Artan Sheshmani
ProfessorGroup: 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
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
- 2024 China National Talent Award
- 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
Publication
- [1] Jacob Kryczka, Artan Sheshmani and Shing-Tung Yau, Derived Moduli Spaces of Nonlinear PDEs II: Variational Tricomplex and BV Formalism, arXiv:2406.1682(2024)
- [2] 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)
- [3] Caucher Birkar, Jia Jia, and Artan Sheshmani, Sheaf Stable Pairs, Quot Schemes, and Birational Geometry, arXiv.2406.00230(2024)
- [4] Artan Sheshmani and Shing-Tung Yau, Higher rank flag sheaves on surfaces, European Journal of Mathematics, 10(2024), 44
- [5] 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)
- [6] 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)
- [7] Yuxiang Liu, Artan Sheshmani, Shing-Tung Yau, Rigid Schubert classes in partial flag varieties, arXiv:2401.11375(2024)
- [8] Jacob Kryczka, Artan Sheshmani, Shing-Tung Yau, Derived moduli Spaces of Non-linear PDEs I: Singular Propagations, ArXiV(2023)
- [9] Dennis Borisov, Ludmil Katzarkov and Artan Sheshmani, Shifted symplectic structures on derived Quot-stacks II -- Derived Quot-schemes as dg manifolds, arXiv:2312.02815(2023)
- [10] Enno Kessler, Artan Sheshmani, Shing-Tung Yau, Super Gromov-Witten Invariants via torus localization, arXiv:2311.09074(2023)
- [11] Michael Mcbreen, Artan Sheshmani and Shing-Tung Yau, Elliptic stable envelopes and hypertoric loop spaces, Selecta Mathematica, 26(2023), 73
- [12] 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
- [13] Sergei Gukov, Artan Sheshmani and Shing-Tung Yau, 3-manifolds and Vafa-Witten theory, Advances in Theoretical and Mathematical Physics, 27(2023), 2
- [14] Enno Kessler, Artan Sheshmani, Shing-Tung Yau, Torus Actions on Moduli Spaces of Super Stable Maps of Genus Zero, 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(2023), 399, , 1991-2043
- [16] Michael Mcbreen, Artan Sheshmani, Shing-Tung Yau, Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces, Annales de L'Institut Fourier(2023)
- [17] Dennis Borisov, Artan Sheshmani , Ludmil Katzarkov, Shifted symplectic structures on derived Quot-stacks, Advances in Mathematics, 403(2022), 108369
- [18] Enno Kessler, Artan Sheshmani and Shing-Tung Yau, Super J-holomorphic Curves: Construction of the Moduli Space, Mathematischel Annalen, 383(2022), 1391-1449
- [19] Amin Gholampour and Artan Sheshmani, Donaldson-Thomas invariants, linear systems and punctual Hilbert schemes, Mathematical Research Letters, 25(2022), 4, 1049-1064
- [20] Artan Sheshmani, and Yizhuang You, Categorical Representation Learning: Morphism is all you need, Machine Learning: Science and Technology, 3(2021), 1, 015016
- [21] 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
- [22] Emanuel Diaconescu, Artan Sheshmani, Shing-Tung Yau, Atiyah class and sheaf counting on local Calabi Yau 4 folds,, Advances in Mathematics, 368(2020), 13
- [23] 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)
- [24] 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)
- [25] Amin Gholampour, Artan Sheshmani, Shing-Tung Yau, Nested Hilbert schemes on surfaces: Virtual fundamental class,, Advances in Mathematics, 365(2020), 13
- [26] Amin Gholmapour, Artan Sheshmani, Shing-Tung Yau, Localized Donaldson-Thomas theory of surfaces, American Journal of Mathematics, 142(2020), 2
- [27] Melissa Liu, Artan Sheshmani, Stacky GKM Graphs and Orbifold Gromov-Witten Theory, Asian Journal of Mathematics , 24(2020), 5
