孙启航 SUN, Qihang's Personal Website

I am a CNRS postdoc at l'Université de Lille, Laboratoire Paul Painlevé, working with Dr. Danylo Radchenko.

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

I completed my bachelor in Mathematics in 2019 at the Xi'an Jiaotong University (XJTU) in China.

Here is my CV.

My email: qihangsun98 at outlook dot com.

Research interest:

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

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

Profile photo

Publications and Preprints

  1. Fourier interpolation in dimensions 3 and 4 with real-variable Kloosterman sums.
    in preparation.
  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]

Not for publication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)]

Conferences, seminars, etc.

  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. Lightening 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.

My Math Notes

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)

Pari/GP study

  1. Pari/GP official website
  2. 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.
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.