HASAN GVMRAL 1 Education and Academic Degrees 2 Work

CURRICULUM VITA

HASAN GÜMRAL

February 11, 1963, Mersin, TURKEY. Married to Devrim, with a child Ate¸sBora. Addresses: Yeditepe University, Faculty of Science and Letters, Depart- ment of Mathematics, 34755 Ata¸sehir, Istanbul, Turkey. Phones: Work: +90 216 578 15 94, Mobile: +90-543-342 31 51 e-mails : [email protected], [email protected] 1 Education and academic degrees

1. Ph.D, Feb 3, 1993, (3.65/4.00) Department of Mathematics, Bilkent Uni- versity, Ankara, Turkey Dissertation: Poisson structures of dynamical systems and equations of hydrodynamic type, supervisor: Prof. Dr. Yavuz Nutku. 2. M.S, Sep 22, 1988 (28080), Department of Physics, Middle East Technical University, Ankara, Turkey, Dissertation: Symmetries, conservation laws and multi-Hamiltonian structure of equations of hydrodynamic type, supervisor: Assoc. Prof. Dr. Ahmet Eri¸s. 3. B.S, July 11, 1986 (22447), Department of Physics, Middle East Technical University, Ankara, Turkey,

2 Work Experiences

Jun 2003— , Professor, Department of Mathematics, Yeditepe University, Istanbul.· Aug 2014- May 2018, Professor, Department of Mathematics, Australian College of Kuwait. Sep 2014-Jul 2015, Professor and Acting Head of Department of Mathe- matics, Australian College of Kuwait. Dec 2001-Jun 2003, Assoc. Professor, Department of Mathematics, Yeditepe University, Istanbul.· May 2003- Oct 2011, Professor and Chairman of Department of Mathe- matics, Yeditepe University, Istanbul.·

1 Sep 2008-Feb 2009, Visiting Researcher, Dipartimento di Matematica e Informatica, Universita degli Studi di Trieste, Italia. Jun 1997-Nov 2001, Senior Researcher and Assoc. Professor (Nov 1998) at Feza Gürsey Institute (for research in mathematics and theoretical physics), Istanbul,· Turkey. Jul-Oct 2001, Visiting Senior Researcher, Department of Physics and In- stitute for Fusion Studies, University of Texas at Austin, Texas, USA.

Sep 2000-Feb 2001, Part-time Lecturer, Department of Mathematics, Bogaz-¼ içi University, Istanbul. Jul 1993-Feb 1994, Visiting Researcher, Department of Mathematics, Uni- versity of California at Berkeley, California, USA. Apr-Jul 1993, Visiting postdoctoral fellow, Fields Institute For Research in Mathematical Sciences, Waterloo, Canada. Feb 1993-Jun 1997, Researcher, Department of Physics, Tübitak, Mar- mara Research Center, Gebze, Kocaeli, Turkey. Oct 1990-Jan 1993, Research Assistant, Department of Mathematics, Bilkent University, Ankara, Turkey. Sep 1989-Sep 1990, Research Assistant, Department of Physics, Istanbul Technical University, Istanbul, Turkey. Feb 1989-Aug 1989, Visiting researcher, Department of Physics, Research Institute for Basic Sciences, Tübitak, Gebze, Kocaeli, Turkey Sep 1988-Feb 1989, Science Teacher, Tarsus Private Lyceè, Tarsus, Mersin, Turkey. Dec 1986-Sep 1988, Research Assistant, Department of Physics, Middle East Technical University, Ankara, Turkey.

2 3 Publication List 3.1 Articles in International Refereed Journals 1. H. Gümral, Y. Nutku, Multi-Hamiltonian structure of equations of hydrodynamic type, J. Math. Phys. 31(11) 1990, 2606-2611. 2. H. Gümral, Bi-Hamiltonian structure of N-component Kodama equations, J. Phys. A: Math. Gen. 25 (1992) 5141-5149. 3. H.Gümral, Y. Nutku, Poisson structure of dynamical systems with three degrees of freedom, J. Math. Phys. 34 (1993) 5691-5723. 4. H.Gümral, Y. Nutku, Bi-Hamiltonian structures of dispersionless-Boussinesq and Benney equations, J. Phys. A: Math. Gen. 27 (1994) 193-200. 5. H.Gümral, Contravariant geometry of time-dependent dynamical systems, Phys. Lett. A 218 (1996) 235-239. 6. H.Gümral, Lagrangian description, symplectic structure, and invariants of 3D ‡uid ‡ow, Phys. Lett. A 232 (1997) 417-424. 7. H.Gümral, A time-extended Hamiltonian formalism, Phys. Lett. A 257 (1999) 43-52. 8. H.Gümral, Kinematical symmetries of 3D incompressible ‡ows, Physica D 135 (2000) 117-136. 9. H.Gümral, Helicity invariants in 3D: Kinematical aspects, Physica D 139 (2000) 335-359. 10. E. Abadoglu,¼ H. Gümral, Bi-Hamiltonian structure in Frenet-Serret frame, Physica D 238 (2009) 526-530. 11. H. Gümral, Existence of Hamiltonian Structure in 3D, Adv. in Dyn. Sys. and Appl., 5 (2010) 159-171. 12. H. Gümral, Geometry of Plasma Dynamics I: Group of Canonical Di¤eomorphisms, J. Math. Phys. 51 (2010) 083501 (23pages). 13. O. Esen, H. Gümral, Lifts, Jets and Reduced Dynamics, Int. J. of Geom. Meth. in Mod. Phys. 8 (2011) 331-344. 14. E. Abadoglu,¼ H. Gümral, Poisson Structures for the Aristotelian Model of Three-Body Motion, J. Phys. A: Math. Theor. 44 (2011) 325204 (15pages). 15. O. Esen, H. Gümral, Geometry of Plasma Dynamics II: Lie Algebra of Hamiltonian Vector Fields, J. Geom. Mech. 4 (2012) 239-269. 16. O. Esen, H. Gümral, Tulczyjew Triplets for Lie Groups I: Trivializations and Reductions, J. Lie Theory 24 (2014) 1115-1160.

