JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 25(10) Sep 2016

The dual jacobian of a generalised hyperbolic tetrahedron, and volumes of prisms

Kolpakov, Alexander; Murakami, Jun

Tokyo Journal of Mathematics 39(1) 45-67 Jun 2016

We derive an analytic formula for the dual Jacobian matrix of a generalised hyperbolic tetrahedron. Two cases are considered: a mildly truncated and a prism truncated tetrahedron. The Jacobian for the latter arises as an analytic continuation of t...

On a q-deformation of PSL(2) representation of knot groups

Jun Murakami

Low dimensional topology and number theory X 28 Mar 2018

Presentation of knots by a braided Hopf algebra

Jun Murakami

Modular Forms and Quantum Knot Invariants 13 Mar 2018 Banff International Research Station

Braided Wirtinger presentation of knots

Jun MUrakami

Representation Spaces, Teichmüller Theory, and their Relationship with 3-manifolds from the Classical and Quantum Viewpoints 2 Feb 2018 Centre International de Rencontres Mathemiques

On the volume conjecture of quantum knot invariants

Jun Murakami

Low-dimensional Topology and Number Theory 25 Aug 2017 Oberwolfach Research Institute for Mathematics

Quantization of the fundamental group by dual quantum group

Project Year: Jun 2017 - Mar 2020

Discrete quantization of low-dimensional geometry with quantum invariants

Project Year: Apr 2013 - Mar 2017

The aim of this research is to construct discretized quantum geometry for 2 and 3 dimensional case. To do this, various quantum invariants and their relations are studied. For example, we study the colored Jones invariant, the colored Alexander ...

Study in phantom of the quantum groups

Project Year: Apr 2013 - Mar 2016

Quantum groups whose quantum parameter q are roots of unity have projective representations which is not always semisimple. In this research, properties of such representations are studied, invariants of knots and 3-maniolfds related to such rep...

Study of modular/quasimodular forms and multiple zeta values appearing in various aspects of mathematics and physics

Project Year: Apr 2011 - Mar 2016

For modular forms of one variable, we obtained some congruence results on Fourier coefficients of certain meromorphic modular forms, constructed newforms associated to elliptic curves over the rationals which can be written as eta products via dif...

Quantum Topology and Modular Forms in Mathematical Physics

Project Year: Apr 2011 - Mar 2015

Quantum invariants of knots and 3-manifolds has been developed since Jones and Witten. We have studied a geometric aspect of the colored Jones polynomial. Some of the colored Jones polynomial was shown to have a nearly-modular property.We have app...