北京师范大学教师主页程志云首页中文主页

个人简介

I am currently an associate professor in the School of Mathematical Sciences at Beijing Normal University.
My Erdős number is 3 (Z. Cheng-L. Kauffman-F. Harary-P. Erdős).

基本信息

电子邮箱：
所在单位：数学科学学院
学历：博士毕业
学位：理学博士学位
学科：基础数学

研究方向

低维拓扑

教育教学

授课信息（近三年）

微分流形初步, 春学期, 2025-2026, 本科生课程
代数学基础III, 秋学期, 2025-2026, 本科生课程
代数学基础Ⅰ, 秋学期, 2024-2025, 本科生课程
直观拓扑, 春学期, 2024-2025, 本科生课程
代数学基础 Ⅱ, 春学期, 2024-2025, 本科生课程

学生信息

博士

雷子逸

科学研究

研究概况

Low-dimensional Topology, Quantum Topology, Knot Theory

曾获荣誉

2020-12-31
励耘优秀青年教师奖(二等)
2020-01-01
仲英青年学者
2014-07-06
京师英才(一等)

程志云

副教授 、 博士生导师

程志云

副教授 、 博士生导师

个人简介

基本信息

教育背景

研究方向

低维拓扑

教育教学

授课信息（近三年）

微分流形初步, 春学期, 2025-2026, 本科生课程

代数学基础III, 秋学期, 2025-2026, 本科生课程

代数学基础Ⅰ, 秋学期, 2024-2025, 本科生课程

直观拓扑, 春学期, 2024-2025, 本科生课程

代数学基础 Ⅱ, 春学期, 2024-2025, 本科生课程

学生信息

博士

硕士

科学研究

研究概况

论文成果

Cheng, Zhiyun; He, Zhiyi| Fundamental generalized Legendrian rack and classical invariants, INTERNATIONAL JOURNAL OF MATHEMATICS, 2026, 37 (04)

Cheng, Zhiyun| Region Crossing Change on Plane Trivalent Graphs, GRAPHS AND COMBINATORICS, 2025, 41 (5)

Cheng, Zhiyun| Partial-dual genus polynomial of graphs, EUROPEAN JOURNAL OF COMBINATORICS, 2025, 130

Cheng,Z.;Cheng,Z.;Gao,H.;Gao,H.;Xu,M.| Transcendental linking polynomials of virtual string links, 28 (3)

Cheng, Zhiyun; Gao, Hongzhu| Coloring invariants for links in Sg x S1, CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2025, 68 (3) :927-938

Cheng, Zhiyun| INTERSECTION GRAPH AND WRITHE POLYNOMIAL, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 153 (1) :395-404

Cheng, Zhiyun; Gao, Hongzhu; Xu, Mengjian| Chord index for knots in thickened surfaces, ILLINOIS JOURNAL OF MATHEMATICS, 2022, 66 (4) :491-508

Cheng, Zhiyun; Lei, Ziyi; Wang, Yitian; Zhang, Yanguo| A Categorification for the Signed Chromatic Polynomial, ELECTRONIC JOURNAL OF COMBINATORICS, 2022, 29 (2)

Cheng, Jiawei; Cheng, Zhiyun; Xu, Jinwen; Zheng, Jieyao| Region crossing change on surfaces, MATHEMATISCHE ZEITSCHRIFT, 2022, 300 (3) :2289-2308

Cheng, Zhiyun| The Chord Index, its Definitions, Applications, and Generalizations, CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2021, 73 (3) :597-621

Cheng, Zhiyun; Fedoseev, Denis A.; Gao, Hongzhu; Manturov, Vassily O.; Xu, Mengjian| From chord parity to chord index, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2020, 29 (13)

Cheng, Zhiyun; Gao, Hongzhu; Xu, Mengjian| Some remarks on the chord index, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2020, 29 (10)

