BIMSA > Artan Sheshmani
Professor Artan Sheshmani

Group: Algebraic Geometry

Office: A6-205

Email: artan@bimsa.cn

Research Field: Algebraic Geometry, Enumerative and Derived Geometry, Mirror Symmetry, Mathematics of String Theory

Webpage: https://sites.google.com/view/artan-sheshmani

CV

Biography

Artan Sheshmani is a Professor of pure Mathematics, specialized in Algebraic geometry, Enumerative and Derived Geometry, and Mathematics of String Theory. He is a Professor at Beijing Institute of Mathematical Sciences and Applications in Beijing, and a senior personnel (Professor) at Simons Collaboration Program on Homological Mirror Symmetry ( Harvard University Center for Mathematical Sciences and Applications), and an Affiliate Faculty Member at Harvard University- MIT IAiFi (Institute for Artificial Intelligence and Fundamental Interactions). Between 2020 and 2023, he jointly held the visiting professor position at Institute for the Mathematical Sciences of the Americas at University of Miami, where he was part of the research collaboration program on "Hodge theory and its applications". During the past 5 years while at Harvard CMSA he was also a visiting professor at Harvard Physics department (2020-2022), and an Associate Professor of Mathematics at Institut for Mathematik (formerly the Center for Quantum Geometry of Moduli Spaces) at Aarhus University in Denmark (2016-2022). His work is mainly focused on Gromov Witten theory, Donaldson Thomas theory, Calabi-Yau geometries, and mathematical aspects of String theory. He 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. In joint work with Shing-Tung Yau (BIMSA, YMSC, Tsinghua, Harvard Math, Harvard CMSA, and Harvard Physics departments), Cody Long (Harvard Physics), and Cumrun Vafa (Harvard Math and Physics departments) he worked on geometry moduli spaces of sheaves with non-homolomorphic support and their associated non-BPS (non-holomorphic) counting invariants. In 2019 he was one of the 30 winners of the IRFD "Research Leader" grant (approx 1M USD) on his project "Embedded surfaces, dualities and quantum number theory". The project was additionally co-financed by Harvard University CMSA and Aarhus University (Approx total. 400K USD). Detail of IRFD "Research Leader" grant: https://dff.dk/en/grants/research-leaders-2018.

Research Interest

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

Education Experience

  • 2008 - 2011      University of Illinois at Urbana-Champaign      Mathematics      Ph.D      (Supervisor: Sheldon Katz and Tom Nevins)
  • 2006 - 2008      University of Illinois at Urbana-Champaign      Mathematics      Master
  • 1999 - 2003      Sharif University of Technology      Mechanical/ Civil Engineering      Bachelor
  • 1992 - 1999      National Organization of Development of Exceptional Talents (NODET), Tabriz, IRAN.      Mathematics and Physics      Diploma

Work Experience

  • 2022 -      BIMSA      Professor
  • 2021 -      Harvard University-MIT IAiFi (Institute for Artificial Intelligence and Fundamental Interactions)      Affiliate Faculty Member
  • 2021 - 2022      Physics Department, Harvard University      Visiting Scholar (Visiting Professor)
  • 2020 - 2021      Department of Physics, Harvard University      Visiting Professor
  • 2017 -      Simons Collaboration on Homological Mirror Symmetry, Harvard University CMSA      Senior Personnel (Professor)
  • 2016 - 2016      Massachusetts Institute of Technology      Visiting Associate Professor
  • 2016 - 2016      Massachusetts Institute of Technology      Visiting Assistant Professor
  • 2016 - 2021      Harvard University CMSA      Senior Member (Associate Professor)
  • 2016 - 2021      Harvard University CMSA      Senior pure Mathematician
  • 2016 - 2022      Institut for Matematik, Aarhus Universitet      Associate Professor
  • 2015 - 2016      Kavli Institute for the Physics and Mathematics of the Universe      Adjunct Assistant Professor
  • 2013 - 2016      The Ohio State University      Zassenhaus Assistant Professor
  • 2012 - 2013      Max Planck Institut fur Mathematik      Member
  • 2011 - 2012      University of British Columbia      Postdoctoral Research Fellow
  • 2010 - 2011      Isaac Newton Institute, University of Cambridge      Postdoctoral research affiliate Member
  • 2006 - 2010      University of Illinois at Urbana-Champaign      Research and Teaching assistant

Honors and Awards

  •      Invited to speaker to ICCM 2024
  • 2024      Invited speaker to ICBS 2024
  • 2023      Ruolin best paper award 2023
  • 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

