# Dimakis Aristophanes

Since 2000 I am teaching at the Department of Financial and Management Engineering. I am currently serving as Head of Department. I also served as Head of Department from 2004 to 2008.

My current research interests lie in the field of mathematics of integrable dynamical systems. I got a degree in Physics at the University of Athens and my doctorate at the Institute of Theoretical Physics of the University of Göttingen in Germany in the field of the General Theory of Relativity.

I was born in 1953 and served in non permanent positions in the Institute of Theoretical Physics at the University of Göttingen, in the Department of Mathematics at the University of Crete and in the Department of Mathematics at the University of the Aegean.

- "Grassmannian-parameterized solutions to direct-sum polygon and simplex equations" (with Igor Korepanov), J. Math. Phys. 62, 051701 (2021); https://doi.org/10.1063/5.0035760, arXiv:2009.02352.
- "Tropical limit of matrix solitons and entwining Yang-Baxter maps" (with F. Müller-Hoissen),
*Lett Math Phys*(2020). https://doi.org/10.1007/s11005-020-01322-9, arXiv:2001.09688 [nlin.SI]. - "Matrix Boussinesq solitons and their tropical limit" (with F. Müller-Hoissen and Xiao-Min Chen),Phys. Scr.
**94**(2019) 035206, arXiv:1805.09711. - "Differential Calculi on Associative Algebras and Integrable Systems" (with F. Müller-Hoissen), preprint arXiv:1801.00589.
- "Matrix KP: tropical limit, Yang-Baxter and pentagon maps" (with F. Müller-Hoissen), Theor. Math. Phys.
**196**(2018) 1164-1173, arXiv:1709.09848. - "Matrix KP: tropical limit and Yang-Baxter maps" (with F. Müller-Hoissen), Lett. Math. Phys., arXiv:1708.05694.
- "Self-consistent sources for integrable equations via deformations of binary Darboux Transformations" (with O. Chvartatskyi and F. Müller-Hoissen), Lett. Math. Phys.
**106**(2016) 1139-1179 , arXiv:1510.05166. - "Higher Bruhat and Tamari orders and their realizations" (with F. Müller-Hoissen), J. Generalized Lie Theory Appl.
**9**(2015) e103. - "Simplex and polygon equations" (with F. Müller-Hoissen), SIGMA
**11**(2015) 042, arXiv:1409.7855. - "KdV soliton interactions: a tropical view" (with F. Müller-Hoissen), J. Phys. Conf. Series
**482**(2014) 012010, arXiv:1308.1545. - "Darboux Transformations in Bidifferential Calculus, and the Integrable Case of Vacuum Einstein Equations" (with F. Müller-Hoissen), SIGMA 9 (2013) 009.
- "KP solitons, higher Bruhat and Tamari orders" (with F. Müller-Hoissen), in
*Associahedra, Tamari Lattices and Related Structures*, Tamari Memorial Festschrift, eds. F. Müller-Hoissen, J. Pallo and J. Stasheff, Progress in Mathematics**299**(Birkhäuser, 2012) 391-423, arXiv:1110.3507 [math.CO]. - "The non-autonomous chiral model and the Ernst equation of General Relativity in the bidifferential calculus framework", (with N. Kanning and F. Müller-Hoissen), SIGMA 7 (2011) 118.
- "On a (2+1)-dimensional generalization of the Ablowitz-Ladik lattice and a discrete Davey-Stewartson system", (with T. Tsuchida), arXiv:1103.4953 [nlin], J. Phys. A: Math. Theor. 44 (2011) 325206.
- "Bidifferential calculus, matrix SIT and sine-Gordon equations", (with N. Kanning and F. Müller-Hoissen), arXiv:1011.1737 [nlin], Acta Polytechnica 51 (2011) 33--37.
- "KP line solitons and Tamari lattices", (with F. Müller-Hoissen), arXiv:1009.1886 [math-ph], J. Phys. A: Math. Theor. 44 (2011) 025203, IOPselect
- "Bidifferential calculus approach to AKNS hierarchies and their solutions", (with F. Müller-Hoissen), arXiv:1004.1627 [nlin], SIGMA 6 (2010) 055.
