# Arman Taghavi-Chabert

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

- Optical geometries (with A. Fino and T. Leistner), accepted for publication in
*Ann. Sc. Norm. Super. Pisa, Cl. Sci.*, arXiv:2009.10012 - Almost Robinson geometries (with A. Fino and T. Leistner), Lett. Math. Phys.
**113**(2023), no.3, Paper No. 56,103 pp., arXiv:2102.05634 - 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 - 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 - Conformal Patterson-Walker metrics (with M. Hammerl, K. Sagerschnig, J. Šilhan and V. Žádník),
*Asian J. Math.***23**(2019), no. 5, 703-734 - Decomposable (4,7) solutions in eleven-dimensional supergravity (with D. Alekseevsky and I. Chrysikos),
*Classical Quantum Gravity***36**(2019), pp 075002 - 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 - A projective-to-conformal Fefferman-type construction (with M. Hammerl, K. Sagerschnig, J. Šilhan and V. Žádník),
*SIGMA***13**(2017), 081, 33 pages - Pure spinors, intrinsic torsion and curvature in odd dimensions,
*Differential Geom. and Appl.***51**(2017), 117-152 - Twistor geometry of null foliations in complex Euclidean space,
*SIGMA***13**(2017), 005, 42 pages - Pure spinors, intrinsic torsion and curvature in even dimensions,
*Differential Geom. and Appl.***46**(2016), 164-203 - A Goldberg-Sachs theorem in dimension three (with P. Nurowski),
*Classical Quantum Gravity***32**(2015), pp 115009 - 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 - The complex Goldberg-Sachs theorem in higher dimensions,
*J. Geom. Phys.***62**(2012), no. 5, 981-1012 - Optical structures, algebraically special spacetimes and the Goldberg-Sachs theorem in five dimensions,
*Classical Quantum Gravity***28**(2011), pp 145010 - Killing-Yano tensors and multi-hermitian structures (with L. J. Mason),
*J. Geom. Phys.***60**(2010), no. 6-8, 907-923

#### Preprints

- Perturbations of Fefferman spaces over almost CR manifolds, available at arXiv:2309.16986
- Perturbations of Fefferman spaces over CR three-manifolds, arXiv:2303.07328
- 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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