3 17. H. Gümral, Lagrangian Description, Symplectisation and Eulerian Dy- namics of Incompressible Fluids, Turkish J. Math. 40 (2016) 925-940. 18. O. Esen, A Ghose Choudhury, Partha Guha, H. Gümral, Superintegrable Cases of Four Dimensional Dynamical Systems, Regular and Chaotic Dy- namics 21 (2016) 175-188. 19. O. Esen, H. Gümral, Tulczyjew Triplets for Lie Groups II: Dynamics, Journal of Lie Theory 27 (2017) 329-356.

20. F. Çagatay-Uçgun,¼ O. Esen, H. Gümral, Reductions of Topologically Mas- sive Gravity I: Hamiltonian Analysis of Second Order Degenerate La- grangians, J.Math.Phys. 59 (2018) 013510 (16 pages)

21. Ogul¼ Esen, Miroslav Grmela, Hasan Gümral and Michal Pavelka, Lifts of Symmetric Tensors: Fluids, Plasma and Grad Hierarchy, Entropy 21 (2019) 907 (33 pages)

22. F. Çagatay-Uçgun,¼ O. Esen, H. Gümral, Reductions of Topologically Mas- sive Gravity II: First Order Realizations of Second Order Lagrangians, J. Math. Phys. 61 (2020) 073504 (30 pages) (First four publications are from PhD Thesis)

3.2 Articles in Turkish 1. Kontakt Parçac¬klar¬nKinetik Denklemleri, “XVII. Ulusal Mekanik Kon- gresi, Elaz¬g¼ F¬ratÜniversitesi, 5–9 Eylül 2011, bildiriler-“ (Yay¬nahaz¬r- layanlar: Hasan Engin, Mehmet Hakk¬ Omurtag, Can Fuat Delale ve Nalan Antar) (2013) 370-378 (O. Esen ile).

2. Kanonik Dönü¸sümler Grubu ve Plazma Dinamigi,¼ “XVI. Ulusal Mekanik Kongresi, Kayseri Erciyes Üniversitesi-bildiriler-“ (Yay¬na haz¬rlayanlar: A.Y. Aköz, H. Engin, Ü. Gülçat, A. Hac¬nl¬yan) (Nisan 2010) 631-649. 3. Yavuz Nutku, “An¬larla/With Memories Yavuz Nutku”, (Yay¬na haz¬r- layan: Y¬lmazAky¬ld¬z)Uygulamal¬Matematik Enstitüsü, ODTÜ (Ankara, 2010) 3-16. 4. Halk¬nve Yöneticilerin Trajedisi, Nisan 2012 (unpublished). 5. Marks ve sonsuz küçükler sorunu, Ekim 2017 (unpublished).

3.3 Articles in preparation and works in progress (or research projects in brief)

O. Esen, H. Gümral, S. Sütlü, Tulczyjew Triplets for Lie Groups III: dynamics on iterated bundles

4 O. Esen, H. Gümral, S. Sütlü, Group structure and dynamics on iterated tangent bundle of Lie Groups (to be expanded on O. Esen, H. Gümral, Reductions of Dynamics on Second Iterated Bundles of Lie Groups, arXiv: 1503.06568 H. Gümral, Poisson Bi-vectors in Four Dimensions, E. Abadoglu,¼ H. Gümral, Bi-Hamiltonian Structure of Gradient Systems in Three Dimensions and Geometry of Potential Surfaces, arXiv: 1502.03238 H. Gümral, Kinetic Theories and Local Lie Algebras, H. Gümral, Y. Y¬lmaz, Extensions of di¤eomorphism algebras for ‡uid and kinetic theories,

