BIMSA > 阿尔坦·谢什马尼
研究员 阿尔坦·谢什马尼

团队: 代数几何

办公室: A6-205

邮箱: artan@bimsa.cn

研究方向: 代数几何、微分几何、弦理论

个人主页: https://sites.google.com/view/artan-sheshmani

CV

个人简介

Artan Sheshmani主要研究方向为代数几何、 微分几何和弦理论的数学方面。他于2022年加入BIMSA任研究员一职，曾任哈佛大学数学科学及其应用研究所（CMSA）西门斯同调镜像对称合作项目资深成员（教授），及美国哈弗-麻省理工人工智能和基本交互作用研究所成员。

2020年至2023年期间，他在美国迈阿密大学美国数学科学研究所担任访问教授一职，并参与了关于“霍奇理论及其应用”的研究合作项目。2020-2022年，他在哈佛大学物理系担任访问教授。2016-2022年，他在丹麦奥胡斯大学数学学院（原量子几何与模空间中心）担任副教授。

他的主要研究方向集中在Gromov Witten理论、Donaldson Thomas理论、Calabi-Yau几何以及弦理论的数学方面。他研究在Calabi Yau空间上的束和曲线的模空间的几何学，其中部分工作在研究弦理论理论的数学方面起到重要作用。在他的研究中，他致力于理解在复变化的各个维度上的这些模空间的几何对偶性，并目前正在从导出几何和几何表示理论的角度拓展这些项目。

在与丘成桐（北京雁栖湖应用数学研究院、清华大学）、Cody Long（哈佛大学物理系）以及Cumrun Vafa（哈佛大学数学系及物理学系）的合作工作中，他负责具有非同调支持的束的几何模空间及其相关的非BPS（非全纯）计数不变量的相关研究。

他的名为“嵌入曲面，对偶和量子数论”的项目于2019年获得IRFD“研究领袖”基金100万美金资助，成为该项目的30名资助人之一，该项目还获得了哈佛大学CMSA研究所和奥胡斯大学的40万美金额外资助。关于IRFD“研究领袖”项目的详细信息请参阅：https://dff.dk/en/grants/research-leaders-2018。

研究兴趣

  • Algebraic Geometry: Enumerative Algebraic Geometry, Derived Algebraic Geometry
  • Gromov-Witten theory, Donaldson-Thomas theory
  • Mirror Symmetry, Calabi-Yau Geometry, Mathematics of String theory

教育经历

  • 2008 - 2011      伊利诺伊大学香槟分校      数学      博士      (Supervisor: Sheldon Katz and Tom Nevins)
  • 2006 - 2008      伊利诺伊大学香槟分校      数学      硕士
  • 1999 - 2003      谢里夫科技大学      机械/土木工程      学士
  • 1992 - 1999      伊朗全国特殊人才发展组织      数学和物理      哲学博士

工作经历

  • 2022 -      北京雁栖湖应用数学研究院      研究员
  • 2021 -      Harvard University-MIT IAiFi (Institute for Artificial Intelligence and Fundamental Interactions)      Affiliate Faculty Member
  • 2021 - 2022      哈佛大学物理学院      访问学者
  • 2020 - 2021      哈佛大学物理学院      访问教授
  • 2017 -      Simons Collaboration on Homological Mirror Symmetry, Harvard University CMSA      Senior Personnel (Professor)
  • 2016 - 2016      麻省理工学院      访问副教授
  • 2016 - 2016      麻省理工学院      访问助理教授
  • 2016 - 2021      哈佛大学      资深数学学者
  • 2016 - 2021      哈佛大学      资深基础数学学者
  • 2016 - 2022      奥尔胡斯大学      副教授
  • 2015 - 2016      Kavli Institute for the Physics and Mathematics of the Universe      助理教授
  • 2013 - 2016      俄亥俄州立大学      Zassenhaus助理教授
  • 2012 - 2013      马克思普朗克数学研究所      会员
  • 2011 - 2012      不列颠哥伦比亚大学      博士后研究员
  • 2010 - 2011      剑桥大学牛顿数学科学研究所      Postdoctoral research affiliate Member
  • 2006 - 2010      伊利诺伊大学香槟分校      助教