Abrosimov, Nikolay; Cheng, Zhiyun; Kauffman, Louis H.; Vesnin, Andrei; Yang, Zhiqing| The sixth Russian-Chinese conference on knot theory and related topics, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2020, 29 (10)

Cheng,Zhiyun; Mukherjee,Sujoy; Przytycki,Jozef H.; Wang,Xiao; Yang,Seung Yeop| ROOTED TREES WITH THE SAME PLUCKING POLYNOMIAL, OSAKA JOURNAL OF MATHEMATICS, 2019, 56 (3) :661-674

Cheng,Zhiyun; Elhamdadi,Mohamed; Shekhtman,Boris| On the classification of topological quandles, TOPOLOGY AND ITS APPLICATIONS, 2018, 248 :64-74

Cheng,Zhiyun; Mukherjee,Sujoy; Przytycki,Jdzef H.; Wang,Xiao; Yang,Seung Yeop| Strict unimodality of plucking polynomials of rooted trees, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2018, 27 (7)

Cheng,Zhiyun| A transcendental function invariant of virtual knots, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2017, 69 (4) :1583-1599

Cheng,Zhiyun; Manturov,V. O.; Matveev,S. V.; Vesnin,A. Y.; Yang,Zhiqing| Special Issue on Second Russia-China Conference Preface, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2017, 26 (6)

Cheng,Zhiyun| Bowling ball representation of virtual string links, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2017, 26 (6)

Cheng,Zhiyun; Mukherjee,Sujoy; Przytycki,Jozef H.; Wang,Xiao; Yang,Seung Yeop| Realization of plucking polynomials, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2017, 26 (2)

Cheng,Zhiyun; Gao,Hongzhu| Integral positive (negative) quandle cocycle invariants are trivial for knots, TOPOLOGY AND ITS APPLICATIONS, 2016, 202 :127-134

Fedoseev,Denis A.; Manturov,Vassily O.; Cheng,Zhiyun| On marked braid groups, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2015, 24 (13)

Cheng,Zhiyun| Kauffman-Harary conjecture for alternating virtual knots, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2015, 24 (8)

Cheng,Zhiyun; Gao,Hongzhu| Positive quandle homology and its applications in knot theory, ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2015, 15 (2) :933-963

Cheng,Zhiyun| A POLYNOMIAL INVARIANT OF VIRTUAL KNOTS, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (2) :713-725

Cheng,Zhiyun; Gao,Hongzhu| A POLYNOMIAL INVARIANT OF VIRTUAL LINKS, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2013, 22 (12)

Cheng,Zhiyun| When is region crossing change an unknotting operation?, MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2013, 155 (2) :257-269

Cheng,Zhi Yun; Gao,Hong Zhu| Mutation on knots and Whitney's 2-isomorphism theorem, ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2013, 29 (6) :1219-1230

Cheng Zhiyun; Gao Hongzhu| A NOTE ON THE INDEPENDENCE OF REIDEMEISTER MOVES, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2012, 21 (9)

Cheng ZhiYun; Gao HongZhu| On region crossing change and incidence matrix, SCIENCE CHINA-MATHEMATICS, 2012, 55 (7) :1487-1495

Cheng Zhiyun; Gao Hongzhu| SOME APPLICATIONS OF PLANAR GRAPH IN KNOT THEORY, ACTA MATHEMATICA SCIENTIA, 2012, 32 (2) :663-671

科研项目

纽结理论中的若干不变量, 2023

纽结与quandle, 2020

纽结理论，辫群和流形的三角剖分, 2020

低维拓扑中的一些量子不变量, 2017

纽结中的同调理论, 2013

纽结理论与虚纽结理论中的一些问题, 2013-2016

获奖信息

北京师范大学励耘优秀青年教师奖, 2021, 北京师范大学

北京师范大学第十三届青年教师教学基本功比赛, 2012, 北京师范大学

曾获荣誉

副教授、博士生导师

副教授、博士生导师