Welcome to Yi Zhang's Homepage

Talk:

• The Expansion Complexity of Ultimately Periodic Sequences over Finite Fields, School of Data Sciences, Jiaxing University, Jiaxing, China, November, 2024. [pdf]
• Rational Solutions of First-Order Algebraic Ordinary Difference Equations, School of Mathematics and Statistics, Fujian Normal University, Fuzhou, China, June, 2024. [pdf]
• Rational Solutions of First-Order Algebraic Ordinary Difference Equations, Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China, May, 2024. [pdf]
• Rational Solutions of First-Order Algebraic Ordinary Difference Equations, School of Mathematics, Shandong University, Jinan, China, January, 2024. [pdf]
• On Some Combinatorial Sequences Associated to Invariant Theory, School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China, January, 2024. [pdf]
• Rational Solutions of First-Order Algebraic Ordinary Difference Equations, School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China, September, 2023. [pdf]
• Rational Solutions of First-Order Algebraic Ordinary Difference Equations, Tianyuan Mathematics International Exchange Center, Kunming, China, August, 2023. [pdf]
• Rational Solutions of First-Order Algebraic Ordinary Difference Equations, Institute of Information Technology, Warsaw University of Life Sciences, Warsaw, Poland, July, 2023. [pdf]
• Mahler Discrete Residues and Summability for Rational Functions, School of Mathematical Sciences, Dalian University of Technology, Dalian, China, June, 2023. [pdf]
• Mahler Discrete Residues and Summability for Rational Functions, School of Mathematical Sciences, Luoyang Normal University, Luoyang, China, May, 2023. [pdf]
• Mahler Discrete Residues and Summability for Rational Functions, School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China, December, 2022. [pdf]
• Mahler Discrete Residues and Summability for Rational Functions, School of Mathematics and Physics, Xi'an Jiaotong-Liverpool University, Suzhou, China, November, 2022. [pdf]
• Mahler Discrete Residues and Summability for Rational Functions, School of Mathematics, Beihang University, Beijing, China, October, 2022. [pdf]
• Mahler Discrete Residues and Summability for Rational Functions, School of Mathematics, Shandong University, Jinan, China, September, 2022. [pdf]
• Apparent Singularities of D-finite Systems, Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China, October, 2021. [pdf]
• Desingularization in the q-Weyl algebra, School of Mathematics, Soochow University, Suzhou, China, October, 2021. [pdf]
• On Sequences Associated to the Invariant Theory of Rank Two Lie Algebras, School of Mathematics, Soochow University, Suzhou, China, September, 2021. [pdf]
• On Sequences Associated to the Invariant Theory of Rank Two Lie Algebras, Virtual, Online, July, 2021. [pdf]
• On Sequences Associated to the Invariant Theory of Rank Two Lie Algebras, Guilin University of Electronic Technology, Guilin, China, June, 2021. [pdf]
• On Sequences Associated to the Invariant Theory of Rank Two Lie Algebras, School of Mathematics, Beihang University, Beijing, China, October, 2020. [pdf]
• On Sequences Associated to the Invariant Theory of Rank Two Lie Algebras, Mahidol University International College, Bangkok, Thailand, January, 2020. [pdf]
• Apparent Singularities of D-finite Systems, Kolchin Seminar, CUNY Graduate Center, New York, USA, December, 2019. [pdf]
• Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix, Southern Methodist University, Dallas, USA, November, 2019. [pdf]
• Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix, Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China, July, 2019. [pdf]
• Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Austria, May, 2019. [pdf]
• Desingularization in the q-Weyl algebra, Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China, July, 2018. [pdf]
• Desingularization in the q-Weyl algebra, the Faculty of Mathematics, The University of Santiago de Compostela, Santiago, Spain, June, 2018. [pdf]
• Laurent Series Solutions of Algebraic Ordinary Differential Equations, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria, November, 2017. [pdf]
• Apparent Singularities of D-finite Systems, Jerusalem College of Technology, Jerusalem, Israel, July, 2017. [pdf]
• Contraction of Linear Difference and Differential Operators, Wilfrid Laurier University, Waterloo, Canada, July, 2016. [pdf]
• Contraction of Linear Difference and Differential Operators, Center for Combinatorics, Nankai University, Tianjin, China, June, 2016. [pdf]
• An Algorithm for Contraction of an Ore Ideal, Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Vienna, Austria, October, 2015. [pdf]
• The Restriction Problem for D-finite Functions, The University of Tokyo, Tokyo, Japan, March, 2015. [pdf]
• An Algorithm for Decomposing Multivariate Hypergeometric Terms, Jilin University, Changchun, China, August, 2013. [pdf]