荣誉与奖项

  • 2025      Invited speaker to ICBS 2025
  • 2024      Invited speaker to ICCM 2024
  • 2024      Invited speaker to ICBS 2024
  • 2023      Ruolin best paper award
  • 2023      Invited speaker to ICCM 2023
  • 2017      Honorary Member of the MIT Imaginarium of Technology, MIT Media Lab ( and got featured in IMT/ MIT news).
  • 2017      current Associate member, International laboratory for Mirror Symmetry and Automorphic Forms, National Research University Higher School of Economics, Russian Federation
  • 2010      University of Illinois Dissertation Completion Fellowship
  • 2009      Member of Phi Kappa Phi national honor society
  • 2009      David G. Bourgin Fellowship
  • 2009      James D. Hogan and university of Illinois Fellowships      2009, 2010
  • 2007      R.E.G.S 2 Fellowship      2007, 2009
  • 2006      NSF graduate student travel awards (5 consecutive years)      2006-2010
  • 2006      Outstanding instructor at the University of Illinois (4 consecutive years)      2006-2009
  • 2006      Department of Mathematics internal Fellowship      2006, 2008
  • 2004      Ranked 1'st place in M.Sc. level in M.E.
  • 2003      Ranked 3'rd place in B.Sc. level (out of 152) in M.E.
  • 2003      Brilliant talent award by IRAN's Ministry of Science, Research and Technology. M.Sc. entrance without nationwide exam
  • 2000      Brilliant talent award by IRAN's Ministry of Science, Research and Technology. Permission to double major in M.E. and C.E.
  • 1999      Ranked 61'st place in IRAN's nationwide university entrance exam among 500000+ participants

