王智拓科研成果

基本信息/About me 科学研究 / Research 教学 / Teaching Talks 新建主栏目 基本信息 名称 哈工大数学研究院副教授。/ Associate Professor. 教育经历 / Education 标题 Education 起讫时间 所学专业 学习机构 University of Paris-sud 11 学历 Ph. D 简单介绍 Advisor: Vincent Rivasseau 标题 Posdoc 起讫时间 2013.01-2014.12 所学专业 Mathematics 学习机构 Department of Mathematics, University of Roma 3 学历 简单介绍 Mentors: Alessandro Giuliani and Vieri Mastropietro. Posdoc supported by ERC Research / 科学研究 名称 Research area: Mathematical Physics, Probability, Noncommutative geometry Current interest: Constructive renormalization theory, and its applications in: Quantum Many-body systems and Statistical Mechanics models, Noncommutative quantum field theory, Stochastic Loewner Evolution and Liouville theory. Research Gate: https://www.researchgate.net/profile/Zhituo_Wang2 Erdos Index: 4 (one path: Paul Erdos-Pavol Hell-Eugene Speer-Vincent Rivasseau -Zhituo Wang) Einstein Index: 4 (one path: Albert Einstein-Valentine Bargmann-Ivan Todorov -Harald Grosse-Zhituo Wang) 主持国家自然科学基金青年（2018-2020）、面上（2021-2024）项目各一项。 Publication 论文标题 Phase Transitions in Square Hubbard Model 作者 Zhituo Wang 发表时间 期刊名称 arXiv:2303.13628 期卷 简单介绍 Non-Fermi liquid behaviors in square Hubard model deviated from half-filling. 论文标题 Honeycomb Hubbard Model at van Hove Filling 作者 Vincent Rivasseau, Zhituo Wang* 发表时间 2023.03 期刊名称 Communications in Mathematical physics 期卷 401, pages 2569–2642 (2023) 简单介绍 74 pages. The ground state of the two-dimensional honeycomb Hubbard mode with chemical potential equal to one is proved not to be a Fermi liquid. Online version: https://rdcu.be/c8IMB https://doi.org/10.1007/s00220-023-04696-8 论文标题 On the Sector Counting Lemma 作者 Zhituo Wang 发表时间 2021.10 期刊名称 Letters in Mathematical Physics 期卷 简单介绍 14 pages. A sector counting lemma for quasi-symmetric Fermi surfaces with C2 regularity has been proved.Link to the online version: https://rdcu.be/cyPuM 论文标题 Non-Fermi Liquid Behaviors in the Hubbard model on the Honeycomb lattice 作者 Zhituo Wang 发表时间 期刊名称 arXiv:1907.12553, 56 pages 期卷 简单介绍 论文标题 Constructive Renormalization of the 2-Dimensional Grosse–Wulkenhaar Model 作者 Zhituo Wang 发表时间 期刊名称 Annales Henri Poincaré 期卷 Ann. Henri Poincare 19 (2018), 2435–2490 简单介绍 56 pages; The first fully constructed non-solvable matrix model. 论文标题 Corrected loop vertex expansion for Φ42 theory 作者 Vincent Rivasseau, Zhituo Wang 发表时间 期刊名称 Journal of Mathematical Physics 期卷 56, 062301 (2015); https://doi.org/10.1063/1.4922116 简单介绍 23 pages; Multi-scale loop vertex expansions for the simplest renormalizable QFT model. The slice-testing expansions was introduced for the first time. 论文标题 How to resum Feynman graphs 作者 Vincent Rivasseau, Zhituo Wang 发表时间 期刊名称 Annales Henri Poincaré 期卷 November 2014, Volume 15, Issue 11, pp 2069–2083 简单介绍 15 pages; Clarify how Feynman graphs from ordinary perturbation expansions are resumed in the Loop vertex expansions. 论文标题 Quantum quench for inhomogeneous states in the nonlocal Luttinger model 作者 Vieri Mastropietro, Zhituo Wang 发表时间 期刊名称 PHYSICAL REVIEW B 期卷 Volume: 91 Issue: 8 Article Number: 085123 简单介绍 Mathematically rigorous results concerning steady states in non-equilibrium statistical mechanics. A damping behavior for the time evolution of the one-particle initial state was derived for the first time, with full mathematical rigor, with the method of Mattis-Lieb. We confirmed the results with the Bosonization formulas a la E. Langmann. 论文标题 Construction of the noncommutative complex ball 作者 Zhituo Wang 发表时间 期刊名称 Journal of Mathematical Physics 期卷 Volume: 55 Issue: 9 Article Number: 092302 简单介绍 Deformation quantization of rank 1 Bergman domain with coherent states quantization. 论文标题 Construction of the noncommutative rank I Bergman domain 作者 Zhituo Wang 发表时间 期刊名称 Springer Proc. Math. Stat., 期卷 36 Lie theory and its applications in physics, 381–388, 简单介绍 论文标题 Quantum field theory on quantized Bergman domain 作者 Harald Grosse, Peter Presnajder, Zhituo Wang 发表时间 期刊名称 Journal of Mathematical Physics 期卷 Volume: 53 Issue: 1 Article Number: 013508 简单介绍 Construction of a rank 2 noncommutative Bergman domain with coherent states quantization. Possible QFT model was discussed. 论文标题 Loop vertex expansion for Phi(2k) theory in zero dimension 作者 Vincent Rivasseau, Zhituo Wang 发表时间 期刊名称 Journal of Mathematical Physics 期卷 Volume: 51 Issue: 9 Article Number: 092304 简单介绍 We generalize the LVE techniques to higher order interactions. A first step towards construction of P(PHI)2 QFT model with LVE, or Multi-scale LVE. 