Publication

  • [1] Dennis Borisov, Ludmil Katzarkov and Artan Sheshmani, Shifted symplectic structures on derived Quot-stacks II -- Derived Quot-schemes as dg manifolds, accepted by Advances in Mathematics (2024)
  • [2] Jacob Kryczka and Artan Sheshmani, D-Geometric Hilbert and Quot DG-Schemes, arXiv:2411.02387 (2024)
  • [3] Yuxiang Liu, Artan Sheshmani and Shing-Tung Yau, Multi-rigidity of Schubert classes in partial flag varieties, arXiv:2410.21726 (2024)
  • [4] Artan Sheshmani and Angel Toledo, Relative Monoidal Bondal-Orlov, arXiv:2410.20942 (2024)
  • [5] Jacob Kryczka, Artan Sheshmani and Shing-Tung Yau, Derived Moduli Spaces of Nonlinear PDEs II: Variational Tricomplex and BV Formalism, arXiv:2406.1682(2024)
  • [6] Artan Sheshmani, Yi-Zhuang You, Baturalp Buyukates, Amir Ziashahabi, and Salman Avestimehr, Renormalization Group flow, Optimal Transport and Diffusion-based Generative Model, accepted by Physical Review E(2024)
  • [7] Caucher Birkar, Jia Jia, and Artan Sheshmani, Sheaf Stable Pairs, Quot Schemes, and Birational Geometry, arXiv.2406.00230(2024)
  • [8] Artan Sheshmani and Shing-Tung Yau, Higher rank flag sheaves on surfaces, European Journal of Mathematics, 10(2024), 44
  • [9] Amir Ziashahabi, Baturalp Buyukates, Artan Sheshmani, Yi-Zhuang You, and Salman Avestimehr, Frequency-Domain Diffusion Model with Scale-Dependent Noise Schedule, IEEE International Symposium on Information Theory (IEEE ISIT ’24)(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] Jacob Kryczka, Artan Sheshmani, Shing-Tung Yau, Derived moduli Spaces of Non-linear PDEs I: Singular Propagations, ArXiV(2023)
  • [13] Enno Kessler, Artan Sheshmani, Shing-Tung Yau, Super Gromov-Witten Invariants via torus localization, arXiv:2311.09074(2023)
  • [14] Michael Mcbreen, Artan Sheshmani and Shing-Tung Yau, Elliptic stable envelopes and hypertoric loop spaces, Selecta Mathematica, 26(2023), 73
  • [15] Artan Sheshmani, Yizhuang You, Wenbo Fu, and Ahmadreza Azizi, Categorical Representation Learning and RG flow operators for Algorithmic Classifiers, Machine Learning: Science and Technology, 4(2023), 1, 015012
  • [16] Sergei Gukov, Artan Sheshmani and Shing-Tung Yau, 3-manifolds and Vafa-Witten theory, Advances in Theoretical and Mathematical Physics, 27(2023), 2
  • [17] Enno Kessler, Artan Sheshmani, Shing-Tung Yau, Torus Actions on Moduli Spaces of Super Stable Maps of Genus Zero, arXiv:2306.09730.(2023)
  • [18] Cody Long, Artan Sheshmani, Cumrun Vafa and Shing-Tung Yau, Non-Holomorphic Cycles and Non-BPS Black Branes, Communications in Mathematical Physics(2023), 399, , 1991-2043
  • [19] Michael Mcbreen, Artan Sheshmani, Shing-Tung Yau, Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces, Annales de L'Institut Fourier(2023)
  • [20] Dennis Borisov, Artan Sheshmani , Ludmil Katzarkov, Shifted symplectic structures on derived Quot-stacks, Advances in Mathematics, 403(2022), 108369
  • [21] Enno Kessler, Artan Sheshmani and Shing-Tung Yau, Super J-holomorphic Curves: Construction of the Moduli Space, Mathematischel Annalen, 383(2022), 1391-1449
  • [22] Amin Gholampour and Artan Sheshmani, Donaldson-Thomas invariants, linear systems and punctual Hilbert schemes, Mathematical Research Letters, 25(2022), 4, 1049-1064
  • [23] Mehdi Saadat, Florian Berlinger, Artan Sheshmani, Radhika Nagpal, George V. Lauder , Hossein Haj-Hariri, Hyrdodynamic advantage of in-line schooling, Bioinspiration and Biomimetics,, 16(2021), 046002
  • [24] Artan Sheshmani, and Yizhuang You, Categorical Representation Learning: Morphism is all you need, Machine Learning: Science and Technology, 3(2021), 1, 015016
  • [25] Emanuel Diaconescu, Artan Sheshmani, Shing-Tung Yau, Atiyah class and sheaf counting on local Calabi Yau 4 folds,, Advances in Mathematics, 368(2020), 13
  • [26] Amin Gholampour, Artan Sheshmani, Shing-Tung Yau, Nested Hilbert schemes on surfaces: Virtual fundamental class,, Advances in Mathematics, 365(2020), 13
