (CP^infty) MathHomotopy theoryFormal groups
  50. Some Thoughts on Dynamical Systems MathHomotopy theoryPhysics
  51. A Precursor to Characteristic Classes MathHomotopy theoryAlgebraic & arithmetic geometry
  52. Oriented Cobordism Cohomology MathHomotopy theoryGeometry & topology
  53. Spectrum of a Ring MathAlgebraic & arithmetic geometryAlgebra & representation theory
  54. A Swashbuckling Tour of Elliptic Cohomology MathHomotopy theoryFormal groups
  55. A Recipe for Constructions ((R_F(G)), (A(G)), (K_0(X)), …) MathHomotopy theoryAlgebra & representation theory
  56. Understanding the Lazard Ring MathHomotopy theoryFormal groups
  57. Maps of a Torus MathHomotopy theoryGeometry & topology
  58. Swashbuckling Notes on Topos Theory MathAlgebra & representation theory
  59. Spin Manifolds MathGeometry & topology
  60. Notes on Covering Spaces as Extensions MathHomotopy theoryNumber theory
  61. A Gentle Introduction to Tensors and Monoids MathAlgebra & representation theory
  62. An Informal Categorical Introduction to Lie’s Theorems MathAlgebra & representation theory
  63. Introduction to Bundles MathHomotopy theoryGeometry & topology
  64. Studying Symmetry MathAlgebra & representation theoryAnalysis & calculus
  65. A Unifying Language MathAlgebra & representation theoryCombinatorics & puzzles
  66. Graphical Supersymmetry Algebras MathAlgebra & representation theoryCombinatorics & puzzles
  67. An Autodidact’s Topology Curriculum MathHomotopy theoryAlgebra & representation theory
  68. Basic Topology MathGeometry & topologyRobotics & machine learning
  69. Introduction to Algebraic Structures MathAlgebra & representation theoryDrawing, painting & comics
  70. Quick Basics of Enumerative Combinatorics MathCombinatorics & puzzles
  71. SPOILERS: Using Simple Combinatorics MathNumber theoryCombinatorics & puzzles
  72. A Method to Not Prove the Collatz Conjecture MathNumber theory
  73. Natural Transformation MathAlgebra & representation theory
  74. The Monads Trilogy (Categories, Functors, Monads) MathAlgebra & representation theory
  75. What Does This Wobbly “d” Do? MathAnalysis & calculus
  76. The Handwritten Greek Alphabet: A Quick Guide MathLife, study & work
  77. Small Math Puzzles Make My Day MathCombinatorics & puzzlesProgramming & tools
  78. Matlab: Lorenz Attractor MathPhysicsProgramming & tools
  79. MinutePhysics is Naively Incorrect: Finding the Limit of a Geometric Series MathAnalysis & calculusPhysics
  80. Are These 3 Points Collinear? MathGeometry & topology
  81. Find the Fractional Form of a Repeating Decimal MathNumber theory
  82. Implementation of Prime Number Algorithms MathNumber theoryProgramming & tools