- "Solutions of matrix NLS systems and their discretizations: A unified treatment", (with F. Müller-Hoissen), Inverse Problems 26 (2010) 095007, arXiv:1001.0133 [nlin].
- "Quasi-symmetric functions and the KP hierarchy" (with F. Müller-Hoissen), arXiv:0901.2562 [math-ph], J. Pure and Applied Algebra 214 (2010) 449--460.
- "Multicomponent Burgers and KP hierarchies, and solutions from a matrix linear system" (with F. Müller-Hoissen), arXiv:0811.0110 [nlin.SI], SIGMA 5 (2009) 002.
- "BKP and CKP revisited: The odd KP system" (with F. Müller-Hoissen), arXiv:0810.0757 [nlin.SI], Inverse Problems 25 (2009) 045001.
- "Bidifferential graded algebras and integrable systems" (with F. Müller-Hoissen), arXiv:0805.4553 [nlin.SI], Discrete and Continuous Dynamical Systems (DCDS) Supplements 2009, 208--219 (Proceedings AIMS Conference, Arlington 2008).
- "Weakly non-associative algebras and the Kadomtsev-Petviashvili hierarchy" (with F. Müller-Hoissen), Glasgow Math. J. 51A (2009) 49--57.
- "From the Kadomtsev-Petviashvili equation halfway to Ward's chiral model" (with F. Müller-Hoissen), arXiv:0712.3689 [nlin.SI], J. Gen. Lie Theory Appl. 2 (2008) 141-146.
- "Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions" (with F. Müller-Hoissen), arXiv:0706.1373 [nlin.SI], J. Phys. A: Math. Theor. 41 (2008) 265205.
- "A new approach to deformation equations of noncommutative KP hierarchies" (with F. Müller-Hoissen), math-ph/0703067, J. Phys. A: Math. Theor. 40 (2007) 7573-7596.
- "With a Cole-Hopf transformation to solutions of the noncommutative KP hierarchy in terms of Wronski matrices" (with F. Müller-Hoissen), nlin.SI/0701052, J. Phys. A: Math. Theor. 40 (2007) F321-F329.
- "Weakly nonassociative algebras, Riccati and KP hierarchies" (with F. Müller-Hoissen), nlin.SI/0701010, in "Generalized Lie Theory in Mathematics, Physics and Beyond", eds. S. Silvestrov, E. Paal, V. Abramov and A. Stolin, (Springer, 2008) (Proceedings of the workshop "Algebra, Geometry, and Mathematical Physics", Lund, October 2006), 9--27.
- "Burgers and KP hierarchies: A functional representation approach" (with F. Müller-Hoissen), nlin.SI/0610045, Theor. Math. Phys. 152 (2007) 933-947. (Note: The publishers incorrectly shifted part of footnote 3 to the end of proposition 1. The download offered here yields a corrected version.)
- "From nonassociativity to solutions of the KP hierarchy" (with F. Müller-Hoissen), nlin.PS/0608017, Czech. J. Phys. 56 (2006) 1123-1130.
- "From AKNS to derivative NLS hierarchies via deformations of associative products" (with F. Müller-Hoissen), nlin.SI/0603048, J. Phys. A: Math. Gen. 39 (2006) 14015-14033.
- "Functional representations of integrable hierarchies" (with F. Müller-Hoissen), nlin.SI/0603018, J. Phys. A: Math. Gen. 39 (2006) 9169-9186.
- "Nonassociativity and integrable hierarchies" (with F. Müller-Hoissen), nlin.SI/0601001.
- "Algebraic identities associated with KP and AKNS hierarchies" (with F. Müller-Hoissen), math-ph/0507024, Czech. J. Phys. 55 (2005) 1385-1390.
- "An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions" (with F. Müller-Hoissen), nlin.SI/0501003, J. Phys. A: Math. Gen. 38 (2005) 5453-5505.
- "Extension of Moyal-deformed hierarchies of soliton equations" (with F. Müller-Hoissen), nlin.SI/0408023, published in XI International Conference Symmetry Methods in Physics, eds C. Burdik, O. Navratil and S. Posta, Joint Institute for Nuclear Research, Dubna, 2004.
- "Differential calculi on quantum spaces determined by automorphisms" (with F. Müller-Hoissen), math.QA/0407273, Czech. J. Phys. 54 (2004) 1235-1242.
