Topology of mapping class group
Topology is the branch of mathematics which studies global properties of geometric objects and describes it in terms of rigorous algebra. Recently, the tools developed in topology have had applications to the real-world science/technology such as analysis of big data, and new models of proteins. I will continue to study the topology of mapping class group of surface as well as its applications to the moduli space of Riemann surfaces, taking account of the applications as mentioned above.
Current research topics
Educational background
Professional background
Licenses
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Courses
* Courses provided in English are shown with (E) mark
Undergraduate school
Mathematics 3
Mathematics 4
Mathematics 7
Geometry 2
Introduction to Geometry
Graduate school
Topics in Geometry I
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Authors: 笠原 泰
Title: On visualization of the linearity problem for mapping class groups of surfaces
Journal: Geometriae Dedicata, Springer Netherlands
Year: 2014
Authors: KASAHARA Yasushi
Title: Addendum to: "An expansion of the Jones representation of genus 2 and the Torelli group"
Journal: Journal of Knot Theory and Its Ramifications, Vol. 20, No. 6, pp. 939-941, World Scientific Publishing
Year: 2011
Authors: 笠原 泰
Title: Remarks on the faithfulness of Jones representations
Journal: Advanced Studies in Pure Mathematics 52
Year: 2008
Authors: 笠原 泰
Title: The Jones representation of genus 1
Journal: Intelligence of Low Dimensional Topology 2006, World Sci. Publ., River Edge, NJ
Year: 2006
Authors: KASAHARA Yasushi
Title: An expansion of the Jones representation of genus 2 and the Torelli group II
Journal: J. Knot Theory and its Ramifications, Vol. 13, No. 2, pp. 297-306
Year: 2004
Authors: KASAHARA Yasushi
Title: The Jones representation of genus 2 at the 4th root of unity and the Torelli group
Journal: Topology and its Applications, Vol. 124, pp. 129-138
Year: 2002
Authors: Yasushi Kasahara
Title: An expansion of the Jones representation of genus 2 and the Torelli group
Journal: Algebraic and Geometric Topology, Vol. 1, pp. 39-55
Year: 2001
Grants-in-Aid for Scientific Research from the Japanese government
Project title: Fosterage of the visualization of the linearity for mapping class groups of surfaces Category: Grant-in-Aid for Scientific Research (C) Project number: 23540102 Project period: 2011-2013 Total budget amount: 3,380,000 yen Keywords:
Project title: Visualization of the linearity for mapping class group and its relation to topology Category: Grant-in-Aid for Scientific Research (C) Project number: 16K05154 Project period: 2016-2018 Total budget amount: 4,030,000 yen Keywords:
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Social activities
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