孙启航 SUN, Qihang's Personal Website 中文

I am a CNRS postdoc at l'Institut des Hautes Études Scientifiques (IHES), working with Dr. Danylo Radchenko. We relocated here together in 2026/03 from l'Université de Lille, Laboratoire Paul Painlevé, where we had been based since 2024/09.

I got my Ph.D. in Mathematics in 2024/05 at the University of Illinois Urbana-Champaign (UIUC) under the supervision of Professor Scott Ahlgren.

I completed my Bachelor's degree in Mathematics (Honors Program) in 2019/06 at Xi'an Jiaotong University (XJTU) in China, having entered via its Honors Youth Program (少年班) in 2013/09.

Here is my CV.  |  Email: qihangsun98 [at] outlook [dot] com

Research interests:

  1. Partitions and related analytic properties
  2. Kloosterman sums
  3. Automorphic forms
  4. Fourier interpolation and sphere packing
  5. ...

Useful links: My ORCID, MathSciNet, zbMath, Google scholar, arXiv, Google site.

Academic visits:

  1. Morningside Center of Mathematics, Chinese Academy of Sciences, Beijing, China.
    Visiting student. 2022/04 – 2022/06
  2. Georgia Institute of Technology, Atlanta, USA.
    Undergraduate Exchange Program. 2018/01 – 2018/05

Profile photo

Publications and Preprints

  1. The basis functions of Fourier interpolation.
    (with David Berghaus, Andriy Bondarenko, Danylo Radchenko, Kristian Seip)
    submitted. [arXiv]
  2. Fourier interpolation in dimensions 3 and 4 with real-variable Kloosterman sums.
    (with Danylo Radchenko)
    submitted. [arXiv]
  3. Vanishing properties of Kloosterman sums and Dyson's conjectures.
    The Ramanujan Journal, vol. 66, no. 50, 2025. [arXiv] [journal]
  4. Exact formulae for ranks of partitions.
    Transactions of the American Mathematical Society, vol. 379, no. 3, 2026, pp. 1649-1707. [arXiv] [journal]
  5. Uniform bounds for Kloosterman sums of half-integral weight, same-sign case.
    Journal of Number Theory, vol. 274, 2025, pp. 104-139. [arXiv] [journal]
  6. Uniform bounds for Kloosterman sums of half-integral weight with applications.
    Forum Mathematicum, vol. 37, no. 1, 2025, pp. 75-109. [arXiv] [journal]
  7. Effective estimates for traces of singular moduli.
    (with Oscar E. González)
    Research in Number Theory, vol. 10, no. 29, 2024. [arXiv] [journal]

Not for publication

  1. Vanishing properties of Kloosterman sums and Dyson's conjectures, whole proof. [PDF]
    (This is the full version of 5. above, because the whole proof is long and tedious). [GitHub repository] (including the Mathematica files)
  2. Half-integral weight Kloosterman sums and integer partitions.
    Ph.D. Thesis, University of Illinois Urbana-Champaign, 2024. [PDF] [IDEALS - UIUC access (permalink)]

Contributed referee service: Proc. Amer. Math. Soc. (1); Ramanujan J. (1); Izv. Math. (1).

Invited talks

  1. Rademacher-type exact formulas for rank of partitions with a new proof of Ramanujan congruences.
    Michigan Technological University, Houghton, USA. Seminar in Partition Theory, q-Series and Related Topics. 2026/03/03
  2. Integer partition, Kloosterman sums, and further applications.
    Hunan University, Changsha, China. Combinatorics & Number Theory Seminar. 2025/12/30
  3. Exact formulae for ranks of partitions.
    International Seminar on Automorphic Forms. (Online YouTube channel) 2024/10/29
  4. Exact formulae for ranks of partitions.
    Universität zu Köln, Germany. Number Theory Seminar. 2024/10/07
  5. Asymptotics in partitions: circle method and Kloosterman sums.
    UIUC, USA. Number Theory Seminar. 2023/10/17
  6. Integer partitions and Kloosterman sums.
    UIUC, USA. Graduate Number Theory Seminar. 2023/10/12
  7. Sums of Kloosterman sums with applications to partitions.
    XJTU, Xi'an, China. Number Theory Seminar. 2023/07/21

Conference talks

  1. 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. 2024/09/10
  2. Sums of Kloosterman sums and their applications.
    École Polytechnique Fédérale de Lausanne (EPFL), Switzerland. Workshop on “Arithmetic Statistics in Automorphic Forms and Analytic Number Theory”. 2023/06/08
  3. Uniform bounds on sums of Kloosterman sums and the applications to partitions.
    Louisiana State University, USA. 35th Automorphic Forms Workshop. 2023/05/24
  4. Uniform bounds on sums of Kloosterman sums and their application on partitions.
    Technische Universität Darmstadt, Germany. Early Number Theory Researchers Workshop. 2022/10/28

Speed / lightning talks

  1. Fourier interpolation and continuous Kloosterman sums.
    Max-Planck-Institut f¨ur Mathematik, Bonn, Germany. Conference on ”Progress and Emergent Theories in Zeta and L-Functions” (PRETZL). 2025/07/22
  2. Exact formulas for rank of partitions.
    Universität zu Köln, Germany. International Conference on Modular Forms and q-Series. 2024/03/12
  3. Exact formulas for rank of partitions.
    Tulane University, USA. Annual Clifford Lectures. 2024/02/25
  4. 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. 2023/04/24

My Math Notes

Notes / Blogs in Chinese: 应襄 (Zhihu)

Classical Automorphic Forms

  1. Multiplier system
  2. Poincaré series

Weak Maass Form, Harmonic Maass Form, etc.

  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 study

  1. Notation, defining function, .gp file

Teaching

Here is my teaching statement.

Spring 2024: Math 453 (Number Theory), TA.
Fall 2023: Math 220 (Calculus), Recitations.
Spring 2023: Math 444 (Elementary Real Analysis), TA and Math 241 (Calculus III), TA.
Fall 2022: Math 444 (Elementary Real Analysis), TA.
Spring 2022: Worked for NetMath®.
Fall 2021: Math 241 (Calculus III), Recitations.
Spring 2021: Math 234 (Calculus for Business I), Recitations. Ranked as Excellent by students: CITL link
Fall 2020: Math 231 (Calculus II), TA and worked for CBTF.
Spring 2020: Math 347 (Fundamental Mathematics), TA and Math 416 (Abstract Linear Algebra), TA.
Fall 2019: Math 285-286 (Intro Differential Equations), TA and Math 416 (Abstract Linear Algebra), TA.

About me

I like to play chess in my spare time. This is the link to my page at chess.com.

I got Amateur 3 Dan in Weiqi (围棋, Go) when I was 9 (this level of 3 Dan means... an intermediate amateur I guess :).

In music I recommend Guzheng (古筝) and Guqin (古琴) as traditional Chinese instruments to listen. Here are the songs I like the most: 雪山春晓；潇湘水云。

The background color is RGB #F3DFC1.