
孔德荣
基本信息
孔德荣,博士生导师,重庆大学百人计划研究员。祖籍:江苏-泰兴。
教育背景
2009.09--2012.09 荷兰Delft University of Technology 博士 (导师:F.Michel Dekking教授)
2006.09--2012.09 华东师范大学 硕博连读 (导师:李文侠教授)
2001.09--2005.06 扬州大学 本科
工作经历
2019.04--至今 重庆大学 百人计划研究员
2016.09--2018.09 荷兰Leiden University 博士后(合作导师:Charlene Kalle博士)
2012.12--2016.08 扬州大学 讲师
研究方向
分形几何与动力系统
科研项目
正在主持的科研项目
(1)国家自然科学基金面上项目11971079(2020-2023),主持
已经结题的科研项目
(1)国家自然科学基金青年项目11401516(2015-2017),主持
(2)江苏省自然科学基金青年项目BK20130433(2013-2016),主持
(3)国家自然科学基金天元项目11326207(2014),主持
(4)教育部留学回国人员启动基金(2014),主持
(5)英国伦敦数学会合作基金41706(2018-2019),参与
(6)重庆市自然科学基金面上项目cstc2019jcyj-msxmX0338(2019-2022),主持
(7)重庆市留创计划cx2019067(2020-2021),主持
专著、译著和教材等
主讲课程
2022春:实变函数(2021数学班)
2022春:分形几何(研究生)
2022春: 初等数论(2018数学班)
2022春: 数论(研究生)
2021春: 数学分析II(2020级强基班)
2020秋: 数学分析I(2020级强基班)
学术与社会兼职
”美国数学评论“评论员;德国zbMath评论员
主要成果
Submitted Papers
- (1) Density spectrum of Cantor measure, (with Pieter Allaart). https://arxiv.org/abs/2008.04474
- (2) On a class of self-similar sets which contain finitely many common points, (with Zhiqiang Wang, Kan Jiang and Wenxia Li). https://arxiv.org/abs/2109.10014
- (3) Intersections of middle-α Cantor sets with a fixed translation, (with Yan Huang). http://arXiv.org/abs/2201.07446
- (4) q-adic expansions of negative powers of p, (with Kan Jiang, Wenxia Li and Zhiqiang Wang). https://arxiv.org/abs/2204.04624
- (5) Univoque bases of real numbers: simply normal bases, irregular bases and multiple rationals, (with Yu Hu and Yan Huang). http://arxiv.org/abs/2207.07263
Published Papers
- (1) Intersections of homogeneous Cantor sets and beta-expansions, (with Wenxia Li and Michel Dekking), Nonlinearity 23 (2010), no. 11, 2815–2834. https://arxiv.org/abs/1110.3192
- (2) Multimodality of the Markov binomial distribution, (with Michel Dekking), J. Applied Probability 48 (2011), no. 4, 938–953. https://arxiv.org/abs/1102.3613
- (3) Plumes in kinetic transport: How the simple random walk can be too simple, (with Michel Dekking and Annegreet van Opbroek), Stochastic Models 28 (2012), 635-648. https://arxiv.org/abs/1110.3178
- (4) A simple stochastic kinetic transport model, (with Michel Dekking), Adv. in Applied Probability 44 (2012), 874–885. https://arxiv.org/abs/1106.2912
- (5) Hausdorff dimension of unique beta expansions, (with Wenxia Li), Nonlinearity 28 (2015), no. 1, 187–209. https://arxiv.org/abs/1401.6473
- (6) On a problem of countable expansions, (with Yuru Zou), J. Number Theory 158(2016), 134–150. https://arxiv.org/abs/1503.07434
- (7) On small univoque bases of real numbers, Acta Math. Hungar. 150 (2016), 194– 208. https://arxiv.org/abs/1602.06173
- (8) Hausdorff dimension of univoque sets and devil’s staircase, (with Vilmos Komoronik and Wenxia Li), Adv. Math. 305 (2017), 165–196. https://arxiv.org/abs/1503.00475
- (9) On small bases which admit points with two expansions, (with Wenxia Li and Yuru Zou), J. Number Theory, 173 (2017), 100–128. https://arxiv.org/abs/1507.08135
- (10) Unique expansions and intersections of Cantor sets, (with Simon Baker), Nonlinearity, 30 (2017), 1497–1512. https://arxiv.org/abs/1604.00858
- (11) Univoque bases and Hausdorff dimension, (with Wenxia Li, Fan Lv and Martijn de Vries), Monatsh. Math., 184 (2017), 443–458. https://arxiv.org/abs/1606.03791
- (12) Algebraic sums and products of univoque bases, (with Karma Dajani, Vilmos Komornik and Wenxia Li), Indag. Math., 29 (2018), 1087–1104. https://arxiv.org/abs/1710.03291