Publication:

• Dmitrii Karp, Anna Vishnyakova, and Yi Zhang. Unimodality Preservation by Ratios of Functional Series and Integral Transforms, July, 2024. [pdf] arXiv 2408.01755
• Carlos E. Arreche and Yi Zhang. Twisted Mahler Discrete Residues, September, 2023. Accepted by International Mathematics Research Notices. [pdf] [DOI] arXiv 2308.16765
• Dmitrii Karp and Yi Zhang. Log-concavity and Log-convexity of Series containing Multiple Pochhammer Symbols. Fractional Calculus and Applied Analysis, 27, pp. 458-486, 2024. [pdf] [DOI] arXiv 2305.09029
• Dmitrii Karp and Yi Zhang. Convergent Expansions and Bounds for the Incomplete Elliptic Integral of the Second Kind near the Logarithmic Singularity. Mathematics of Computation, 92 (344), pp. 2769-2794, 2023. [pdf] [DOI] arXiv 2208.05242
• Carlos E. Arreche and Yi Zhang. Mahler Discrete Residues and Summability for Rational Functions, In Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, pp. 525–533, ACM Press, 2022. [pdf] [DOI] arXiv 2202.09805
• Alin Bostan, Jordan Tirrell, Bruce W. Westbury, and Yi Zhang. On Some Combinatorial Sequences Associated to Invariant Theory. European Journal of Combinatorics, 105, 103554, 2022. [pdf] [DOI] arXiv 2110.13753
• Sebastian Falkensteiner, Yi Zhang, and Thieu N. Vo. On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations. Mediterranean Journal of Mathematics, 19, 74, 2022. [pdf] [DOI] arXiv 1803.09646
• Carlos E. Arreche and Yi Zhang. Computing Differential Galois Groups of Second-order Linear q-Difference Equations. Advances in Applied Mathematics, 132, 102273, 2022. [pdf] [DOI] arXiv 2009.14026
• Zhimin Sun, Xiangyong Zeng, Chunlei Li, Yi Zhang, and Lin Yi. The Expansion Complexity of Ultimately Periodic Sequences over Finite Fields. IEEE Transactions on Information Theory, 67 (11), pp. 7550-7560, 2021. [DOI]
• Nobuki Takayama, Lin Jiu, Satoshi Kuriki, and Yi Zhang. Computation of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix. Journal of Multivariate Analysis, 179, 104642, 2020. [pdf] [DOI] arXiv 1903.10099
• Thieu N. Vo and Yi Zhang. Rational Solutions of First-Order Algebraic Ordinary Difference Equations. Advances in Applied Mathematics, 117, 102018, 2020. [pdf] [DOI] arXiv 1901.11048
• Thieu N. Vo and Yi Zhang. Rational Solutions of High-Order Algebraic Ordinary Differential Equations. Journal of Systems Science and Complexity, 33, pp. 821-835, 2020. [pdf] [DOI] arXiv 1709.04174
• Shaoshi Chen, Manuel Kauers, Ziming Li, and Yi Zhang. Apparent Singularities of D-finite Systems. Journal of Symbolic Computation, 95, pp. 217-237, 2019. [pdf] [DOI] arXiv 1705.00838
• Ting Guo, Christian Krattenthaler, and Yi Zhang. On (shape-)Wilf-equivalence for Words. Advances in Applied Mathematics, 100, pp. 87-100, 2018. [pdf] [DOI] arXiv 1802.09856
• Christoph Koutschan and Yi Zhang. Desingularization in the q-Weyl Algebra. Advances in Applied Mathematics, 97, pp. 80-101, 2018. [pdf] [DOI] arXiv 1801.04160
• Yi Zhang. Contraction of Ore Ideals with Applications, In Proceedings of the 2016 International Symposium on Symbolic and Algebraic Computation, pp. 413-420, ACM Press, 2016. [pdf] [DOI] arXiv 1511.07922 [Distinguished Student Author Award]