F. Çagatay¼ Uçgun, O. Esen, H. Gümral, Reductions of Topologically Mas- sive Gravity III: light cone dynamics, Ostrogradsky ghosts and reductions of dynamics H. Gümral, Analytic solutions of Pechukas-Yukawa equations for motion of energy levels, H. Gümral, Analytic solutions of nonlinear Bloch equations for NMR 4 Research Interests 4.1 General interests Geometric mechanics: symplectic, multi-symplectic, Poisson, contact, Jacobi and multi-Hamiltonian structures with applications to non-linear di¤erential equations of physical importance, in particular, to ‡uids and plasmas. Tul- czyjew’s construction of generalized Legendre transformations for theories on di¤eomorphism groups and, for higher order and degenerate Lagrangian theories.

4.2 Research Summary The published works may be grouped under six headings: 1) geometry of plasma dynamics and kinetic theories, including in…nite dimensional Lie theory, 2) Tulczyjew’s construction of Legendre transformations and higher order dynamics on Lie groups, 3) Hamiltonization methods for higher order Lagrangian theories (Dirac, Legendre a la Tulczyjew, Skinner-Rusk, etc with applications to gravity theories), 4) generalized Hamiltonian formulation for non-autonomous dynamical systems with applications to (magneto-)hydrodynamic motions in Lagrangian description,

5 5) local and global aspects of Poisson structures in three and four dimensions with applications to dynamical systems, 6) multi-Hamiltonian structure of equations of hydrodynamic type in one space dimension.

1. In J. Math. Phys. 51 (2010) 083501 (23pp), The dynamics of colli- sionless plasma described by the Poisson–Vlasov equations is connected to the Hamiltonian motions of particles and their symmetries. The Poisson equation is obtained as a constraint arising from the gauge symmetries of particle dynamics. Lie–Poisson reduction for the group of canonical dif- feomorphisms gives the momentum-Vlasov equations. Plasma density is given a momentum map description associated with the action of additive group of functions of particle phase space. Equivalence of Hamiltonian functionals in momentum and density formulations is shown. An alter- native formulation in momentum variables is described. A comparison of one-dimensional plasma and two-dimensional incompressible ‡uid is presented. In the second paper J. Geom. Mech. 4 (2012) 239-269, the underlying geometry of the momentum-Vlasov equations is elaborated. These equations are obtained as vertical equivalence of complete cotangent lift of Hamiltonian vector …eld generating the particle motion. This technique is also applied, in Int. J. of Geom. Meth. in Mod. Phys. 8 (2011) 331-344, to kinetic theories of particles whose con…guration space is the group of contact di¤eomorphisms. 2. The investigation of coadjoint orbit structure of canonical di¤eomorphisms requires geometric construction of Legendre transformation in the sense of Tulczyjew. This is performed in J. Lie Theory 24 (2014) 1115-1160 for general Lie groups and for both right and left trivializations. Tulczy- jew’s triplet and its symplectic reductions with the underlying Lie group are obtained. Based on this work, in Journal of Lie Theory 27 (2017) 329-356 Lie-Poisson and Euler-Poincaré equations, as well as their unre- duced versions, are realized as Lagrangian submanifolds of certain special symplectic structures. Morse families, as generating functions of Legendre transformations, relating these equations at various levels of trivializations are obtained. In arXiv: 1503.06568 Lagrangian and Hamiltonian dynamics on second iterated bundles of Lie groups are studied in a trivialization that preserve lifted group actions. All possible Poisson, symplectic and Lagrangian reductions are performed. In particular, Euler-Poincaré and Lie-Poisson reductions of higher order dynamics de…ned on second iterated bundles of Lie groups are obtained. 3. In J.Math.Phys. 59 (2018) 013510 (16 pages), we study second order degenerate Clément and Sar¬oglu-Tekin¼ Lagrangians obtained as reductions of topologically massive gravity theory. Skinner-Rusk, Dirac-Bergmann and Gotay-Nester-Hinds algorithms are applied for Hamiltonian realizations. In the second part published in J. Math. Phys. 61 (2020) 073504 (30 pages) we consider exhaustively all …rst order Lagrangian theories

