Ali BLEYBEL

Passionate Associate Professor with 14 years of experience administering education and classroom procedures both autonomously and in collaboration with department faculty and leaders. Building foundations for next generation of academics and workforce pioneers.

• Proved an important result towards algebraic independence of p-adic exponential using a novel approach.
• Applied results from order theory to obtain new results concerning the conformal group of a two-dimensional globally hyperbolic spacetime
• Proved a Theorem for temporal splitting of an arbitrary causal set; for a particular class of causal set, causal automorphisms are shown to be foliation preserving (so they are either time translations or space maps).
• Provided a new proof of Geroch's Theorem on temporal splitting of globally hyperbolic spacetimes.

• P-adic exponential and related subjects:
  I proved an important result on algebraic independence of p-adic exponential using a novel approach. More precisely using Ax-Schanuel conjecture for differential fields, I obtained results towards the algebraic independence of p-adic exponentials for almost all primes. This is paper “A note on complex p-adic exponential fields” below.
• Applications of non-archimedean geometry:
  Applying results from non-archimedean geometry allows to obtain answers to some open question in standard algebraic geometry. Work in this direction is still in progress.
• Conformal field theory and applications to cosmology:
  Using a novel approach, I apply results from order theory to obtain new results concerning the conformal group of a two-dimensional globally hyperbolic spacetime. This is work in preparation.
• The causal sets approach to quantum gravity:
  We showed a Theorem for temporal splitting of an arbitrary causal set; for a particular class of causal set, causal automorphisms are shown to be foliation preserving (so they are either time translations or space maps).
  Using these results, I obtained a new proof of Geroch’s Theorem on temporal splitting of globally hyperbolic spacetimes.
  This work is generalized to the case of Chronological spaces (please see below).
  In a separate paper (in preparation), using novel tools, I obtain results on the causal automorphism groups of arbitrary causal sets.

1. Bleybel, A.; “Cell decomposition for two dimensional local fields”.
Ali BLEYBEL - CV, April 2022 P. 3 of 5
Rendiconti del Seminario Matematico della Università di Padova, volume 117 (2007), 51–67.
2. Bleybel, A.; “P-adically closed fields with non-standard analytic structure”.
Journal of Symbolic logic, volume 75, Issue 3 (2010), 802-816.
3. Bleybel, A.; “The field of LE series with a nonstandard analytic structure”.
Notre Dame Journal of Formal Logic, volume 52, number 3, (2011), 255-265. 

4. Bleybel, A.; “A note on complex p-adic exponential fields”, P-Adic Num Ultrametr Anal Appl (2018) 10: 267. https://doi.org/10.1134/S2070046618040039.
5. Bleybel, A. & Zaiour, A.; “A general theorem on temporal foliations of causal sets”, Found. Phys. (2018) 48: 456. https://doi.org/10.1007/s10701-018-0157-0 6. Bleybel, A.; “A new proof of Geroch's theorem on temporal splitting of globally hyperbolic spacetimes”, arXiv:2103.13157.
7. Bleybel, A.; “A temporal splitting theorem for chronological spaces”, Gravitation and Cosmology volume 28, pages362–374 (2022)
(Springer-Pleiades Publishing). https://link.springer.com/article/10.1134/S0202289322040041
8. Bleybel, A.; “On the conformal group of a globally hyperbolic spacetime”, preprint (On the conformal group of a globally hyperbolic spacetime - Archive ouverte HAL (archives-ouvertes.fr)).
9. Bleybel, A.; “On causal automorphisms of random causal sets”, preprint.

1. A. Bleybel, T. Amari, L. van Driel-Gesztelyi and K.D. Leka: “Global budget for an eruptive active region I. Equilibrium reconstruction approach”, November 2002, Astron. & Astro. 395(2):685-695. 

2. A. Bleybel, T. Amari, L. van Driel-Gesztelyi and K.D. Leka: “Non Linear Force-Free Reconstruction of a Flaring Active Region”, Magnetic Fields and
Ali BLEYBEL - CV, April 2022 P. 4 of 5
Solar Processes, 9th European Meeting on Solar Physics, 12-18 Sep. 1999, Florence, Italy. Edited by A. Wilson. European Space Agency, ESA SP-448, 1999. ISBN: 92-9092-792-5., p.709. 

3. F El Haj Hassan, A Bleybel, A Hijazi, A Alaeddine, B Beydoun, M Zoaeter “Structural and electronic properties of Zn1− xMgxSySe1− y alloys”, Materials Letters, Vol. 61, 2007, p. 1178-1182.

1. Bleybel, A. (2019): “A quantization procedure of causal sets and applications”. Talk presented at 3rd Bangkok workshop on Discrete Geometry, Dynamics and Statistics, Chula University, Bangkok, Thailand.
2. Bleybel, A. (2022) : “The causal automorphism group of a two-dimensional globally hyperbolic Lorentzian manifold”. Talk presented at European Conference in Interdisciplinary Model Theory, University of Münster, Germany.

Taught several mathematics courses at various private universities in Lebanon (e.g. Notre Dame University (NDU), AUL, etc …).

• Reviewer for zbMATH (formerly Zentralblatt MATH), 2020-present.

• Have been a referee for a couple of international mathematics journals.