Research Note:

• Ziming Li and Yi Zhang. A Note on Groebner Bases of Ore Polynomials over a PID, 2016. [pdf]

Teaching Experience:

Spring 2024	Lecturer (Multivariate Calculus), Xi'an Jiaotong-Liverpool University.
Fall 2023	Lecturer (Linear Algebra), Xi'an Jiaotong-Liverpool University.
Spring 2023	Lecturer (Multivariate Calculus), Xi'an Jiaotong-Liverpool University.
Fall 2022	Lecturer (Linear Algebra), Xi'an Jiaotong-Liverpool University.
Spring 2022	Lecturer (Multivariate Calculus), Xi'an Jiaotong-Liverpool University.
Fall 2021	Lecturer (Analysis 1), Xi'an Jiaotong-Liverpool University.
Spring 2021	Lecturer (Multivariate Calculus), Xi'an Jiaotong-Liverpool University.
Fall 2020	Lecturer (Analysis 1), Xi'an Jiaotong-Liverpool University.
Spring 2020	Lecturer (Multivariate Calculus), Xi'an Jiaotong-Liverpool University.
Fall 2019	Instructor (Integral Calculus), The University of Texas at Dallas.
Spring 2019	Instructor (Linear Algebra), The University of Texas at Dallas.

Software:

Unless otherwise stated, the software provided on this web site is free. You can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software foundation; either version 2 of the licence, or (at your option) any later version. The program is distributed in in the hope that they will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public Licence for more details.

• Discrete_Log_Concavity_Hyper.nb, a Mathematica notebook for proving the discrete log-concavity of certain hypergeometric functions by using Cylindrical Algebraic Decomposition. It is based on joint work with Dmitrii Karp.
• Fake_Degree_Sequence.nb, a Mathematica notebook for computing a linear q-difference equation satisfied by the fake degree sequence associated to a given representation and a given simple complex Lie algebra by the method of creative telescoping and the closure properties of the class of q-holonomic sequences. It is based on joint work with Bruce W. Westbury. The notebook requires the availability of Koutschan's package HolonomicFunctions.m.
• Mihailovs_Conjecture.nb, a Mathematica notebook for proving Mihailovs' conjecure by the method of creative telescoping. It is based on joint work with Alin Bostan, Jordan Tirrell, and Bruce W. Westbury. The notebook requires the availability of Koutschan's package HolonomicFunctions.m.
• TestNonvanishing.nb, a Mathematica notebook for checking the nonvanishing property of algebraic ordinary differential equations in Kamke's collection. It is based on joint work with Sebastian Falkensteiner and Thieu N. Vo. The notebook requires the availability of the Mathematica package Kamke_ODE.m.
• zof.m, a Mathematica package for generating 0-1-fillings of a Ferrers board (shape), checking the number of sigma-avoiding 0-1-fillings of a Ferrers board, generating generalized 0-1-fillings of a Ferrers board, and checking the number of generalized 0-1-fillings of a Ferrers board with weight n such that the longest ne-chain has length u and the longest se-chain has length v. It is based on joint work with Ting Guo and Christian Krattenthaler. For a demonstration of the package, see the zof.nb notebook.
• Example1_HGM.nb, a Mathematica notebook for the demonstration of the holonomic gradient method for the evaluation of expection of an Euler characteristic number. It is based on joint work with Nobuki Takayama, Lin Jiu and Satoshi Kuriki . The notebook requires the availability of Koutschan's package HolonomicFunctions.m.
• KamkeODEs.mw, a Maple worksheet for checking the (completely) maximal comparability and noncriticality of algebraic ordinary differential equations in Kample's collection. It is based on joint work with Thieu N. Vo. The worksheet requires the availability of the Maple package KamkeODEs.mpl.
• qDesingularization.m, a Mathematica package for computing desingularized operators and the q-Weyl closure of a given q-difference operator in the first q-Weyl algebra. It is based on joint work with Christoph Koutschan. The package requires the availability of Koutschan's package HolonomicFunctions.m and Kauers's package Singular.m. For a description of the usage of the package, see the Example.nb notebook.

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