- "Explorations of the extended ncKP hierarchy" (with F. Müller-Hoissen), hep-th/0406112, J. Phys. A: Math. Gen. 37 (2004) 10899--10930.
- "Extension of noncommutative soliton hierarchies" (with F. Müller-Hoissen), hep-th/0401142, J. Phys. A: Math. Gen. 37 (2004) 4069-4084.
- "Automorphisms of associative algebras and noncommutative geometry" (with F. Müller-Hoissen), math-ph/0306058, J. Phys. A: Math. Gen. 37 (2004) 2307-2330.
- "Automorphisms of real four-dimensional Lie algebras and the invariant characterization of homogeneous 4-spaces" (with T Christodoulakis and G O Papadopoulos) J.Phys. A: Math, Gen. 36 (2003) 427--441, Corrigendum.
- Five contributions (jointly with F. Müller-Hoissen) to: Concise Encyclopedia of Supersymmetry, eds S. Duplij, W. Siegel and J. Bagger (Kluwer, Dordrecht, 2004).
- "Riemannian geometry of bicovariant group lattices" (with F. Müller-Hoissen), math-ph/0212054, J. Math. Phys. 44 (2003) 4220-4259 Additional material.
- "Differential geometry of group lattices" (with F. Müller-Hoissen), math-ph/0207014, J. Math. Phys. 44 (2003) 1781-1821.
- "On generalized Lotka-Volterra lattices" (with F. Müller-Hoissen), nlin.SI/0207010, Czech. J. Phys. 52 (2002) 1187-1193.
- "Noncommutative NLS equation" (with F. Müller-Hoissen), Czech. J. Phys. 51 (2001) 1285-1290.
- "Bicomplexes and Bäcklund transformations" (with F. Müller-Hoissen), nlin.SI/0104071, J. Phys. A: Math. Gen. 34 (2001) 9163-9194.
- "Bicomplex formulation and Moyal deformation of (2+1)-dimensional Fordy-Kulish systems" (with F. Müller-Hoissen), nlin.SI/0008016, J. Phys. A: Math. Gen. 34 (2001) 2571-2581.
- "Moyal deformation, Seiberg-Witten map, and integrable models" (with F. Müller-Hoissen), hep-th/0007160, Lett. Math. Phys. 54 (2000) 123-135.
- "The Korteweg-de-Vries equation on a noncommutative space-time" (with F. Müller-Hoissen), hep-th/0007074, Phys. Lett. A 278 (2000) 139-145.
- "A noncommutative version of the nonlinear Schrödinger equation" (with F. Müller-Hoissen), hep-th/0007015.
- "Bicomplexes and integrable models" (with F. Müller-Hoissen), nlin.SI/0006029, J. Phys. A: Math. Gen. 33 (2000) 6579-6591.
- "Bicomplexes, integrable models, and noncommutative geometry" (with F. Müller-Hoissen), hep-th/0006005, Int. J. Mod. Phys. B14 (2000) 2455-2460.
- "Dynamical evolution in non-commutative discrete phase space and the derivation of classical kinetic equations" (with C. Tzanakis), math-ph/9912016, J.Phys. A: Math. Gen.
- "Bicomplexes and finite Toda lattices" (with F. Müller-Hoissen), solv-int/9911006, in: Quantum Theory and Symmetries, eds. H.-D. Doebner, V.K. Dobrev, J.-D. Hennig and W. Lücke (World Scientific, 2000) 545-549.
- "Bi-differential calculus and the KdV equation" (with F. Müller-Hoissen), math-ph/9908016, Rep. Math. Phys. 46 (2000) 203-210.
- "Bi-differential calculi and integrable models" (with F. Müller-Hoissen), math-ph/9908015, J. Phys. A: Math. Gen. 33 (2000) 957-974.
- "Pseudo-Riemannian metrics in models based on noncommutative geometry" (with F. Müller-Hoissen), gr-qc/9908022, Czech. J. Phys. 50 (2000) 45-52.
- "Noncommutative geometry and a class of completely integrable models" (with F. Müller-Hoissen), math-ph/9809023, Czech. J. Phys. 48 (1998) 1319-1324.