6 equivalent to Clément and Sar¬oglu-Tekin¼ Lagrangians and elaborate their constraint structures. All theories are shown to possess second class constraints only. The remaining issues like light-cone dynamics for Clément Lagrangian, Ostrogradskii’s ghosts and rotational symmetry reductions are considered in ????. Clément theories possess a scalar whereas Sar¬oglu-¼ Tekin has vectorial ghost states. Symmetry reduction results in description of Clément dynamics by a system of three nonlinear ode with a constraint. 4. A Hamiltonian formulation for non-autonomous dynamical systems in the framework of contravariant geometry is given in Phys. Lett. A 218 (1996) 235-239 (MR 97e: 58080). This is further elaborated to show that any Poisson bi-vector in time-extended space possesses two in…nitesimal automorphism and applied to the investigations of the phase space geometry and of the invariants of hydrodynamical motions in Phys. Lett. A 257 (1999) 43-52 (MR 00e: 37078). The time-extended Hamiltonian formalism is used to investigate the invariants of hydrodynamical equations in three dimensions. In a series of articles (Phys. Lett. A 232 (1997) 417-424 (MR 98i: 76003), Physica D 135 (2000) 117-136, Physica D 139 (2000) 335- 359 (MR 01i: 76027)) the symplectic geometry of Lagrangian motions are given. The implications of this structure to kinematical symmetries and invariants of motion are discussed. The equivalence of Lagrangian and Eulerian types of helicity conservation laws are shown and, this equivalence is characterized in the framework of symplectic and conformally symplectic, or more generally, in the language of Jacobi structures. In Turkish J. Math 40 (2016) 925-940, under certain conditions on pres- sure functions, the viscous Lagrangian ‡ow is shown to be Hamiltonian in time-extended space. Generators of in…nitesimal symplectic dilation are connected with helicity conservation law. Contact hypersurfaces implied by symplectic dilation and associated with streamlines and Bernoulli function are constructed. Implications for Eulerian equations in the framework of symplectisation are discussed. Time-extended formalism is also applied for Aristotelian model of three-body motion in J. Phys. A: Math. Theor. 44 (2011) 325204 (15pp) where it is also shown to be an autonomous bi-Hamiltonian system. 5. A survey of Poisson structures in three dimensions and a discussion of integrability in this framework is given in J. Math. Phys. 34 (1993) 5691- 5723 (MR 94i: 58066). The problem in Lichnerowicz complex is converted into the one on de Rham complex. Frobenius theorem is used to charac- terize integrable bi-Hamiltonian systems. Godbillon-Vey invariants are obtained as obstruction to global integrability in three dimensions. Ap- plications to dynamical systems from general relativity, biology, epidemi- ology, atomic physics, etc. are given. In Physica D 238 (2009) 526-530, it is shown that in three dimensions, the construction of bi-Hamiltonian structure can be reduced to the solutions of a Riccati equation with the

7 arclength coordinate of a Frenet-Serret frame being the independent vari- able. All explicitly constructed examples in the literature are exhausted by constant solutions. It is proved that vector …elds which are not eigen- vectors of the curl operator are locally bi-Hamiltonian. Based on this, the work Adv. in Dyn. Sys. and Appl., 5 (2010) 159-171 shows that explicit integration of conserved quantities are connected with the coe¢ cients of Riccati equation which are elements of the third cohomology class. The Darboux-Halphen system, as the only non-trivial example of locally bi- Hamiltonian system in the literature, is revisited and it is concluded that the Godbillon-Vey invariant arises as obstruction to integrability of inte- grating factor for Hamiltoian functions. In J. Phys. A: Math. Theor. 44 (2011) 325204 (15pp) Aristotelian model of three-body motion on the line is shown to be bi-Hamiltonian for all physical parameters involved. In arXiv: 1502.03238 it is proved that conserved quantities of gradient systems in three dimensions can be obtained from geodesic coordinates of level surfaces of potential function. In Regular and Chaotic Dynamics 21 (2016) 175-188, superintegrable cases of some hyperchaotic systems in four dimensions are presented for certain values of physical parameters and with degenerate Poisson structures. 6. Integrability of equations of hydrodynamic type in one space dimension is studied in the framework of multi-Hamiltonian structure. Gas dynamics hierarchy is completed with the inclusion of new conserved quantities and a continuum limit of Toda lattice J. Math. Phys. 31(11) 1990, 2606-2611 (MR 91j: 35229). In J. Phys. A: Math. Gen. 25 (1992) 5141-5149 (MR 93h: 35164) a combinatorial method is developed for the construction of bi-Hamiltonian structures and is applied to N-component Kodama equations. Some transformations are used in J. Phys. A: Math. Gen. 27 (1994) 193-200 (MR 95e: 58085) for the same purpose and the integrability of dispersionless-Boussinesq, Benney-Lax equations are proved.

http://arxiv.org/…nd/grp_q-bio,grp_math,grp_physics/1/au:+G*mral/0/1/0/all/0/1

4.3 References to Mathematical Reviews 1. 1990, MR1075743, 35Q35, 58F05, 76B15, 76N15. 2. 1992, MR1184300, 35Q35, 58F07. 3. 1993, MR1246244, 58F05, 34A26, 58F07, 70H05. 4. 1994, MR1288005, 58F07, 35Q58. 5. 1996, MR1400627, 58F05, 70H05, by Charles-Michel Marle. 6. 1997, MR1468426, 76A02, 58D05, 58F05, by Yuri E. Gliklikh.

