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INDIAN INSTITUTE OF TECHNOLOGY PALAKKAD
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Dr. Arpan Kabiraj
Assistant Professor
Mathematics
arpaninto@iitpkd.ac.in
Research Area: Low-dimensional Topology
View Website
  • Biosketch

    Education:

    Integrated PhD (MS+PhD) in Mathematics (2011-2016)  : Indian Institute of Science, Bangalore, India

    B.Sc.  in Mathematics (2006-2009)  : Jadavpur University, Kolkata, India

     

    Experience:

    Assistant Professor (December 2019-May 2020) : IIT Bhubaneswar, India

    INSPIRE Faculty (September 2016 - March 2020) : Chennai Mathematical Institute (CMI), Chennai, India

     Postdoctoral fellow (October  2017 - September 2018) : Ben-Gurion University, Israel

  • Research

    My principle areas of research are topological, combinatorial and geometric group theory. I am primarily interested in the study of geometric, combinatorial, computational and algebraic aspects of geometric objects namely curves on hyperbolic surfaces arising naturally in the study of low-dimensional topology and Riemann surface theory. In this context I am interested in certain problems related to the length function on Teichmüller space and various combinatorial objects associated to the Teichmüller space.

    I am also interested in quasimorphisms on groups associated to geometry and topology of surfaces.

    Apart from geometry, I am interested in logic, in particular first order theory of groups which occurs naturally while studying geometric objects, e.g. Braids groups, Mapping class groups etc.

  • Teaching

    IIT Bhubaneswar:

    1) Instructor of the course “Mathematics-II”, January-May, 2020.

    2) Instructor of the course “Algebraic Topology”, January-May, 2020

     

    Chennai Mathematical Institute:

    1) Instructor of the course “Riemannian Geometry” (REGO), August-November,2017.

    2) Instructor of the course “Geometric Group Theory” (GGTH), August-November, 2019.

     

    IISc:

    1) Teaching Assistant for MA 231 Topology, August-December, 2011.

    2) Teaching Assistant for UM 101 Analysis and Linear Algebra I, August-December, 2012.

    3) Teaching Assistant for MA 221 Real Analysis, August-December 2013.

    4) Teaching Assistant for MA 232 Introduction to Algebraic Topology, August-December 2014.

    5) Teaching Assistant for UM 101 Analysis and Linear Algebra I, August-December, 2015.

  • Publications
    Lie bracket of undirected closed curves on a surface
    Moira Chas and Arpan Kabiraj
    Trans. Amer. Math. Soc. 375 (4) 2365–2386 (2022)
    On the entropy norm on the group of diffeomorphisms of closed oriented surface
    Michael Brandenbursky and Arpan Kabiraj
    Journal of Topology and Analysis 12 (1) 105-111 (2020)
    Equal angles of intersecting geodesics for every hyperbolic metric
    Arpan Kabiraj
    New York Journal of Mathematics 24 167-181 (2018)
    Elementary equivalence in Artin groups of finite type
    Arpan Kabiraj, T. V. H. Prathamesh and Rishi Vyas
    International Journal of Algebra and Computation 28 (2) 331-344 (2018)
    Center of the Goldman Lie algebra
    Arpan Kabiraj
    Algebraic & Geometric Topology 16 2839–2849 (2016)

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Kerala | Pin: 678623

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