Department of Mathematics, Waseda University
Web Page of Jun MURAKAMI
http://www.f.waseda.jp/murakami/jun-home-j.html

Jun Murakami
Department of Mathematics, Waseda University
3-4-1 Ohkubo, Shinjuku-ku Tokyo, 169-8555, JAPAN

WASEDA RIKO Topology seminor

T.B.A.

### Workshop on Volume Conjecture and Quantum Topology -- a new perspective on low-dimensional geometry --

Video of the talks are available here.
Many thanks to Seonhwa Kim for preparing these videos.

What I am working on...
I am working on invariants of knots, links and 3-manifolds.

• Volume conjecture
We propose volume conjecture of knots with Hitoshi Murakami from Kashaev's conjecture, suggesting that the hyperbolic volume of the complement of a hyperbolic knot is determined by the Jones polynomial and its generalizations.
• Universal perturbative invariant
The universal perturbative invariant of 3-manifolds is constructed with T. T. Q. Le and T. Ohtsuki. I am studying on the representation of the mapping class groups constructed from the Topological Quantum Field Theory of the universal perturbative invariant.

Recent papers and preprints

• Combinatorial decompositions, Kirillov-Reshetikhin invariants and the Volume Conjecture for hyperbolic polyhedra (with Alexander Kolpakov)
to appear in Experimental Mathematics.
• Yokota type invariants derived from non-integral highest weight representations of Uq(sl2) (with Atsuhiko Mizusawa)
J. Knot theory and its Applications, 25 (2016), no.10, 1650054, 21 pp.
Proceedings of Symposia in Pure Mathematics, Volume 93, 2016, 343--352.
• The Dual Jacobian of a Generalised Hyperbolic Tetrahedron, and Volumes of Prisms (with Alexander Kolpakov)
Tokyo J. Math. 39 (2016), no. 1, 45--67.
• Generalized Kashaev invariants for knots in three manifolds
arXiv:1312.0330, to appear in Quantum Topology
• Volume of a doubly truncated hyperbolic tetrahedron (with Alexander Kolpakov)
Aequationes Mathematicae, 85 (2013), no. 3, 449--463.
Erratum: Aequationes Math. 88 (2014), no. 1-2, 199--200.
• Invariants of Handlebody-Knots via Yokota's Invariants (with Atsuhiko Mizusawa)
J. Knot theory and its Applications, 22 (2013), no.11, online.
• The volume formulas for a spherical tetrahedron
Proc. Amer. Math. Soc. 140 (2012), no. 9, 3289--3295.
• Optimistic limits of the colored Jones polynomials (with Jinseok Cho)
J. Korean Math. Soc. 50 (2013), no. 3, 641--693.
• On SL(2, C) quantum 6j-symbol and its relation to the hyperbolic volume, (with Francesco Costantino)
Quantum Topology, 4 (2013), no.3, 303--351.
• Actual computation for the complexified hyperbolic volume conjecture (2002/7/2)
• Generalized volume and geometric structure of 3-manifolds (revised on 2002/4/8)
• Finite-type invariants detecting the mutant knots
Knot Thoery - Dedicated to Professor Kunio Murasugi for his 70th birthday -
Editors: M. Sakuma et al., Published at Osaka University, March 2000.
• On web diagrams
Abstract: In this paper, web diagrams and web spaces are introduced and the construction of the universal perturbative invariant, taking values in the web space, is explained. Applying this invariant to the mapping cylinders of elements of the mapping class group Mg of the surface of genus g, we get web representations of Mg on the web space. The web space has two natural filtrations and these representations are compatible with these filtrations. This fact seems to explain that the representations are not so simple ones.
• List of my papers

.... errata ....