8 7. 1999, MR1696180, 37J05, 37C60, 53D17, 70H05, by David Martin de Diego. 8. 2000, MR1733490, 37K65, 37N10, 76M60, 9. 2000, MR1753088, 76B99, 37K05, 37N10, 76A25, 76W05, by Hans-Peter Kruse. 10. 2009, MR2591295, 37J35 (70H06) 11. 2010 MR2771307, 37J15 (37J35 37K05 53D17) by Olga Bernardi 12. 2010, MR2683543, 37K65 (58D05 76X05 82D10) 13. 2011, MR2793054, 58A32 (37J05 58A20 70H05) by Marco Modugno 14. 2011, MR2821935, 70F07 (70H05) by Shanzhong Sun 15. 2012, MR2989719, 82Dxx (53Dxx 70G55 70H05) 16. 2014, MR3328738, 53D05 (22E60) by Luca Degiovanni 17. 2016, MR3486004, 34C14 (34C20 37J35) 18. 2016, MR3570805, 70G45 (76Bxx) by Anatoliy K. Prykarpatsky 19. 2017, MR3537182, 70G45 (22E60 70H03 70H05 70K65) by Luca Vitagliano 20. 2018, MR3754324, 83D05 (81T20) by Vladimir Dzhunushaliev

from https://mathscinet.ams.org/mathscinet/search/publications.html?pg1=INDI&s1=293779&sort=Newest&vfpref=html&r=1&extend=1 With reference to Mathematical Reviews my research works may be catego- rized in (in order of decreasing frequency) 70: Mechanics of particles and systems (14, primary 3), 37: Dynamical systems and ergodic theory (13, primary 5), 58: Global analysis, analysis on manifolds (11, primary 4), 76: Fluid mechanics (9, primary 2), 81,82,83: Physics (4, primary 2) 34: Ordinary di¤erential equations (3, primary 1) 35: Partial di¤erential equations (3, primary 2), 53: Di¤erential geometry (3, primary 1) 22: Lie groups (2)

9 5 Conferences, Seminars, Meetings

: participation with invited talks, lectures or anouncements 1. (Online) Workshop on Nonlinear systems, (organizer) Department of Math- ematics, Gebze Technical University, Sep 29, 2020.

2. Hamiltonian formulations of second order degenerate Lagrangians, De- partment of Physics, Mimar Sinan University of Fine Arts, Apr. 11, 2019, Istanbul.

3. Geometry and physics on di¤eomorphism groups, Seminar, Department of Mathematics, Istanbul University, Feb. 20, 2019, Istanbul.

4. Poisson bivectors in four dimensions, Workshop on Nonlinear Systems, Department of Mathematics, Gebze Technical University, Nov. 26, 2018, Kocaeli.

5. On geometric problems of plasma dynamics, Seminar, Department of Mathematics, Gebze Technical University, Nov. 20, 2018, Kocaeli. 6. *Nonlinearities in NMR and Debye-Hückel theory, Research seminar in School of Engineering, Australian College of Kuwait, Nov. 2016.

7. Marx and the problem of in…nitesimals, Joint Symposia on Philosophy and Mathematics, Yeditepe University, Feb. 27-28, 2014, Istanbul. 8. *Con…guration spaces of Poisson-Vlasov equations, "Workshop on Geom- etry of Mechanics and Control" National Mathematics Initiative, Indian Institute of Science (January 2-10, 2014) Bangalore, India. 9. *Poisson structures in 3D and Darboux-Halphen system, colloquium talk at "Workshop on Geometry of Mechanics and Control" National Mathe- matics Initiative, Indian Institute of Science (January 2-10, 2014) Banga- lore, India. 10. *Eulerian equations and geometry of Lagrangian ‡ows, International Work- shop on Di¤erential Equations and Applications, At¬l¬m University (Au- gust 12-15, 2013) Ankara. 11. *Local vs global integrability, seminar at Department of Mathematics, Yeditepe University, May 14, 2013, Istanbul. 12. *Hamiltonyen Parçac¬klar¬n Kinetik Denklemleri I, XVI. Ulusal Mekanik Kongresi, Erciyes Üniversitesi, 22-26 Haziran 2009, Kayseri. 13. *Üç Boyutta iki-Hamiltonlu Yap¬n¬nVarl¬g¬,¼ 9. Dinamik Sistemler Çal¬¸s- tay¬, Izmir· Üniversitesi, 18-19 Haziran 2009, Izmir.·

14. Geometry of Vlasov-Poisson Equations, Seminars at Department of Physics and Institute For Fusion Studies, Sep. 21, 2001, University of Texas at Austin, USA.

10 15. Symplectic Geometry of Incompressible Flows, talk at NEEDS 2000, June 29-July 7, Gökova, Turkey.