- (13) Bases in which some numbers have exactly two expansions, (with Vilmos Komornik), J. Number Theory, 195 (2019), 226–268. https://arxiv.org/abs/1705.00473
- (14) Entropy, topological transitivity and dimensional properties of unique q-expansions, (with Rafael Alcaraz Barrera and Simon Baker), Trans. Amer. Math. Soc., 371 (2019), 3209–3258. https://arxiv.org/abs/1609.02122
- (15) Multiple expansions of real numbers with digits set {0, 1, q}, (with Karma Dajani, Kan Jiang and Wenxia Li), Math. Z., 291 (2019), 1605–1619. https://arxiv.org/abs/1508.06138
(16) On the bifurcation set of unique expansions, (with Charlene Kalle, Wenxia Li and Fan Lv), Acta Arith., 188-4 (2019), 367–399. https://arxiv.org/abs/1612.07982
(17) On the structure of λ-Cantor set with overlaps, (with Karma Dajani and Yuanyuan Yao), Adv. Appl. Math., 108 (2019), 97–125. https://arxiv.org/abs/1810.08324
(18) Bifurcation sets arising from non-integer base expansions, (with Pieter Allaart and Simon Baker). J. Fractal Geom., 6-4 (2019), 301--341. https://arxiv.org/abs/1706.05190
(19) Numbers with simply normal beta-expansions, (with Simon Baker), Math. Proc. Camb. Phil. Soc. 167 (2019), 171--192. https://arxiv.org/abs/1707.01013
(20) On the continuity of the Hausdorff dimension of the univoque set, (with Pieter Allaart), Adv. Math., 354 (2019), 106729, 24pp. https://arxiv.org/abs/1804.02879
(21) The beta-transformation with a hole at 0, (with Charlene Kalle, Niels Langeveld and Wenxia Li), Ergodic Theory Dynam. Systems. 40 (2020), 2482--2514. https://arxiv.org/abs/1803.07338
(22) On the complexity of the set of codings for self-similar sets and a variation on the construction of Champernowne, (with Simon Baker), Adv. Math., 360 (2020), 106934, 29pp. https://arxiv.org/abs/1810.07083
(23) Two bifurcation sets arising from the beta transformation with a hole at $0$, (with Simon Baker), Indag. Math. 31(2020), 436--449. https://arxiv.org/abs/1904.07007
(24) Critical base for the unique codings of fat Sierpinski gasket, (with Wenxia Li), Nonlinearity 33 (2020), 4484--4511. https://arxiv.org/abs/1812.00585
(25) Univoque bases of real numbers: local dimension, Devil's staircase and isolated points}, (with Wenxia Li, Fan Lv, Zhiqiang Wang and Jiayi Xu). Adv. Appl. Math., 121 (2020), 102103, 31pp. https://arxiv.org/abs/1911.05910
(26) Multiple codings for self-similar sets with overlaps, (with Karma Dajani, Kan Jiang, Wenxia Li and Lifeng Xi). Adv. Appl. Math., 124 (2021), 102146, 49pp. https://arxiv.org/abs/1603.09304
(27) On a kind of self-similar sets with complete overlaps, (with Yuanyuan Yao). Acta Math. Hungar. 163(2) (2021), 601--622. https://arxiv.org/abs/2005.03280
(28) Pointwise densities of homogeneous Cantor measure and critical values, (with Wenxia Li and Yuanyuan Yao). Nonlinearity 34 (2021), 2350--2380. https://arxiv.org/abs/2005.03269
(29) Relative bifurcation sets and the local dimension of univoque bases, (with Pieter Allaart), Ergodic Theory Dynam. Systems. 41 (2021), 2241--2273. https://arxiv.org/abs/1809.00323
(30) On the smallest base in which a number has a unique expansion, (with Pieter Allaart), Trans. Amer. Math. Soc. 374 (2021), 6201--6249. https://arxiv.org/abs/2006.07927
(31) How likely can a point be in different Cantor sets, (with Kan Jiang and Wenxia Li), Nonlinearity, 35(2022), 1402--1430. https://arxiv.org/abs/2102.13264
(32) Critical values for the
β -transformation with a hole at0, (with Pieter Allaart). To appear in Ergodic Theory Dynam. Systems. https://arxiv.org/abs/2109.10012
研究生培养
2021级博士:黄 燕
2021级硕士:鲍思敏、张会星
2020级硕士:胡 宇、孙贝贝