Research Keywords 【 display / non-display

  • Algebraic Geometry, Noncommutative Hodge Theory, Moduli

Research Pursuits 【 display / non-display

  • Noncommutative Hodge theory is an extension of the Hodge theory for cohomorogy theory with non-abelian groups as its coefficients. Its first cohomorogy are moduli stacks of Higgs bundles. It is very important to study Hodge structures on them. Thohgh it was difficult to define higher cohomology, higher category theory enables the definition. My research purpose is to develop non-commutative Hodge theory in this framework. Moreover, higher category theory enables us for introduction of higher stacks which extends the notion of sheaves. This means a possibility of homotopical mathematics that enlarges mathematics build up on the set theory. Homotopical mathematics seems well for getting and representing any information that we have been neglecting
    via higher categorical structures.

Educational Pursuits 【 display / non-display

  • My lectures concerns mainly on algebra. In the seminar for 4th grader students, it has been used textbooks concerning on number theory, commutative algebra, algebraic geometry and cryptgraphical theory. For students in master course, my lectures are usually concerns on number theory, algerraic geometry, complex geometry and homotopy theory.

Campus Career 【 display / non-display

  • Graduate School of Humanities and Sciences, Research Organization, the Core Section The Natural/Applied Sciences Division, Professor

  • Faculty of Core Research Natural Science Division, Professor

  • Graduate School of Humanities and Sciences, Education Organization, Doctral Program Advanced Sciences

  • Graduate School of Humanities and Sciences, Education Organization, Doctral Program Advanced Sciences

  • Graduate School of Humanities and Sciences, Education Organization, Master's Program Advanced Sciences

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Research Field 【 display / non-display

 

Books 【 display / non-display

  • Lecture Notes in Pure and Applied Mathematics, 179 Moduli of vector bundles

    Moduli of parabolic Higgs sheaves, Dekker, 1996, 横川光司, 丸山正樹, Book, 287-296

Papers 【 display / non-display

  • Pre-Tango structures on curves

    Tohoku Journal of Mathematics, 2002, 横川光司 武田好史, Original, Research paper (scientific journal), Capital Author

  • Rationality of Moduli of parabolic sheaves on curves

    Journal of London Mathemaical Society, 1999, 横川光司 Hans U. Boden, Original, Research paper (scientific journal), Capital Author

  • Moduli spaces of parabolic Higgs bundles and parabolic K(D) pairs over a smooth curves: I

    International Journal of Mathematics, 1996, 横川光司 Hans U. Boden, Original, Research paper (scientific journal), Capital Author

  • Infinitesimal deformations of parabolic Higgs sheaves

    International Journal of Mathematics, 1995, 横川光司, Original, Research paper (scientific journal), Single Author

Presentations 【 display / non-display

  • Simpson の非可換コホモロジー理論入門

    横川光司, Domestic, 2001.02, 代数幾何及び可換環論の小研究集会, 琉球大学, 森脇淳(京都大学), Invited, Main Speaker