16. Geometric Mechanics, seminar at Physics Department of Bogaziçi¼ Uni- versity, Dec. 15, 1999, Istanbul. 17. International Conference on New Applications of Multisymplectic Geom- etry, Sep. 20-24, 1999, Universidad de Salamanca, Spain.

18. Neo-Klasik Mekanik, Geometrik Mekanik ba¸sl¬kl¬iki çagr¬l¬konu¸sma.12.¼ Ulusal Matematik Kongresi, 6-10 Eylül, 1999, Inönü· Üniversitesi, Malatya.

19. Hydrodynamical Invariants and Jacobi Structures, talk at IX. Regional Conference on Mathematical Physics, Aug. 9-14, 1999, Feza Gürsey In- stitute, Istanbul.

20. Fen fakültesi ögrencilerine Feza Gürsey Enstitüsünü tan¬t¬c¬konu¸sma,4 Haz. 1999, Istanbul· Üniversitesi, Vezneciler.

21. Lectures on Symplectic Geometry, in: Research semester on Geometry and Integrability, Feb. 15-June 15, 1999, Feza Gürsey Institute, Istanbul, Turkey.

22. Colloqium on Geometry and Integrability, at Physics Departments of Middle East Technical University (Feb 11, 1999), Bilkent University (Feb 11, 1999) and Bogaziçi¼ University (Feb 18, 1999).

23. Poisson Geometry and Time-dependent Motions, seminars at Mathemat- ics Department of Bogaziçi¼ University (Nov 3, 1998) and, Physics Depart- ment of Istanbul Technical University (Nov. 12, 1998), Istanbul. 24. Research semester on Seiberg-Witten monopoles and M-theory, summer, 1998, Feza Gürsey Institute, Istanbul, Turkey. 25. 6th Gökova Conference on Geometry and Topology, May 25-30, 1998, Akyaka-Gökova, Turkey.

26. Geometrik Mekanigin¼ Yap¬s¬, Sicimler, Zarlar ve Dualite Simetrileri K¬¸s Okulunda yap¬lan konu¸sma,19-23 Ocak 1998, Izzet· Baysal Üniversitesi, Bolu, Türkiye.

27. A time-extended Hamiltonian formalism, talk at VIII. Regional Confer- ence on Mathematical Physics, June 27-July 4, 1997, Yerevan, Armenia.

28. General Helicity conservation, talk at Anatolian Lectures on Dynami- cal Systems, June 15-19, 1997, Department of Mathematics, Middle East Technical University, Ankara, Turkey. 29. Workshop on Turbulence Modelling and Vortex dynamics, Sep. 2-6, 1996, Istanbul Technical University, Maçka, Istanbul, Turkey.

11 30. Poisson geometrisi, Fizikte Geometri ve Topoloji K¬¸sOkulunda yap¬lan konu¸sma,29 Ocak-2 ¸Subat 1996, Izzet· Baysal Üniversitesi, Bolu, Türkiye. 31. Variational and local methods in the study of Hamiltonian systems, 24-28 October, 1994 (with certi…cate) ICTP, Trieste, Italy. 32. Research workshops on Mathematical Ecology (May 26-29, 1993) and, Pattern Formation and Lattice Gas Automata (Jun 7-12, 1993) at Fields Institute, Waterloo, Canada.

33. N-bile¸senli Kodama denklemlerinin iki-Hamiltonlu yap¬s¬, VI. Diferan- siyel Denklemler Sempozyumu’nda yap¬lan konu¸sma,28-29 Eylül, 1992, Ankara Üniversitesi, Fen Fakültesi, Ankara, Türkiye. 34. International Workshop on Geometry and Arithmetic, July 19-Aug 1, 1992, Akdeniz University, Antalya, Turkey.

35. Poisson structures and 2-monopole problem, talk at Dynamics Days, June 19-20, 1992, Department of Mathematics, Middle East Technical Univer- sity, Ankara, Turkey. 36. 1st Gökova Conference on Geometry and Topology: Low Dimensional Topologies, May 25-29, 1992, Akyaka-Gökova, Turkey.

37. 2-monopole problem, talk at V. Regional Conference on Mathematical Physics, Dec 15-22, 1991 Trakya University, Edirne, Turkey.

38. 3-boyutta korunum yasalar¬için bir yöntem, V. Diferansiyel Denklemler Sempozyumu’nda yap¬lan konu¸sma, 25-27 Eylül, 1991, Anadolu Üniver- sitesi, Eski¸sehir, Türkiye. 39. I. International Colloquium on Recent Developments in Theoretical Physics, May 27-31, 1991, Trakya University, Edirne, Turkey.

40. Multi-Hamiltonian structure of hydrodynamic type equations, talk at NATO-Advanced Research Workshop: Singular Limits of Dispersive Waves, July 7-12, 1991, ENS-Lyon, France.

