... For Angling may be said to be so like the Mathematics that it can never be fully learned; at least not so fully but that there 
will still be more new experiments left for the trial of other men that succeed us. 

                                                      -- from The Compleat Angler by Izaak Walton 

Research Interests:

• Symbolic Computation (Symbolic Integration and Summation)
• Differential and Difference Algebra (Galois Theory)
• Combinatorics (Wilf-Zeilberger Method)
• Arithmetic Dynamics (Dynamics of P-Recursive Sequences)

Education:

• 2001/09 -- 2005/07, B.Sci., Mathematics, Jiangsu University , Jiangsu, China.
• 2005/09 -- 2010/12, Ph.D., Applied Mathematics, Academy of Mathematics and Systems Science , Chinese Academy of Sciences, Beijing, China.

Supervisor:  Ziming Li (AMSS, China).

• 2007/12 -- 2011/02, Ph.D., Computer Science, co-directed between Academy of Mathematics and Systems Science (Beijing, China) and École Polytechnique (Paris, France).

Co-supervisors:  Frédéric Chyzak (INRIA, France) and Ziming Li (AMSS, China).

Dissertation: Some Applications of Differential-Difference Algebra to Creative Telescoping (version in Chinese)

Positions:

• 2024/04 -- present, Full Professor, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China.
• 2017/03 -- 2024/04, Associate Professor, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China.
• 2013/07 -- 2017/03, Assistant Professor, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China.
• 2015/10 -- 2016/08, Fields-Ontario Postdoctoral Fellow, Fields Institute and Faculty of Mathematics, University of Waterloo, Ontario, Canada

  Working with Stephen M. Watt and George Labahn.

• 2011/08 -- 2013/07, Post-Doctoral Fellow, Department of Mathematics, North Carolina State University, Raleigh, USA.

  Working with Michael F. Singer.

• 2011/02 -- 2011/08, Post-Doctoral Fellow, Research Institute for Symbolic Computation, Johannes Kepler University Linz, Hagenberg, Austria.

  Working with Manuel Kauers.

Preprints:

1. Single-exponential Bounds for Diagonals of D-finite Power Series, 2025.
   with Frederic Chyzak, Pingchuan Ma, and Chaochao Zhu: [PDF]

2. Telescoping Algorithms for Sigma*-Extensions via Complete Reductions, 2025.
   with Yiman Gao, Hui Huang, and Carsten Schneider: [PDF]

3. Creative Telescoping, 2025.
   with Manual Kauers and Christoph Koutschan: [PDF] These notes on creative telescoping is based on a series of lectures at the Institut Henri Poincare in November and December of 2023.

4. Flip Graphs for Polynomial Multiplication, 2025 (updated).
   with Manual Kauers: [PDF]

5. Non-minimality of Minimal Telescopers Explained by Residues, 2025.
   with Manual Kauers, Christoph Koutschan, Xiuyun Li, Rong-hua Wang and Yisen Wang: [PDF] To appear in Proceedings of ISSAC2025.

6. Symbolic Summation of Multivariate Rational Functions, 2025 (updated).
   with Lixin Du and Hanqian Fang: [PDF] [Maple package] To appear in Foundations of Computational Mathematics

Published Papers: publist

PhD Students:

1. Chen Li (李宸，2024/09-2029/07)

2. Huajun Bian (边华俊，2023/09-2028/07)

3. Hanqian Fang (方涵芊，2022/09-2027/07)

4. Xiuyun Li (李秀云，2021/09-2026/07, joint PhD student with Manuel Kauers)

5. Yisen Wang (王艺森，2021/09-2026/07, joint PhD student with Christoph Koutschan)

6. Pingchuan Ma (马平川，2019/09-2024/07, joint PhD student with Frederic Chyzak，now at Tsinghua University High School)

7. Lixin Du (杜丽欣，2017/09-2022/07, joint PhD student with Manuel Kauers and now postdoc at INRIA)

8. Chaochao Zhu (朱超超，2016/09-2021/07, now at West Anhui University)

Postdocs:

1. Candice X.T. Zhang (张旭彤， 2024/07-2026/08)

2. Yingrui Zhang (张英瑞， 2022/07-2024/08)

3. Tianlong Yu (虞天龙， 2021/07-2024/05)

Talks:

1. Rational-Transcendental Dichotomy Theorems on Power Series with Arithmetic Restrictions. Number Theory Web Seminar, February 27, 2025. [Slides]

2. Separability Problems in Creative Telescoping. ISSAC2021, Saint Petersburg, Russia, July 20, 2021. [Slides] [Paper]

3. A Reduction Approach to Creative Telescoping. ISSAC2019 Tutorial Lectures, Beihang University, Beijing, China, 2019. [Slides] [Extended Abstract]

4. How to generate all possible WZ-pairs algorithmically? Chinese Mathematical Society 2018 Annual Conference, Guiyang, Guizhou, China, 2018. [Slides]

5. Symbolic Integration: A Brief Introduction. Seminar at the School of Mathematics, Liaoning Normal University, Dalian, China, 2018. [Slides]

6. D-finite Generating Functions in Enumerative Combinatorics. Chinese Congress on Combinatorics and Graph Theory 2018, Hefei, China, 2018. [Slides]

7. Rationality Theorems on D-finite Power Series. Seminar at the School of Mathematical Sciences, East China Normal University, Shanghai, China, 2018. [Slides]

8. Reduction-based Algorithms for Creative Telescoping. Joint International Meeting of CMS-AMS, Shanghai, China, 2018. [Slides]

9. D-finite Functions: Algorithmic, Analytic and Arithmetic Aspects. Computer Mathematics 2017, Xiangtan, China, 2017. [Slides]

10. Power Series with Coefficients from a Finite Set. Lattice walks at the Interface of Algebra, Analysis and Combinatorics (2017), Banff, Canada, 2017. [Slides]

11. Creative Telescoping: Theory and Algorithms. MITACS Seminar Series/ORCCA Joint Lab Meeting, Western University, Canada, 2016. [Slides]

Research Notes (unpublished):

1. A Note on Lipshitz's Lemma 3.
   with Ziming Li, 2011: [PDF].

2. A Note on Ostrogradsky and Horowitz's Method.
   with Ziming Li, 2010: [PDF].

3. A Exercise on Real Elementary Functions in the Book "Symbolic Integration I" (second edition) .
   with Ruyong Feng, Ziming Li, Huaifu Wang, 2008: [PDF].

Teaching:

1. Linear Algebra (2014-2015) at University of Chinese Academy of Sciences.
2. Linear Algebra (2016-2017) at University of Chinese Academy of Sciences.
3. Abstract Algebra II (2019-2020) at Beihang University.
4. Abstract Algebra II (2021-2021) at Beihang University.

Seminar and Conferences:

1. Workshop on the Frontiers in Arithmetic Dynamics (FIAD2024)
2. Computer Mathematics Seminar
3. ACA 2022 Special Session: D-finite Functions and Beyond: Algorithms, Combinatorics, and Arithmetic
4. Workshop on Combinatorics and Symbolic Computation

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