- "Discrete Riemannian geometry" (with F. Müller-Hoissen), gr-qc/9808023, J. Math. Phys. 40 (1999) 1518-1548.
- "Deformations of classical geometries and integrable systems" (with F. Müller-Hoissen), preprint GOET-TP 100/97, physics/9712002. Talk presented at the workshop "Quantum Groups, Deformations and Contractions", Bogazici University, Istanbul, September 1997. Submitted to the proceedings which apparently never appeared in print.
- "Some aspects of noncommutative geometry and physics" (with F. Müller-Hoissen), physics/9712004, in: Novelties in String Theory, eds. L. Brink and R. Marnelius (World Scientific, 1999) 327-347.
- "Connes' distance function on one-dimensional lattices" (with F. Müller-Hoissen), q-alg/9707016, Int. J. Theor. Phys. 37 (1998) 907-913.
- "Noncommutative geometry and its relation to stochastic calculus and symplectic mechanics" (with C. Tzanakis), q-alg/9606011, in:
*Proceedings of the 4th International Gongress of Geometry,*eds. N K Artemiadis and N K Stephanidis, Academy of Athens and Aristotle University of Thessaloniki, Thessaloniki 1996. - "A generalization of sigma-models and complete integrability" (with F. Müller-Hoissen), in GROUP21, Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, Vol. 2, Eds: H.-D. Doebner, W. Scherer and C. Schulte, World Scientific 1997, pp. 602-606.
- "Soliton equations and the zero curvature condition in noncommutative geometry" (with F. Müller-Hoissen), hep-th/9608009, J. Phys. A 29 (1996) 7279-7286.
- "Noncommutative geometry and integrable models" (with F. Müller-Hoissen), Lett. Math. Phys. 39 (1997) 69-79.
- "Differential calculi and linear connections" (with J. Madore), J. Math. Phys. 37 (1996) 4647-4661 .
- "Umbral calculus, discretization, and quantum mechanics on a lattice"(with F. Müller-Hoissen and T. Striker), quant-ph/9509014, J. Phys. A 29 (1996) 6861-6876.
- "Integrable discretizations of chiral models via deformation of the differential calculus" (with F. Müller-Hoissen), hep-th/9512007, J. Phys. A: Math. Gen. 29 (1996) 5007-5018.
- "Noncommutative geometry and kinetic theory of open systems" (with C. Tzanakis), J. Phys. A: Math. Gen. 29 (1996), 577-594.
- "Noncommutative geometry of finite groups" (with K. Bresser, F. Müller-Hoissen and A. Sitarz), q-alg/9509004, J. Phys. A 29 (1996) 2705-2735.
- "Discrete differential manifolds and physics" (with F. Müller-Hoissen), in: Nonlinear, Dissipative, Irreversible Quantum Systems, eds. H.-D. Doebner, V.K. Dobrev and P. Nattermann (World Scientific,1995) pp. 469-474.
- "Differential calculi on commutative algebras" (with H. Baehr and F. Müller-Hoissen), preprint MPI-PhT/94-83, hep-th/9412069, J. Phys. A 28 (1995) 3197-3222.
- "Discrete differential manifolds and dynamics on networks" (with F. Müller-Hoissen und F. Vanderseypen) hep-th/9408114, J. Math. Phys. 36 (1995) 3771-3791.
- "Discrete differential calculus: Graphs, topologies, and gauge theory" (with F. Müller-Hoissen) hep-th/9404112, J. Math. Phys. 35 (1994) 6703-6735.
- "Differential calculus and discrete structures" (with F. Müller-Hoissen), hep-th/9401150, in: Generalized Symmetries in Physics, eds. H.-D. Doebner, V.K. Dobrev and A.G. Ushveridze (World Scientific, Singapore, 1994), pp. 213-218.
- "Noncommutative differential calculus: quantum groups, stochastic processes, and the antibracket" (with F. Müller-Hoissen), hep-th/9401151, in: Proceedings of the XXII International Conference on Differential Geometric Methods in Theoretical Physics, Ixtapa, Mexico, Sept. 1993, published in: Advances in Applied Clifford Algebras (Proc. Suppl.) 4(S1) (1994) 113-124.
- "Differential forms and gauge theory on discrete sets and lattices" (with F. Müller-Hoissen), in the proceedings of the workshop `Symmetry Methods in Physics' in memory of Ya. A. Smorodinsky, Dubna, July 1993, Vol. 2, 351-357.