41. Poisson structure of 3-dimensional dynamical systems, seminar at Physics Department, March 28, 1991, Middle East Technical University, Ankara. 42. Summer School on High Energy Physics and Cosmology, June 18-July 28, 1990 Trieste, ICTP, Italy. 43. Trieste Conference on Topological Methods in Quantum Field Theory, June 11-15, 1990, ICTP, Trieste, Italy. 44. Recent Developments in Quantum Electrodynamics and Quantum Optics, NATO-ASI, Augost 14-26, 1989, Bogaziçi¼ Univ. Istanbul, Turkey.

12 45. Partially Integrable Nonlinear Evolution Equations and Their Physical Applications, NATO-ASI, March 21-30, 1989 Centre de Physique, Les Houches, Haute-Savoie, France

6 Educational works 6.1 Teaching statement My aims in teaching mathematics are, to communicate important concepts com- mon to various …elds of mathematics and science, to convey the joy and sat- isfaction of discovering new relations and ideas during the learning process, as well as the beauty, excitement and e¤ectiveness of mathematics. Based on the fact that an intellectual activity is personal and can be learned by actually doing it, I try to have students actively participate into the lectures. Sometimes I ask their suggestions on how to perform a computation and do it (if does not take much time) even if their suggestion is not useful or wrong, explain why their suggestion did not work and present the correct results. For the same purpose, I require students, coming to my o¢ ce with questions, to present their question on the board and show me their di¢ culties. Then I start asking simple questions or give suggestions to orient them to the solution of their problem. On the other hand, mathematics is more about ideas and relations than complicated formulas and long computations. To help students digest the ideas beyond technicalities, I frequently stop and explain with diagrams, pictures etc, why we are doing all those computations, proofs etc. For each subject I try to answer in brief words questions like: what is the problem? What is the idea to solve it? What will be our bene…ts after solving it? At this stage some history and application areas (this may be mathematics itself) may come in and my background in physics may be useful. After showing all mathematical technicalities in detail, I again brie‡y summarize the problem and the ideas to solve it. In a calculus course, for example, I refer, during a semester, to the Fundamental Theorem. For di¤erential equations, I advocate the idea that a di¢ cult problem in mathematics can be reduced to a problem either in calculus or in linear algebra which are more basic parts of mathematics. For di¢ cult and long subjects, I usually present a detailed example …rst, and then go into general theory (for instance, the geometry of sphere before the general theory of surfaces). This way students can see how a general theory works for a speci…c example. As chairman of department of mathematics at Yeditepe University, I learned, on one hand, through long discussions with other faculties, about subjects of mathematics necessary for students of other departments such as engineering, art, architecture, economics, psychology, health sciences, dentistry etc and their proper presentations. On the other hand, I had the opportunity to start new graduate programs and to desing courses in modern di¤erential and symplectic geometry such as applications of Lie groups to di¤erential equations, geometry

13 of plasma dynamics, geometry of manifolds of maps and more recently, an in- troductory course on geometric mechanics. After going through preliminaries that can be found in classic books, materials for these courses are usually chosen from the current literature so that students can easily extend their knowledge to research problems.

6.2 Courses Undergraduate level: Calculus for Engineers I,II, Calculus for Math Stu- dents I,II, Calculus for Health Sciences, Calculus III, Analytic Geometry, Di¤erential Equations, Ordinary Di¤erential Equations, Advanced Ordi- nary Di¤erential Equations, Linear Algebra, Linear spaces, Matrix algebra, Elementary Di¤erential Geometry, Calculus on Manifolds, Geome- tries, Mathematical Foundations of Thermodynamics, Calculus of Varia- tions, Basic Algebraic Structures, Mathematics for architects, Mathemat- ical Modelling (Yeditepe University), Quantitative Decision Techniques (Özyegin¼ University), Calculus for Mathematics Students III (Bogazici University), Precalculus and calculus for engineering students, business mathematics (Australian College of Kuwait) Graduate level: Introduction to Geometric Mechanics, Geometry of Dif- feomorphism Groups, Geometry of Manifolds of Maps, Lie Groups and Lie Algebras, Topics in Geometry (Yeditepe University), Lectures on Symplec- tic Geometry, in: Research Semester on Geometry and Integrability, Feza Gursey Institute, Spring 1999, Lectures on Plasma Physics Geometry, in Research Semester on Qualitative Theory of Nonlinear Partial Di¤erential Equations, FGI, Spring 2001. Teaching assistant to the second year course: Linear Algebra (Bilkent University). Teaching assistant to mechanics, electric, optics laboratories (Istanbul Technical University). Science (physics, astronomy, chemistry, biology) courses to …rst encounters (Tarsus Private Lyceè). Teaching assistant to mechanics, electric, optics laboratories and the second year course: Mathematical Methods of Physics (METU).

6.3 Organizational Summer School of Young Mathematicians (for High School Students), Yeditepe University, August 11-26, 2011. National Mathematics Graduate Students Workshop, June 14-21, 2010, Yeditepe University.