出版物

  • [1] Dennis Borisov, Artan Sheshmani, Ludmil Katzarkov, Shing-Tung Yau, Global shifted potentials for moduli stacks of sheaves on Calabi-Yau four-folds, accepted by American Journal of Mathematics (2025)
  • [2] Michael Mcbreen, Artan Sheshmani, Shing-Tung Yau, Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces, Annales de L'Institut Fourier (2025)
  • [3] D Borisov, L Katzarkov, A Sheshmani, Shifted symplectic structures on derived Quot-stacks II–derived Quot-schemes as dg manifolds, Advances in Mathematics, 462, 110092 (2025)
  • [4] Jacob Kryczka and Artan Sheshmani, D-Geometric Hilbert and Quot DG-Schemes, arXiv preprint arXiv:2411.02387 (2024)
  • [5] Yuxiang Liu, Artan Sheshmani and Shing-Tung Yau, Multi-rigidity of Schubert classes in partial flag varieties, arXiv:2410.21726 (2024)
  • [6] Artan Sheshmani and Angel Toledo, Relative Monoidal Bondal-Orlov, arXiv:2410.20942 (2024)
  • [7] Jacob Kryczka, Artan Sheshmani and Shing-Tung Yau, Derived moduli spaces of nonlinear PDEs II: Variational tricomplex and BV formalism, arXiv preprint arXiv:2406.16825 (2024)
  • [8] Artan Sheshmani and Shing-Tung Yau, Higher rank flag sheaves on surfaces, European Journal of Mathematics, 10(2024), 44
  • [9] A Ziashahabi, B Buyukates, A Sheshmani, YZ You, S Avestimehr, Frequency Domain Diffusion Model with Scale-Dependent Noise Schedule, IEEE International Symposium on Information Theory (2024)
  • [10] Dennis Borisov, Artan Sheshmani, Ludmil Katzarkov and Shing-Tung Yau, Strictification and gluing of Lagrangian distributions on derived schemes with shifted symplectic forms, Advances in Mathematics, 438(2024)
  • [11] Yuxiang Liu, Artan Sheshmani, Shing-Tung Yau, Rigid Schubert classes in partial flag varieties, arXiv:2401.11375 (2024)
  • [12] J Kryczka, A Sheshmani, ST Yau, Derived moduli spaces of nonlinear pdes i: Singular propagations, arXiv preprint arXiv:2312.05226 (2023)
  • [13] Enno Kessler, Artan Sheshmani, Shing-Tung Yau, Super Gromov-Witten Invariants via torus localization, arXiv:2311.09074(2023)
  • [14] Enno Kessler, Artan Sheshmani, Shing-Tung Yau, Torus actions on moduli spaces of super stable maps of genus zero, arXiv preprint arXiv:2306.09730 (2023)
  • [15] Cody Long, Artan Sheshmani, Cumrun Vafa and Shing-Tung Yau, Non-holomorphic cycles and non-BPS black branes, Communications in Mathematical Physics, 399(3), 1991-2043 (2023)
  • [16] Michael Mcbreen, Artan Sheshmani and Shing-Tung Yau, Elliptic stable envelopes and hypertoric loop spaces, Selecta Mathematica, 26(2023), 73
  • [17] Sergei Gukov, Artan Sheshmani and Shing-Tung Yau, 3-manifolds and Vafa-Witten theory, Advances in Theoretical and Mathematical Physics, 27(2023), 2
  • [18] Artan Sheshmani, Yizhuang You, Wenbo Fu, and Ahmadreza Azizi, Categorical Representation Learning and RG flow operators for algorithmic classifiers, Machine Learning: Science and Technology (Accepted), 4, 015012 (2022)
  • [19] Artan Sheshmani, and Yizhuang You, Categorical Representation Learning: Morphism is All You Need, Machine Learning: Science and Technology, 3(1), 015016 (2021)
  • [20] Melissa Liu, Artan Sheshmani, Stacky GKM Graphs and Orbifold Gromov-Witten Theory, Asian Journal of Mathematics, 24(5) (2021)
  • [21] Amin Gholmapour, Artan Sheshmani, Shing-Tung Yau, Localized Donaldson-Thomas theory of surfaces, American Journal of Mathematics, 142(2), 405-442 (2020)
  • [22] DE Diaconescu, A Sheshmani, ST Yau, Atiyah class and sheaf counting on local Calabi Yau fourfolds, Advances in Mathematics, 368(13 ) (2020)
  • [23] Amin Gholampour and Artan Sheshmani, Donaldson-Thomas invariants, linear systems and punctual Hilbert schemes, Mathematical Research Letters (Accepted), 25, 1049-1064 (2019)
  • [24] A Gholampour, A Sheshmani, Donaldson–Thomas invariants of 2-dimensional sheaves inside threefolds and modular forms, Advances in Mathematics, 326(21), 79-107 (2018)
  • [25] Melissa Liu, Artan Sheshmani, Equivariant Gromov-Witten invariants of algebraic GKM manifolds, SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 13, 048 (2017)
