Hasan Gümral

Title:

Prof.

Department:

Mathematics Department

Position:

Faculty Member

Email:

hgumral@yeditepe.edu.tr

Telephone:

0216 578 00 00 (2594)

Office:

Eng. B615

Time:

Full Time

Akademik

Resume

Education and Academic Degrees:

Professor, 2004, Department of Mathematics, Yeditepe University
Associate Professor, 1998, Mathematical Physics, Istanbul Technical University.
Ph.D., 1992, Department of Mathematics, Bilkent University, Ankara.

Thesis: Poisson Structures of Dynamical Systems and Equations of Hydrodynamic Type. Advisor: Prof. Dr. Yavuz Nutku.

M.Sc., 1988, Department of Physics, Middle East Technical University, Ankara.

Thesis: Symmetries, Conservation Laws and Multi-Hamiltonian Structure of Equations of Hydrodynamic Type. Advisor: Assoc. Prof. Dr. Ahmet Eriş.

B.Sc., 1986, Department of Physics, Middle East Technical University, Ankara.

For a more detailed CV please follow this link.

Research Areas:

Geometric mechanics: symplectic, multi-symplectic, Poisson, contact, Jacobi and multi-Hamiltonian structures with applications to geometry and integrability of non-linear differential equations of physical importance, in particular, to fluids and plasmas.

Publications

H. Gümral, Y. Nutku, Multi-Hamiltonian structure of equations of hydrodynamic type, J. Math. Phys. 31(11) 1990, 2606-2611.
H. Gümral, Bi-Hamiltonian structure of N-component Kodama equations, J. Phys. A: Math. Gen. 25 (1992) 5141-5149.
H.Gümral, Y. Nutku, Poisson structure of dynamical systems with three degrees of freedom, J. Math. Phys. 34 (1993) 5691-5723.
H.Gümral, Y. Nutku, Bi-Hamiltonian structures of dispersionless-Boussinesq and Benney equations, J. Phys. A: Math. Gen. 27 (1994) 193-200.
H.Gümral, Contravariant geometry of time-dependent dynamical systems, Phys. Lett. A 218 (1996) 235-239.
H.Gümral, Lagrangian description, symplectic structure, and invariants of 3D fluid flow, Phys. Lett. A 232 (1997) 417-424.
H.Gümral, A time-extended Hamiltonian formalism, Phys. Lett. A 257 (1999) 43-52.
H.Gümral, Kinematical symmetries of 3D incompressible flows, Physica D 135 (2000) 117-136.
H.Gümral, Helicity invariants in 3D: Kinematical aspects, Physica D 139 (2000) 335-359.
E. Abadoğlu, H. Gümral, Bi-Hamiltonian structure in Frenet-Serret frame, Physica D 238 (2009) 526-530.
H. Gümral, Existence of Hamiltonian Structure in 3D, Adv. in Dyn. Sys. and Appl., 5 (2010) 159-171.
H. Gümral, Geometry of Plasma Dynamics I: Group of Canonical Diffeomorphisms, J. Math. Phys. 51 (2010) 083501 (23pages).
O. Esen, H. Gümral, Lifts, Jets and Reduced Dynamics, Int. J. of Geom. Meth. in Mod. Phys. 8 (2011) 331-344.
E. Abadoğlu, H. Gümral, Poisson Structures for the Aristotelian Model of Three-Body Motion, J. Phys. A: Math. Theor. 44 (2011) 325204 (15pages).
O. Esen, H. Gümral, Geometry of Plasma Dynamics II: Lie Algebra of Hamiltonian Vector Fields, J. Geom. Mech. 4 (2012) 239-269.
O. Esen, H. Gümral, Tulczyjew Triplets for Lie Groups I: Trivializations and Reductions, J. Lie Theory 24 (2014) 1115-1160.
H. Gümral, Lagrangian Description, Symplectisation and Eulerian Dynamics of Incompressible Fluids, Turkish J. Math. 40 (2016) 925-940.
O. Esen, A Ghose Choudhury, Partha Guha, H. Gümral, Superintegrable Cases of Four Dimensional Dynamical Systems, Regular and Chaotic Dynamics 21 (2016) 175-188.
O. Esen, H. Gümral, Tulczyjew Triplets for Lie Groups II: Dynamics, Journal of Lie Theory 27 (2017) 329-356.
F. Çağatay-Uçgun, O. Esen, H. Gümral, Reductions of Topologically Massive Gravity I: Hamiltonian Analysis of Second Order Degenerate Lagrangians, J.Math.Phys. 59 (2018) 013510 (16 pages).
Oğul Esen, Miroslav Grmela, Hasan Gümral and Michal Pavelka, Lifts of Symmetric Tensors: Fluids, Plasma and Grad Hierarchy, Entropy 21 (2019) 907 (33 pages).
F. Çağatay-Uçgun, O. Esen, H. Gümral, Reductions of Topologically Massive Gravity II: First Order Realizations of Second Order Lagrangians, J. Math. Phys. 61 (2020) 073504 (30 pages).
O. Esen, H. Gümral, S. Sütlü, Tulczyjew Triplets for Lie Groups III: higher order dynamics and reductions on iterated bundles, Theoretical and Applied Mechanics 48 (2021) 201-236. https://doi.org/10.2298/TAM210312009E
H. Gümral, Dirac’s Analysis and Ostrogradskii’s theorem for a Class of Second Order Degenerate Lagrangians, Int. J. of Geom. Meth. in Mod. Phys. 19 (2022) 2250008 (24pages). WOS:000733361600002
O. Esen, P.Guha, H. Gümral, 3D-flows Generated by the Curl of a Vector Potential and Maurer-Cartan Equations, Turkish J. Math. 46 (2022) 3234-3244 WOS:000890825900011
H Gümral, Symmetry and reduction for second order degenerate Lagrangians, J. of Phys.: Conf. Series 2667 (2023) 012073 doi:10.1088/1742-6596/2667/1/012073
H. Gümral, Oscillator algebra of chiral oscillator, submitted, Rep. on Math. Phys.
O. Esen, P.Guha, H. Gümral, On geometrical couplings of dissipation and curl forces, submitted to Math. Phys. Anal. and Geom.
Ogul Esen, Ayten Gezici, Hasan Gümral, Miroslav Grmela, Michal Pavelka and Serkan Sütlü, Conformal and Contact Kinetic Dynamics and Their Geometrization, July 3, 2023

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Hasan Gümral

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