  • [27] Amin Gholmapour, Artan Sheshmani, Shing-Tung Yau, Localized Donaldson-Thomas theory of surfaces, American Journal of Mathematics, 142(2020), 2
  • [28] Melissa Liu, Artan Sheshmani, Stacky GKM Graphs and Orbifold Gromov-Witten Theory, Asian Journal of Mathematics , 24(2020), 5
  • [29] Dennis Borisov, Artan Sheshmani, Ludmil Katzarkov, Shing-Tung Yau, Global shifted potentials for moduli stacks of sheaves on Calabi-Yau four-folds, arXiv:2007.13194.(2020)
  • [30] Enno Kessler, Artan Sheshmani, Shing-Tung Yau, Super quantum cohomology I: Super stable maps of genus zero with Neveu-Schwarz punctures,, arXiv:2010.15634.(2020)
  • [31] Artan Sheshmani, Hilbert Schemes, Donaldson-Thomas theory, Vafa-Witten and Seiberg-Witten theories,, Notices of International Congress of Chinese Mathematicians,, 7(2019), 2, 25-31
  • [32] Amin Gholampour, Artan Sheshmani,, Donaldson-Thomas Invariants of 2-Dimensional sheaves inside threefolds and modular forms, Advances in Mathematics, 326(2018), 21, 79-107
  • [33] 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), 7, 1679-1728
  • [34] Vincent Bouchard, Thomas Creutzig, Emanuel Diaconescu, Charles Doran, Callum Quigley, Artan Sheshmani, Vertical D4-D2-D0 bound states on K3 brations and modularity,, Communications in Mathematical Physics , 350(2017), 3, 1069-1121
  • [35] Amin Gholampour, Artan Sheshmani, Yukinobu Toda), Stable pairs on nodal K3 brations, International Mathematical Research Notices, 2017(2017), 00, 1-50
  • [36] Melissa Liu, Artan Sheshmani, Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds, SIGMA, 13(2017), 048, 1-21
  • [37] Amin Gholampour, Artan Sheshmani, , Intersection numbers on the relative Hilbert schemes of points on surfaces, Asian Journal of Mathematics, 21(2016), 3, 531-542
  • [38] Artan Sheshmani, Higher rank stable pairs and virtual localization, Communications in Analysis and Geometry, 24(2016), 1
  • [39] Artan Sheshmani, Wall-crossing and invariants of higher rank stable pairs, Illinois Journal of Mathematics, 59(2016), 1, 55-83
  • [40] Artan Sheshmani, Weighted Euler characteristic of the moduli space of higher rank Joyce-Song pairs, European Journal of Mathematics (EJM), 2(2016), 2
  • [41] Amin Gholampour, Artan Sheshmani, , Generalized Donaldson-Thomas Invariants of 2-Dimensional sheaves on local P2, Adv. Theor. Math. Phys, 19(2015), 3, 673-699
  • [42] Amin Gholampour, Artan Sheshmani, Richard Thomas, Counting curves on surfaces in Calabi-Yau threefolds, Mathematische Annalen, 360(2014), 1-2, 67-78
  • [43] Artan Sheshmani, Introduction to higher rank theory of stable pairs, AMS Proc. Symp. Pure Math., 85(2012)
  • [44] Artan Sheshmani, Towards studying the higher rank Pandharipande-Thomas theory of stable pairs, ISBN, 978-1267-16462-9.(2011)
  • [45] Banavara Shashikanth, Artan Sheshmani, Scott David Kelly, Wei Mingjun, Structure and Dynamics of Neutrally Buoyant Rigid Sphere Interacting with Thin Vortex Rings, Journal of Mathematical Fluid Mechanics , 12(2008), 3, 335-353
  • [46] Banavara Shashikanth, Artan Sheshmani, Scott David Kelly, Wei Mingjun, Hamiltonian structure and dynamics of a neutrally buoyant rigid sphere interacting with thin vortex rings, ECI conf. inter. Trans. Phen. V, F., Therm., Bio., Mat. Space Sci. (2007)
  • [47] Banavara Shashikanth, Artan Sheshmani, Scott David Kelly, Jerrold Marsden, Hamiltonian structure for a neutrally buoyant rigid body interacting with N vortex rings of arbitrary shape, Theoretical and Computational Fluid Dynamics, 22(2006), 1
  • [48] Kambiz Behfar, Artan Sheshmani, Reza Naghdabadi, General derivation for conjugate strains of Eshelby-like stress tensors, Proc. ASME(2004)
  • [49] Artan Sheshmani, Reza Naghdabadi,, Objectivity of rates of deformation tensors in nonlinear continuum mechanics, Proc. ASME Conf.(2004)
  • [50] Mohsen Asghari, Artan Sheshmani,, A thermo elastic solution for functionally graded beams using stress function, Proc. ICCES Conf. (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:

     

    Update Time: 2024-12-08 09:38:59