  • [26] V Bouchard, T Creutzig, DE Diaconescu, C Doran, C Quigley et al., Vertical D4–D2–D0 bound states on K3 fibrations and modularity, Communications in Mathematical Physics, 350(3), 1069-1121 (2017)
  • [27] Sergei Gukov, Melissa Liu, Artan Sheshmani, Shing-Tung Yau, On topological approach to local theory of surfaces in Calabi-Yau threefolds, Advances in Theoretical and Mathematical Physics, 21(2017 no 7), 1679-1728 (2016)
  • [28] Artan Sheshmani, Weighted Euler characteristic of the moduli space of higher rank Joyce-Song pairs, European Journal of Mathematics, 2, 661–715 (2016)
  • [29] Amin Gholampour, Artan Sheshmani, , Intersection numbers on the relative Hilbert schemes of points on surfaces, Asian Journal of Mathematics, 21(3), 531-542 (2015)
  • [30] A Gholampour, A Sheshmani, Generalized Donaldson-Thomas Invariants of 2-Dimensional sheaves on local P^ 2, Advances in Theoretical and Mathematical Physics, 19(3), 673 – 699 (2015)
  • [31] A Gholampour, A Sheshmani, R Thomas, Counting curves on surfaces in Calabi–Yau 3-folds, Mathematische Annalen, 360(1), 67-78 (2014)
  • [32] Artan Sheshmani, Higher rank stable pairs and virtual localization, Communications in Analysis and Geometry, 24(1), 139-193 (2010)
  • [33] Banavara Shashikanth, Artan Sheshmani, Scott David Kelly, Wei Mingjun, Hamiltonian structure and dynamics of a neutrally buoyant rigid sphere interacting with thin vortex rings, Journal of Mathematical Fluid Mechanics, 12(3), 335-353 (2010)
  • [34] BN Shashikanth, A Sheshmani, SD Kelly, JE Marsden, Hamiltonian structure for a neutrally buoyant rigid body interacting withvortex rings of arbitrary shape: the case of arbitrary smooth body shape, Theoretical and Computational Fluid Dynamics, 22(1), 37-64 (2006)
  • [35] Mohsen Asghari, Artan Sheshmani,, A thermo elastic solution for functionally graded beams using stress function, Proc. ICCES Conf. (2004)
  • [36] A Sheshmani, YZ You, B Buyukates, A Ziashahabi, S Avestimehr, Renormalization group flow, optimal transport, and diffusion-based generative model, Physical Review E, 111(1) (2025)
  • [37] AS Caucher Birkar, Jia Jia, Sheaf stable pairs, Quot schemes and Birational geometry, Other, 44 (2024)
  • [38] J KRYCZKA, A SHESHMANI, ST YAU, A Derived Geometric Approach to Propagation of Solution Singularities for Non-linear PDEs I: Foundations (2023)
  • [39] M Saadat, F Berlinger, A Sheshmani, R Nagpal, GV Lauder, H Haj-Hariri, Hydrodynamic advantages of in-line schooling, Bioinspiration & Biomimetics, 16(4) (2021)
  • [40] E Keßler, A Sheshmani, ST Yau, Super quantum cohomology I: Super stable maps of genus zero with Neveu-Schwarz punctures, arXiv preprint arXiv:2010.15634 (2020)
  • [41] A Gholampour, A Sheshmani, ST Yau, Nested Hilbert schemes on surfaces: virtual fundamental class, Advances in Mathematics, 365 (2020)
  • [42] D Borisov, A Sheshmani, ST Yau, Global shifted potentials for moduli spaces of sheaves on cy4 (2019)
  • [43] A Sheshmani, Hilbert Schemes, Donaldson-Thomas Theory, Vafa-Witten and Seiberg Witten Theories, Notices of International Congress of Chinese Mathematicians, 7(2), 25-31 (2019)
  • [44] E Keßler, A Sheshmani, ST Yau, Super$ J $-holomorphic Curves: Construction of the Moduli Space, Mathematische Annalen (2019)
  • [45] D Borisov, L Katzarkov, A Sheshmani, Shifted symplectic structures on derived Quot-stacks I: Differential graded manifolds, Advances in Mathematics, 403 (2019)
  • [46] A Gholampour, A Sheshmani, Y Toda, Stable Pairs on Nodal$K3$Fibrations, International Mathematics Research Notices, 17, 5297-5346 (2018)
  • [47] A Sheshmani, Wall-crossing and invariants of higher rank Joyce–Song stable pairs, Illinois Journal of Mathematics, 59(1), 55-83 (2015)
  • [48] A Sheshmani, An introduction to the theory of Higher rank stable pairs and Virtual localization, Proc. Symp. Pure Math., 85, 455-466 (2012)
  • [49] A Sheshmani, Towards studying of the higher rank theory of stable pairs, University of Illinois at Urbana-Champaign (2011)
  • [50] K Behfar, A Sheshmani, R Naghdabadi, General Derivations for Conjugate Strains of Eshelby-Like Stress Tensors, Engineering Systems Design and Analysis, 353-356 (2004)

