Arman Taghavi-Chabert

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Dr Arman Taghavi-Chabert

+48 42 631 36 69
arman.taghavi-chabert@p.lodz.pl ORCID 0000-0002-9796-9875

I am a mathematician working in the fields of differential geometry and mathematical physics. I notably investigate geometric structures arising from a wide range of contexts, such as general relativity and the theory of differential equations. Throughout the years I have delved into a number of research areas which include:

  • Twistor theory, a geometric framework put forward by Roger Penrose, whereby solutions to invariant differential equations in spacetime are constructed in terms of holomorphic data on an auxiliary complex space, referred to as twistor space.
  • Spinor calculus on complex Riemannian manifolds, a closely related approach to general relativity in arbitrary dimensions.
  • Conformal geometry, concerned with angle-preserving transformations of manifolds. Many equations of physics, such as those describing massless particles, are conformally invariant.
  • Projective structures, arising in connection with geodesics.
  • Cauchy-Riemann (CR) geometry, broadly understood as the study of hypersurfaces in complex space.
  • Tractor calculus, a powerful calculus that provides a manifestly invariant formulation of geometric problems in a wide classes of geometries such as the aforementioned conformal, projective and CR geometries (the so-called Cartan parabolic geometries).
  • The interplay of any of these geometries, for instance, Patterson-Walker geometry (projective and conformal structures), Robinson geometry (CR and conformal structures), or the Fefferman construction.

Publications

  1. Optical geometries (with A. Fino and T. Leistner), accepted for publication in Ann. Sc. Norm. Super. Pisa, Cl. Sci., arXiv:2009.10012
  2. Almost Robinson geometries (with A. Fino and T. Leistner), Lett. Math. Phys. 113 (2023), no.3, Paper No. 56,103 pp., arXiv:2102.05634
  3. Distinguished curves and integrability in Riemannian, conformal, and projective geometry (with A. R. Gover and D. Snell), Adv. Theor. Math. Phys., 25 (2021), no. 8, pp 2055-2118, arXiv:1806.09830
  4. Twisting non-shearing congruences of null geodesics, almost CR structures, and Einstein metrics in even dimensions, Ann. Mat. Pura Appl. (4), 201 (2022), pp 655-693
  5. Conformal Patterson-Walker metrics (with M. Hammerl, K. Sagerschnig, J. Šilhan and V. Žádník), Asian J. Math.23 (2019), no. 5, 703-734
  6. Decomposable (4,7) solutions in eleven-dimensional supergravity (with D. Alekseevsky and I. Chrysikos), Classical Quantum Gravity36 (2019), pp 075002
  7. Fefferman-Graham ambient metrics of Patterson-Walker metrics (with M. Hammerl, K. Sagerschnig, J. Šilhan and V. Žádník), Bull. Lond. Math. Soc.50 (2018), no. 2, 316-320
  8. A projective-to-conformal Fefferman-type construction (with M. Hammerl, K. Sagerschnig, J. Šilhan and V. Žádník), SIGMA13 (2017), 081, 33 pages
  9. Pure spinors, intrinsic torsion and curvature in odd dimensions, Differential Geom. and Appl.51 (2017), 117-152
  10. Twistor geometry of null foliations in complex Euclidean space, SIGMA13 (2017), 005, 42 pages
  11. Pure spinors, intrinsic torsion and curvature in even dimensions, Differential Geom. and Appl.46 (2016), 164-203
  12. A Goldberg-Sachs theorem in dimension three (with P. Nurowski), Classical Quantum Gravity32 (2015), pp 115009
  13. Conformal field theories in six-dimensional twistor space (with L. J. Mason and R. A. Reid-Edwards), J. Geom. Phys.62 (2012), no. 12, 2353-2375
  14. The complex Goldberg-Sachs theorem in higher dimensions, J. Geom. Phys.62 (2012), no. 5, 981-1012
  15. Optical structures, algebraically special spacetimes and the Goldberg-Sachs theorem in five dimensions, Classical Quantum Gravity28 (2011), pp 145010
  16. Killing-Yano tensors and multi-hermitian structures (with L. J. Mason), J. Geom. Phys.60 (2010), no. 6-8, 907-923

Preprints

  1. Perturbations of Fefferman spaces over almost CR manifolds, available at arXiv:2309.16986
  2. Perturbations of Fefferman spaces over CR three-manifolds, arXiv:2303.07328
  3. The curvature of almost Robinson manifolds, arXiv:1404.5810