- "Differential calculus and gauge theory on finite sets" (with F. Müller-Hoissen) hep-th/9401149, J. Phys. A: Math. Gen. 27 (1994) 3159-3178
- "Stochastic differential calculus, the Moyal *-product, and noncommutative geometry" (with F. Müller-Hoissen) Lett. Math. Phys. 28 (1993) 123-137.
- "Noncommutative differential calculus and lattice gauge theory" (with F. Müller-Hoissen and T.Striker) J. Phys. A: Math. Gen. 26 (1993) 1927-1949.
- "From continuum to lattice theory via deformation of the differential calculus" (with F. Müller-Hoissen and T.Striker) Phys. Lett. B 300 (1993) 141-144.
- "Quantum mechanics on a lattice and q-deformations" (with F. Müller-Hoissen) Phys. Lett. B 295 (1992) 242-248 .
- Book Reviews: "Orthogonal and Symplectic Clifford Algebras: Spinor Structures" by A Crumeyrolle,
*Class. Quantum Grav.***8**(1991) 249. - "A noncommutative differential calculus and its relation to gauge theory and gravitation" (with F. Müller-Hoissen), in Proceedings of the XXI International Conference on Differential Geometric Methods in Theoretical Physics, Tianjin (China), June 1992, Int. J. Mod. Phys. A (Proc. Suppl.) 3A (1993) 474-477.
- "Noncommutative symplectic geometry and quantum mechanics" (with F. Müller-Hoissen), in Proceedings of the XXI International Conference on Differential Geometric Methods in Theoretical Physics, Tianjin (China), June 1992, Int. J. Mod. Phys. A (Proc. Suppl.) 3A (1993) 214-217.
- "Noncommutative differential calculus, gauge theory and gravitation" (with F. Müller-Hoissen) preprint GOET-TP 33/92.
- "Quantum mechanics as noncommutative symplectic geometry" (with F. Müller-Hoissen) J. Phys. A: Math. Gen. 25 (1992) 5625-5648.
- "Clifform calculus with applications to classical field theories" (with F. Müller-Hoissen) Class. Quantum Grav. 8 (1991) 2093-2132.
- "Spinor fields and the positive energy theorem" (with F. Müller-Hoissen) Class. Quantum Grav. 7 (1990) 283-295.
- "On a gauge condition for orthonormal three frames" (with F. Müller-Hoissen) Phys. Lett. A 142 (1989) 73-74.
- "A new representation of Clifford algebras" J. Phys. A: Math. Gen.
**"**The initial value problem of the Poincare gauge theory in vacuum II. First order formalism" Ann. Inst. H. Poincare- "The initial value problem of the Poincare gauge theory in vacuum I. Second order formalism" Ann. Inst. H. Poincare
- "A new representation for spinors in real Clifford algebras" in Clifford algebras and their applications in mathematical physics J. S. R. Chisholm, A. K. Common (eds.), Dodrecht: D Reidel Publishing Company
*NATO ASI Ser. C***183**(1985) 49-60. - "Solutions of the Einstein-Cartan-Dirac equations with vanishing energy-momentum tensor" (with F. Müller-Hoissen) J. Math. Phys. 26 (1985) 1040-1048.
- "Gauge theory of the post-Galilean groups"
*J. Math. Phys.***26**(1985) 1298-1307. - "Ghost Dirac fields in theories with torsion" (with F. Müller-Hoissen), in 10th International Conference on General Relativity and Gravitation, Padova (Italy) 1983, Contributed Papers, eds. B.Bertotti et al., pp. 505-506.
- "Massive ghost Dirac fields in Einstein-Cartan theory" (with F. Müller-Hoissen) Phys. Lett. A 92 (1982) 431-432.
- "Ein mathematischer Beitrag zur Theorie der Produktionspreise"
*Hefte fuer Politische Oekonomie***1**(1980) 101 - "Zur Linearitaet der Relation zwischen dem Nominallohnsatz und der Profitrate bei post factum gezahlten Loehnen" (with G. Stamatis)
*Jahrbuecher fuer Nationaloekomie und Statistik***196/2**(1980) 147-169