Other mathematical writing

38. An Oberwolfach Snapshot on waves and incidences.
39. Exposition of a beautiful paper of Herr and Kwak, on a sharp discrete Strichartz estimate for the periodic Schrodinger equation in 2+1 dimensions. See also these slides.
40. Slides of a lecture series on Fourier decoupling given at CIRM in 2023. Lecture 1 Lecture 2 Lecture 3
41. Slides of a seminar talk on techniques for proving decoupling inequalities.
42. Slides of a seminar talk on a formula for Sobolev norms. See also the following exposition.
43. Slides of a seminar talk on discrete restriction for the parabola in R².
44. An exposition of Carbery's work on consequences of the reversed square function estimate for the paraboloid in Rⁿ⁺¹, with some additional details.
45. A rigorous write-up of an example showing optimality of ℓ ^p decoupling for the light cone in Rⁿ⁺¹.
46. An exposition of Bourgain's counterexample for the Schrödinger maximal operator, following a survey article by Lillian B. Pierce.
47. Slides of a seminar talk on Maximal functions for Hilbert transform along variable parabolas in R².
48. Slides of a seminar talk on Variational norm estimates for Stein-Wainger operators.
49. An exposition of the Bourgain-Guth iterations, for proving restriction estimates at exponent 10/3 for the paraboloid in 3 dimensions. This is an outcome of an exercise for myself, to make precise all use of the uncertainty principle in the paper of Bourgain and Guth.
50. An informal presentation of Fefferman's proof of Carleson's theorem.
51. An informal proof of the Bourgain-Demeter decoupling theorem for the parabola, written for my own benefit (with Jianhui Li).
52. Slides of a survey talk on "decoupling inequalities".
53. Notes on a mini-course on "joints and multijoints", by Ruixiang Zhang (courtesy of Ruixiang Zhang for me to reproduce the notes here).
54. Notes on a mini-course on the "Szemeredi-Trotter theorem", by Ruixiang Zhang (courtesy of Ruixiang Zhang for me to reproduce the notes here).
55. An exposition of the "Maurey-Nikishin-Pisier factorization theorem, and its application to extension and Kakeya problems".
56. Slides of a popular talk on the "Szemeredi-Trotter theorem via the polynomial method", for an enthusiastic group of math undergrads.
57. Slides of a popular talk on the "Kakeya conjecture", delivered to high school students (To play the animations in the file, first click on the "play button". Then right click on the picture, and then choose "play". To rewind, right click on the picture, and then choose "rewind". You may need to first download the pdf onto your computer for this to work.)
58. Slides of a seminar talk on "A positive mass theorem in 3-dimensional CR geometry"
59. An interesting proof of "the simplicity of sl(n)", written for my own benefit
60. Some notes about "Special isomorphisms of Lie algebras in low dimensions"
61. Slides of a seminar talk on "On a class of pseudodifferential operators with mixed homogeneities"
62. Slides of a seminar talk on "Carleson's Theorem of Radon type with polynomial phases"
63. Slides of a seminar talk on "The Kohn Laplacian on blow-ups of pseudohermitian CR manifolds of dimension 3"
64. Slides of a seminar talk on "Two nonlinear wave equations with conformal invariance"
65. Slides of a seminar talk on "Subelliptic divergence-curl inequalities"
66. Slides of a seminar talk on "Sobolev inequalities for (0,q) forms on CR manifolds of finite type"
67. I have given a sequence of two talks at a number of occasions about the work of Bourgain-Brezis, Lanzani-Stein and van Schaftingen on div-curl inequalities. Below is a write-up of the two talks.
    Div-Curl systems I
    Div-Curl systems II
68. I have also extracted from a paper of Bourgain-Brezis a short proof of the Gagliardo-Nirenberg inequality in 2 dimensions, which can be found here:
    A short proof of the Sobolev inequality in R²
69. I gave a series of 4 lectures in the graduate Fourier analysis course at Princeton in Fall 2009. The first one is about the work of Lanzani-Stein and van Schaftingen on div-curl inequalities. This is part of the previous sequence of two talks (see above). The second and the third are on subelliptic analysis and a subelliptic div-curl inequality, while the last one is the application of the latter to several complex variables. These talks can be found here:
    Talk 2: On some subelliptic real analysis
    Talk 3: On a subelliptic div-curl inequality
    Talk 4: Applications to several complex variables
70. Lecture notes on Introductory Several Complex Variables, written for Princeton Summer School in Analysis and Geometry 2009
71. A talk on Sogge's work on Spectral projection theorems on compact manifolds, given Spring 2007
72. A note on Averages theorem, Restriction theorem and Strichartz estimates, written for Princeton Summer School in Analysis and Geometry 2007
73. A note on the Marcinkiewicz-Zygmund theorem
74. A reflection on Hodge decomposition
75. A note on Yau's gradient estimate written for my own benefit