孙启航 个人主页 English

我目前是法国国家科学研究中心（CNRS）的博士后，工作单位为里尔大学 Paul Painlevé 实验室（数学系）。我的博士后合作导师是 Danylo Radchenko 博士。

2024 年，我于美国伊利诺伊大学香槟分校（UIUC）获得数学博士学位。我的博士导师是 Scott Ahlgren 先生。

2019 年，我本科毕业于西安交通大学数学试验班，获得理学学士学位。我的本科毕业设计指导老师是贾骏雄教授。

这里是我的中文简历。

邮箱：qihangsun98 [at] outlook [dot] com.

研究兴趣：

  1. 整数分拆函数及其解析性质
  2. Kloosterman 和
  3. 自守形式
  4. 球密堆积问题
  5. ……

其他链接：ORCID, MathSciNet, zbMath, Google site, Google scholar.

Profile photo

论文和预印本

  1. Fourier interpolation in dimensions 3 and 4 with real-variable Kloosterman sums.
    准备投稿
  2. Vanishing properties of Kloosterman sums and Dyson's conjectures.
    The Ramanujan Journal, vol. 66, no. 50, 2025. [arXiv] [journal]
  3. Exact formulae for ranks of partitions.
    Transactions of the American Mathematical Society, accepted. [arXiv]
  4. Uniform bounds for Kloosterman sums of half-integral weight, same-sign case.
    Journal of Number Theory, vol. 274, 2025, pp. 104-139. [arXiv] [journal]
  5. Uniform bounds for Kloosterman sums of half-integral weight with applications.
    Forum Mathematicum, vol. 37, no. 1, 2025, pp. 75-109. [arXiv] [journal]
  6. (with O. González) Effective estimates for traces of singular moduli.
    Research in Number Theory, vol. 10, no. 29, 2024. [arXiv] [journal]

非投稿文章

  1. Vanishing properties of Kloosterman sums and Dyson's conjectures, whole proof. [PDF]
    （这是上面文章 5 的证明全文，因为证明中有很多重复的相似步骤，投稿时省略了） [GitHub repository] (包含 Mathematica 文件)
  2. Half-integral weight Kloosterman sums and integer partitions.
    博士毕业论文，伊利诺伊大学香槟分校，2024. [PDF] [IDEALS - UIUC 毕业论文档案馆 (永久链接)]

会议、讨论班等学术活动

  1. Exact formulae for ranks of partitions. International Seminar on Automorphic Forms. Oct. 29, 2024. (Online YouTube channel)
  2. Exact formulae for ranks of partitions. Universität zu Köln, Germany. Number Theory Seminar. Oct. 7, 2024.
  3. Exact formulae for ranks of partitions. Centre international de rencontres mathématiques (CIRM), Marseille, France. Building Bridges: 6th EU/US Summer School & Workshop on Automorphic Forms and Related Topics (BB6). École et Atelier sur les formes automorphes et interactions. Sept. 10, 2024.
  4. Speed talk: exact formulas for rank of partitions. Universität zu Köln, Germany. International Conference on Modular Forms and q-Series. Mar. 12, 2024.
  5. Lightning talk: exact formulas for rank of partitions. Tulane University, USA. Annual Clifford Lectures. Feb. 25, 2023.
  6. Asymptotics in partitions: circle method and Kloosterman sums. UIUC. Number Theory Seminar. Oct. 17, 2023.
  7. Integer partitions and Kloosterman sums. UIUC. Graduate Number Theory Seminar. Oct. 12, 2023.
  8. Sums of Kloosterman sums with applications to partitions. XJTU, Xi'an, China. Number Theory Seminar. Jul. 21, 2023.
  9. Sums of Kloosterman sums and their applications. EPF Lausanne, Switzerland. Workshop on “Arithmetic Statistics in Automorphic Forms and Analytic Number Theory”. Jun. 8, 2023.
  10. Uniform bounds on sums of Kloosterman sums and the applications to partitions. Louisiana State University, USA. 35th Automorphic Forms Workshop. May 24, 2023.
  11. Speed talk: uniform bounds on sums of Kloosterman sums analogue to Goldfeld and Sarnak. Max-Planck-Institut für Mathematik, Bonn, Germany. Arithmetic Statistics, Automorphic Forms and Ergodic Methods. Apr. 24, 2023.
  12. Uniform bounds on sums of Kloosterman sums and their application on partitions. Technische Universität Darmstadt, Germany. Early Number Theory Researchers Workshop. Oct. 28, 2022.

我的数学笔记

古典自守形式

  1. Multiplier system
  2. Poincaré series

弱 Maass 形式、调和 Maass 形式等

  1. An extra transformation formula for Zagier's weight 3/2 harmonic Maass form (Fricke involution)
  2. A modern proof of an integral formula by Hejhal

Pari/GP 学习

  1. Pari/GP 官方网站
  2. Notation, defining function, .gp file

教学经历

这是我的教学陈述（英文）.

2024 春： Math 453 (数论), TA.
2023 秋： Math 220 (微积分), Recitations.
2023 春： Math 444 (实分析初步), TA and Math 241 (微积分 3), TA.
2022 秋： Math 444 (实分析初步), TA.
2022 春： NetMath®.
2021 秋： Math 241 (微积分 3), Recitations.
2021 春： Math 234 (微积分 - 商科 1), Recitations.
2020 秋 Math 231 (微积分 2), TA and worked for CBTF.
2020 春： Math 347 (数学基础), TA and Math 416 (抽象线性代数), TA.
2019 秋： Math 285-286 (微分方程入门), TA and Math 416 (抽象线性代数), TA.

个人爱好

我喜欢下国际象棋，这是我在chess.com的主页。

我9岁时围棋打到了业余3段。

我最喜欢的古筝曲是《雪山春晓》，最喜欢的古琴曲是《潇湘水云》。

我的主页背景颜色是 RGB #F3DFC1.