Research in Detail

Enumerative and Derived Algebraic Geometry, Mirror Symmetry:

In gauge theory, the prominent examples of enumerative invariants are Donaldson polynomials and Seiberg-Witten invariants, which help to distinguish different smooth structures on 4 dimensional manifolds. In recent years, other 4-manifold invariants have been introduced by changing the gauge theory (the PDE’s and the “counting” problem) or, by changing the dimension, similar gauge theory invariants were defined on higher-dimensional manifolds. Notable examples include Donaldson-Thomas (DT) invariants for six-dimensional, Calabi-Yau, manifolds. The study of enumerative geometry (counting of algebraic subspaces) of complex surfaces and threefolds has proven to be deeply related to physical structures, e.g. around Gopakumar-Vafa invariants (GV); Gromov-Witten invariants, DT, as well as Pandharipande-Thomas (PT) invariants; and their “motivic lifts". On the other hand, physical dualities in Gauge and String theory, such as Montonen-Olive duality and heterotic/Type II duality have also been a rich source of spectacular predictions about these counting invariants. An example of this is the modularity properties of GW or DT invariants which is proved mathematically in some cases, as suggested by the heterotic/Type II duality. Professor Sheshmani studies geometry of moduli spaces of sheaves and curves on Calabi Yau spaces, some of which arise in the study of mathematics of string theory. In his research he has worked on understanding dualities between geometry of such moduli spaces over complex varieties of dimension 2,3,4 and currently he is working on extension of these projects from derived geometry and geometric representation theory point of view. Besides enumerative algebraic geometry, recently Artan has been studying the derived geometric structure of the moduli space of solutions to Nonlinear PDE's.

Super Algebraic Geometry:

A major challenge in construction of supergeometric analogue of Gromov-Witten invariants is the suitable generalization of intersection theory. In his joint work with Enno Kessler and Shing-Tung Yau, Artan has introduced the notion of super J-holomorphic curves, and provided a functorial construction moduli space of super curves, and super stable maps from super curves to non-super almost Kahler varieties. In order to compute deformation invariants, given as intersection numbers, counting super stable maps, the team has proposed to circumvent the difficulties around construction of super Chow groups, by assuming a virtual torus localization theorem for the odd directions. That is, to construct a super virtual normal bundle to the torus-fixed loci of the moduli space of super stable maps, and compute the super Gromov-Witten invariants, via dividing by the equivariant Euler class of the super virtual normal bundle and intersecting with the virtual class of the torus fixed superstable maps. Artan and collaborators have been able to define the super Gromov-Witten invariants of genus zero which satisfy generalized Kontsevich-Manin axioms. Furthermore, they present a recipe for calculation of super Gromov-Witten invariants of projective space. 


Current and Former Postdocs / Students in Artan Sheshmani's Group:

  • 2024---current Benjamin Zhou (Postdoc at YMSC, co-mentoring with Shing-Tung Yau)
  • 2024---current Xiaopeng Xia (Postdoc at BIMSA)
  • 2024---current Yang He (Postdoc at BIMSA)
  • 2024---current Aimeric Malter (Postdoc at BIMSA)
  • 2024---current Angel Toledo (Postdoc at BIMSA)
  • 2023---current Jacob Kryczka (Postdoc at BIMSA)
  • 2023---current Yuxiang Liu (Postdoc at BIMSA)
  • 2020---2021 Cody Long (Postdoc at Harvard CMSA and Harvard Physics department)-Co-supervising with Matthew Reece
  • 2019---2021 Michael Mcbreen (Postdoc at Harvard CMSA and center for QGM)-Now Assist. Professor at Chinese University of Hong Kong
  • 2018---2020 Dennis Borisov (Postdoc at Harvard CMSA and center for QGM)-Now Assist. Professor at U. Windsor
  • 2018---2021 Enno Kessler (Postdoc at Harvard CMSA), Co-supervising with Shing-Tung Yau.
  • 2018---2019 Joakim Fargeman, Bsc student at Aarhus University, Now PhD Student at University of Texas Austin.

Lectures:

     

    更新时间: 2025-04-24 10:16:03