论文标题 Topological graph polynomials and quantum field theory Part I: heat kernel theories 作者 Thomas Krajewski, Vincent Rivasseau, Adrian Tanasa, Zhituo Wang 发表时间 期刊名称 JOURNAL OF NONCOMMUTATIVE GEOMETRY 期卷 Volume: 4 Issue: 1 Pages: 29-82 DOI 10.4171/JNCG/49 简单介绍 54 pages. The first mathematically rigorous proof of the equivalence between the Tutte polynomials for random graphs and the Symanzik polynomials for scalar QFT. Also the first rigorous proof of the equivalence between the Bolobas-Riordan polynomials for ribbon graphs and the Symanzik polynomials for non-commutative scalar QFT. 论文标题 Renormalization of orientable non-commutative Complex Phi(6)(3) model 作者 Zhituo Wang, Shaolong Wan 发表时间 期刊名称 Annales Henri Poincaré 期卷 Volume: 9 Issue: 1 Pages: 65-90 简单介绍 26 pages. We constructed the first 2%2B1 dimensional non-commutative quantum field theory model with commutative time variable that is perturbatively renormalizable to all orders. 学术会议 名称 Workshop on Renormalization Theory and Related Fields 教学 / Teaching 名称 1 李群初步 / Theory of Lie Groups， 2017春季学期研究生课程。教材及重要参考文献： Claude Chevalley, Theory of Lie Groups。 2 有限群表示论 / Representation theory for finite groups， 2018春季学期研究生课程。 教材及重要参考文献： Gordan James, Martin Liebeck, Representations and Characters of groups. 3 概率论基础 / Graduate course on Probability Theory, Autumn 2019. ，2019年秋季研究生课程。 教材及参考文献 / References: Sidney Resnick, A Probability Path; Erhan Cinla, Probability and Stochastics. 4 概率论/Undergraduate course on Probability theory，2020年秋季学期本科生课程。教材及重要参考文献：David Williams，Probability with Martingales （概率和鞅）;李贤平，概率论基础。 5 概率论/Undergraduate course on Probability theory，2021年秋季学期本科生课程。教材：《概率论》，苏淳，冯群强，科学出版社。参考文献：David Williams，Probability with Martingales （概率和鞅）;李贤平，概率论基础。 研究生招生信息 名称 拟招收基础数学方向博士研究生一名。欢迎基础较好、对数学物理、非交换几何或概率等方向感兴趣的学生报考。 概率论课程参考资料 名称 参考文献 （A）Schramm-Loewner演化及统计物理 1）Werner: Random planar curves and Schramm-Loewner evolutions 2）Lawler: Schramm-Loewner Evolution 3）Smirnov: Conformal invariance of lattice models （B）随机微分方程 4）Hairer: Regularity structure （C）AMS, What is... 基本信息 名称 Conference and Seminar Talks: Constructive renormalizations of the 2-D Honeycomb-Hubbard model, Itinerant Quantum Math Meetings, Università degli Studi di Milano, Italy, 18 March, 2024 On the Polchinski Equation and the Renormalization group flow, Oberwolfach meeting: QFT and Stochastic PDEs, Oberwolfach Research Institute for Mathematics, Germany, 17-22 December, 2023 Phase Transitions in Quantum Many-body system, Yau Mathematical Sciences Center, Tsinghua University, 26 October, 2023 Phase Transitions in Quantum Many-body Theory, Workshop: From pertubative to non-pertubative QFT, University of Muenster, Germany, 14-16 June, 2023 Phase Transitions in Quantum Many-body system, Probability Seminar, NYU Shanghai, 11 May, 2023 Phase Transitions in Quantum Many-body system, The second International Conference on Probability and Physical models, Xiangtan University, 1 May, 2023 Phase Transitions in the honeycomb-Hubbard Model, Chern Institute of Mathematics, Nankai University, 30 March, 2023 Construction of a non-integrable matrix model, Dynamical system Seminar, Capital Normal University, 08 March 2023 Construction of the two-dimensional Grosse-Wulkenhaar model, Probability Seminar, Beijing Institute of Technology, 07 March, 2023 Phase Transitions in Quantum Many-body system, Seminar in Probability and Statics, Peking University, 06 March, 2023 Phase Transitions in Quantum Many-body system, Westlake University, 05 August, 2022 Phase Transitions in Quantum Many-body system, The First Harbin-Moscow conference in analysis, Harbin Institute of Technology, July, 2022 Construction of a non-integrable matrix model, Fudan University, 09 May, 2021 Renormasation groups in quantum many-body systems, East China Normal University, April, 2021 Construction of a non-integrable matrix model, South China University of Science Technology, April, 2021 Non-Fermi liquid behaviors in the Hubbard model on the Honeycomb lattice, Capital Normal University, November, 2019 Non-fermi liquid behavior in the Hubbard Model on the honeycomb lattice, Dynamical system seminar, Nanjing University, August 2019, Hubbard Model on the honeycomb lattice, September 2017, Workshop on mathematical physics and operator algebra, Dalian Institute of Technology. Hubbard Model on the honeycomb lattice, East China Normal University, July 2017. Constructive renormalisation of the 2-dimensional Grosse-Wulkenhaar model, June, 2016, Special Week on Operator Algebras, East China Normal University, Shanghai, China.