14 Member of the organizing commitee of Special Program on Geometry and Topology, Feza Gürsey Institute, Spring 2000. Organizer of the regular seminars in 1999-2000 academic year (Feza Gürsey Institute).

6.4 Thesis Supervised Ogul¼ Esen, Tulczyjew Construction of Legendre Transformations, MS Thesis, Graduate School of Science and Engineering, Yeditepe University (2006).

Ogul¼ Esen, Fiber Bundles, Di¤eomorphism Groups and Plasma Dynamics, PhD Thesis, Graduate School of Science and Engineering, Yeditepe Uni- versity (2010). (Received Best Work Award in XVIth National Congress on Mechanics (2010) and National Serhat Özyar Prize 2011) First advisor to Yasemin Y¬lmaz, Lie algebra extensions with applications to ‡uids and kinetic theories (completed with the advisor: Ender Abadoglu,¼ Yeditepe University) First advisor to Filiz Çagatay¼ Uçgun, Higher order Lagrangian theories with constraints (completed with the advisor: Ogul¼ Esen, Yeditepe Uni- versity)

7 Administrative works

Acting Head of Department of Mathematics (Sep 2014-July 2015) Aus- tralian College of Kuwait: Integrated the Department of Mathematics as a department in School of Engineering. Performed …rst performance ap- praisal of faculty sta¤. Participated regular review of auspice partners (Central Institute of Technology, Australia). Implemented new curriculum units in transforming CIT units to ACK ones. Interviewed candidates and identify three PhD holder for manpower of department. Introduced new standards for the department in teaching mathematics and physics to di¤erent departments with large number of students. Chairman (May 2003-Oct 2011) Department of Mathematics, Yeditepe University: Substantial revision on undergraduate program was made. Internal report for the department was prepared and presented to referees from Europian Universities Association. Graduate programs (master with and without thesis, PhD) were opened. Program for minor in mathematics, double major program for students of many other departments and, certi…cate program in actuarial sciences were started. The department has enlarged to seventeen full-time and fourty part-time faculty serving more that hundred courses to threethousand students, from four full-time and

15 thirteen part-time faculty serving approximately fourty courses to seven- hundred students. Research output of the department has reached the peak of eighteen articles in the year 2009. A nationwide graduate students meeting was organized in June 14-21, 2010. Every year one week has been spent to visit teachers and students of high schools at various cities around the country. Member of Administrative Commitee of Faculty of Art and Science (June 2003-June 2009) Yeditepe University. Member of Science Advisory Commitee for high schools of ISTEK Foun- dation (2003-2011).

8 Refereeing and Reviewing

For Mathematical Reviews, Physics Letters A, Computer Physics Communica- tions, Turkish Journal of Mathematics, European Physics Journal B, Journal of Nonlinear Mathematical Physics, One Ph.D. Thesis for Department of Mathematics, Bogaziçi¼ University. As Higher Education Council’s jury for Assoc. Professorships of sixteen candidate. Panelist in evaluation of four research projects presented to TÜBITAK.·

9 Scholarships, memberships and awards 9.1 Scholarship NATO-B2 Postdoctoral Research grant 2001 NATO-B Postdoctoral scholarship 1993-1994 TÜBITAK-Graduate· scholarship 1991-1992 9.2 Award Junior science prize, TÜBITAK· (Scienti…c and Technological Research Council of Turkey) 1998

10 References

1. Dr. Ender Abadoglu,¼ Professor of Mathematics and chairman at De- partment of Mathematics, Yeditepe University, Kay¬¸sdag¬¼ 34755, Istan-· bul. [email protected], +90-216-5781695, +90-533-7720060 (for teaching, research and administrative works at Yeditepe University).

16 2. Dr. Muhittin Mungan, Professor of Physics at Department of Physics, Bogaziçi¼ University, Bebek 34342, Istanbul. [email protected], +90- 536-8307680 (colleague). 3. Dr. Partha Guha, Professor of Mathematics, Department of Mathematics, Khalifa University, Zone-1 Abu Dhabi, UAE. [email protected], +91- 9051407709 (colleague, for scienti…c works) 4. Dr. Evgeny V. Ferapontov, Professor of Mathematic at Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU, United Kingdom. [email protected], +44 (0)1509 22 3309 (colleague, for scienti…c works) 5. Dr. Tudor Ratiu, Professor of Mathematics and Chair of Geometric Analysis, Section de Mathematiques, Faculté des Sciences de Base, EPFL (Ecole Polytechnique Federale de Lausanne ), Station 8 CH-1015 Lau- sanne Switzerland, Fax: +41 (0) 21 693 7920, http://cag.ep‡.ch/page- 39504-en.html, tudor.ratiu@ep‡.ch, +41 (0) 21 693 7922) (colleague, for scienti…c works)