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    A Note on Evolution Equation on Manifold
    (Univ Nis, Fac Sci Math, 2021) Ashyralyev, Allaberen; Sözen, Yaşar; Hezenci, Fatih
    In the present paper, considering the differential equations on smooth closed manifolds, we investigate and establish the well-posedness of boundary value problems nonlocal type for parabolic equations and also hyperbolic equations in Ho center dot lder spaces. Furthermore, in various Ho center dot lder norms we establish new coercivity estimates for the solutions of such type parabolic boundary value problems on manifolds and hyperbolic boundary value problems on manifolds as well.
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    A note on exceptional groups and Reidemeister torsion
    (Amer Inst Physics, 2018) Hezenci, Fatih; Sözen, Yaşar
    Let Sigma be a closed orientable surface of genus at least 2 and G be one of the exceptional groups G(2), F-4, and E-6. The present article considers the set Rep(Sigma, G) of G-valued representations from the fundamental group pi(1)(Sigma) of the surface Sigma to the exceptional group G. It proves that for such representations the notion of Reidemeister torsion is well-defined. It also establishes a formula for computing Reidemeister torsion of such representations in terms of the well-known symplectic structure on Rep(Sigma, G), namely, the Atiyah-Bott-Goldman symplectic form for the Lie group G. Moreover, it applies to G-valued Hitchin representations. Published by AIP Publishing.
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    A Note on Stability of Parabolic Difference Equations on Torus
    (Taylor & Francis Inc, 2023) Ashyralyev, Allaberen; Hezenci, Fatih; Sözen, Yaşar
    The present article investigates nonlocal boundary value problems for parabolic equations of reverse type on torus. The first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle T-1 and torus T-2 are presented. For the solutions of the difference scheme, the stability estimates and coercivity estimates in various Holder norms are established. Furthermore, theoretical results are supported by numerical experiments.
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    Representation variety of free or surface groups and Reidemeister torsion
    (Scientific and Technological Research Council Turkey, 2022) Hezenci, Fatih; Sözen, Yaşar
    For G is an element of {GL(n, C), SL(n, C)} , we consider G-valued representations of free or surface group with genus > 1. We establish a formula for computing Reidemeister torsion of such representations in terms of Atiyah-Bott-Goldman symplectic form for G. Furthermore, we apply the obtained results to hyperbolic 3-manifolds.