- [28] 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
- [29] Amin Gholampour, Artan Sheshmani,, Donaldson-Thomas Invariants of 2-Dimensional sheaves inside threefolds and modular forms, Advances in Mathematics, 326(2018), 21, 79-107
- [30] 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
- [31] 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
- [32] Amin Gholampour, Artan Sheshmani, Yukinobu Toda), Stable pairs on nodal K3 brations, International Mathematical Research Notices, 2017(2017), 00, 1-50
- [33] Melissa Liu, Artan Sheshmani, Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds, SIGMA, 13(2017), 048, 1-21
- [34] Artan Sheshmani, Higher rank stable pairs and virtual localization, Communications in Analysis and Geometry, 24(2016), 1
- [35] Artan Sheshmani, Wall-crossing and invariants of higher rank stable pairs, Illinois Journal of Mathematics, 59(2016), 1, 55-83
- [36] Amin Gholampour, Artan Sheshmani, , Intersection numbers on the relative Hilbert schemes of points on surfaces, Asian Journal of Mathematics, 21(2016), 3, 531-542
- [37] Artan Sheshmani, Weighted Euler characteristic of the moduli space of higher rank Joyce-Song pairs, European Journal of Mathematics (EJM), 2(2016), 2
- [38] Amin Gholampour, Artan Sheshmani, , Generalized Donaldson-Thomas Invariants of 2-Dimensional sheaves on local P2, Adv. Theor. Math. Phys, 19(2015), 3, 673-699
- [39] Amin Gholampour, Artan Sheshmani, Richard Thomas, Counting curves on surfaces in Calabi-Yau threefolds, Mathematische Annalen, 360(2014), 1-2, 67-78
- [40] Artan Sheshmani, Introduction to higher rank theory of stable pairs, AMS Proc. Symp. Pure Math., 85(2012)
- [41] Artan Sheshmani, Towards studying the higher rank Pandharipande-Thomas theory of stable pairs, ISBN, 978-1267-16462-9.(2011)
- [42] 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
- [43] 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)
- [44] 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
- [45] Mohsen Asghari, Artan Sheshmani,, A thermo elastic solution for functionally graded beams using stress function, Proc. ICCES Conf. (2004)
- [46] Artan Sheshmani, Reza Naghdabadi,, Objectivity of rates of deformation tensors in nonlinear continuum mechanics, Proc. ASME Conf.(2004)
- [47] Kambiz Behfar, Artan Sheshmani, Reza Naghdabadi, General derivation for conjugate strains of Eshelby-like stress tensors, Proc. ASME(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 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)
- 2023---current Daniel Galviz (PhD student at YMSC Tsinghua)
- 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:
- Counting sheaves and objects in derived category in dimensions 2,3,4,5 (BIMSA, Spring 2024)
- Counting sheaves and objects in derived category in dimensions 2,3,4,5 (BIMSA, Fall 2023)
- Gromov-Witten and Donaldson-Thomas theory (BIMSA, Spring 2023)
- Derived Algebraic / Differential Geometry (BIMSA, Fall 2022)
- Gromov-Witten/ Donaldson-Thomas theory and birational/symplectic invariants for algebraic surfaces--24 lectures (Spring 2021)
- Derived Algebraic/Differential Geometry (Together with Dennis Borisov--18 lectures) (Spring 2019)
- Quantum cohomology, Nakajima varieties and Quantum groups (19 lectures) (Spring 2018)
- Special lectures series on Donaldson-Thomas and Gromov-Witten theories (9 lectures) (Spring 2017)
- Nested Hilbert schemes and DT theory of local threefolds (Spring 2017)
- The theory of nested Hilbert schemes on surfaces (Spring 2017)
- Talk at JDG 2017 (Summer 2017)
- On S-duality Modularity Conjecture for Quintic Threefolds (Fall 2015)
Update Time: 2024-07-31 11:16:30