Employment

  • 10/2023 - current: Assistant professor, Łódź University of Technology
  • 07/2021 - 09/2023: Norway Grants POLS-NCN postdoctoral fellowship, University of Warsaw
  • 10/2020 - 12/2020: GAČR Postdoctoral researcher, "Symmetry and invariance in analysis, geometric modelling and control theory", Masaryk University
  • 01/2018 - 08/2021: Assistant professor (on leave from 01/2020 until resignation), American University of Beirut
  • 09/2017 - 10/2017: Simons semester fellowship "Symmetry and geometric structures", IMPAN
  • 01/2017 - 12/2017: Postdoctoral fellowship "Current problems in Mathematics", University of Turin
  • 01/2016 - 12/2016: Departmental postdoctoral researcher, Masaryk University
  • 01/2014 - 12/2015: GAČR postdoctoral fellowship, Masaryk University
  • 04/2013 - 12/2013: Eduard Čech Institute fellowship, Masaryk University
  • 04/2011 - 03/2013: Cofund Marie Skłodowska-Curie (SoMoPro) fellowship, Masaryk University
  • 01/2011 - 03/2011: Eduard Čech Center fellowship, Masaryk University
  • 10/2009 - 09/2010: Stipendiary lecturer, Lady Margaret Hall, University of Oxford

Grants

  • 07/2021 - 06/2023: Norway Grants - NCN POLS fellowship, No. 2020/37/K/ST1/02788, University of Warsaw
  • 06/2018 - 08/2018: FAS long-term development grant, American University of Beirut
  • 01/2014 - 12/2015: GAČR postdoctoral fellowship, GP14-27885P, Masaryk University
  • 04/2011 - 03/2013: Cofund Marie Skłodowska-Curie (SoMoPro) fellowship, "HigherDimTwistors", No. 229603, Masaryk University

Selected visits

  • 10/2021: Arctic University of Norway, Tromsø, host: Dennis The, TFS Guest Professorship
  • 06/2018 - 08/2018: IMPAN, host: Wojciech Kryński, AUB FAS long-term development grant
  • 10/2010 - 12/2010: The Mathematical Institute, University of Oxford, host: Lionel J. Mason

Habilitation

  • 30/11/2017: Abilitazione Scientifica Nazionale di professore universitario di Seconda Fascia in Analisi e Geometria, University of Turin

Postgraduate studies

  • 2005 - 2009: DPhil in Mathematics, University of Oxford, Supervisor: Lionel J. Mason

Undergraduate studies

  • 2002 - 2005: MSci in Mathematics and Physics, University of Glasgow
  • 1998 - 2002: BMus in Music, University of Glasgow

Graduate scholarships

  • 2008 - 2009: St. Peter's College Graduate Senior Scholarship, University of Oxford
  • 2005 - 2008: Scatcherd European Scholarship, University of Oxford

Lecturer

  • Summer 2024: Mathematical Methods 2: Partial Differential equations, Łódź University of Technology
  • Winter 2023: Mathematics 3: Probability and Statistics, Łódź University of Technology
  • Spring 2022: Conformal geometry and related topics, University of Warsaw
  • 2018 - 2019: Assistant professor, American University of Beirut
    • Undergraduate: Calculus and analytic geometry III, Differential equations, Linear algebra I, Introduction to complex analysis
    • Graduate: Calculus on manifolds
  • Spring 2017: (with I. Chrysikos) A course on spin geometry, University of Turin
  • Spring 2012: An introduction to the Penrose transform, Masaryk University

Tutor

  • Summer 2024: Mathematical Methods 2: Partial Differential equations, Łódź University of Technology
  • Winter 2023: Mathematics 3: Probability and Statistics, Łódź University of Technology
  • Winter 2023: Physics, Łódź University of Technology
  • Winter 2023: Fundamentals of Physics, Łódź University of Technology
  • Autumn 2016: Continuous models and statistics, Masaryk University
  • 2009 - 2010: Stipendiary Lecturer, Lady Margaret Hall, Oxford
    • Part A: Differential equations, Calculus of variations, Classical mechanics, Fluid dynamics and waves
    • Mods: Calculus, Dynamics
  • 2008 - 2009: St. Peter's College, Oxford
    • Part A: Complex analysis, Calculus of variations, Classical mechanics, Electromagnetism, Multivariable calculus

Graduate assistant

  • 2005 - 2008: Mathematical Institute, Oxford
    • Part B: Special relativity, Electromagnetism and quantum mechanics
    • Part C: Advanced general relativity

Mentoring

  • 11/2021 - 06/2023: mentoring a doctoral student on conformal and CR methods in general relativity as part of a POLS-NCN project, University of Warsaw
  • Autumn 2009: mentoring an exchange Master student on Clifford algebras, spinors and twistors, Oxford Programme for Undergraduate Studies

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