Faculty Database - KONO TOSHITAKE

■ Books and Papers

1.	2023	Book	Homological representations of braid groups at roots of unity and the space of conformal blocks Springer Proceedings in Mathematics & Statistics (Single)
2.	2023	Article	Temperley-Lieb-Jones category and the space of conformal blocks Essays in Geometry Dedicated to Norbert A’Campo (ed. A. Papadopoulos) (Single)
3.	2021	Article	Formal connections, higher holonomy functors and iterated integrals Topology and Its Applications (Single)
4.	2021	Article	Higher holonomy and iterated integrals Topology and geometry, A collection of papers dedicated to Vladimir G. Turaev pp.307-325 (Single)
5.	2019	Article	Higher holonomy maps for hyperplane arrangements European Journal of Mathematics (Single)
6.	2017	Article	Homological Representations of Braid Groups and the Space of Conformal Blocks Perspectives in Lie Theory, Springer INdAM Series 19 19,pp.427-442 (Single)
7.	2016	Article	Higher holonomy maps of formal homology connections and braid cobordisms Journal of Knot Theory and Its Ramifications 26 (Single)
8.	2016	Article	Quantum representations of braid groups and holonomy Lie algebras Advanced Studies in Pure Mathematics 72,pp.117-144 (Single)
9.	2014	Article	Free subgroups within the images of quantum representations Forum Math. 26(2),pp.337-355 (Collaboration)
10.	2014	Article	Local systems on configuration spaces, KZ connections and conformal blocks Acta Mathematica Vietnamica 39(4),pp.575-598 (Single)
11.	2014	Article	Novikov homology, jump loci and Massey products Cent. Eur. J. Math. 12(9),pp.1285-1304 (Collaboration)
12.	2013	Article	Circle-valued Morse theory for complex hyperplane arrangements Forum Mathematicum (Collaboration)
13.	2012	Article	Homological representations of braid groups and KZ connections Journal of Singularities 5,pp.94-108 (Single)
14.	2021/10	Book	Curvature and Topology: from Geometry of Surfaces to the Shape of Space (Single)
15.	2002	Book	Conformal field theory and topology (Single)
16.	2012	Article	Hyperplane arrangements, local system homology and iterated integrals Advanced Studies in Pure Mathematics 62,pp.157-174 (Single)
17.	2010	Article	Bar complex, configuration spaces and finite type invariants for braids Topology and Its Applications 157,pp.2-9 (Single)
18.	2009	Article	Orbit configuration spaces associated to discrete subgroups of PSL(2, R) Journal of Pure and Applied Algebra 213,pp.2289-2300 (Collaboration)
19.	2007	Article	The volume of a hyperbolic simplex and iterated integrals Series on Knots and Everything 40,pp.179-188 (Single)
20.	2004	Book	Braids, hypergeometric integrals and conformal field theory Proceedings of the First East Asian School of Knots, Links and Related Topics pp.127-131 (Single)
21.	2002	Article	Loop spaces of configuration spaces and finite type invariants Geometry and Topology Monographs 4,pp.143-160 (Single)
22.	2002	Article	Bar complex on the Orlik-Solomon algebra Topology and its Applications 118,pp.147-157 (Single)
23.	2000	Article	Vassiliev invariants of braids and iterated integrals Advanced Studies in Pure Math. 27,pp.157-168 (Single)
24.	1998	Article	Topological quantum field theories with focus on their applications to three-manifolds Sugaku Expositions, Amer. Math. Soc. 11(2),pp.1-16 (Single)
25.	1997	Book	Chern-Simons perturbative invariants Lectures at Knots 96 (Single)
26.	1997	Article	Elliptic KZ system, braid group of the torus and Vassiliev invariants Topology and Its Applications 20,pp.1-16 (Single)
27.	1996	Article	Level-rank duality of Witten's 3-manifold invariants Advanced Studies in Pure Mathematics 24,pp.243-264 (Collaboration)
28.	1994	Article	Vassiliev invariants and de Rham complex on the space on knots Contemp. Math. Amer. Math. Soc. 179,pp.123-138 (Single)
29.	1994	Article	Tunnel numbers of knots and Jones-Witten invariants Advanced Series in Mathematical Physics 17,pp.275-293 (Single)
30.	1994	Article	Topological invariants for 3-manifolds using representations of mapping class groups II: Estimating tunnel number of knots Contemp. Math. Amer. Math. Soc. 175,pp.193-217 (Single)
31.	1994	Article	Monodromy representations of braid groups Sugaku Expositions, Amer. Math. Soc. 7(2),pp.688-696 (Single)
32.	1993	Article	Symmetry of Witten's 3-manifold invariants for sl(n,C) 2(2),pp.149-169 (Collaboration)
33.	1992	Article	Three-manifold invariants derived from conformal field theory and projective representations of modular groups International Journal of Modern Physics 6,pp.341-349 (Single)
34.	1992	Article	Topological invariants of 3-manifolds based on conformal field theory and Heegaard splitting Lectures Notes in Mathematics 1510,pp.341-349 (Single)
35.	1992	Article	Topological invariants for 3-manifolds using representations of mapping class groups I Topology 31(2),pp.203-230 (Single)
36.	1990	Article	Integrable connections related to Manin and Schechtman's higher braid groups Illinois J. of Math. 34(2),pp.476-484 (Single)
37.	1989	Article	Holonomy Lie algebras, logarithmic connections and the lower central series of fundamental groups Contemp. Math. Amer. Math. Soc. 90,pp.171-182 (Single)
38.	1988	Book	Monodromy of braid groups in conformal field theory on P^1 and Yang-Baxter equations Proc. of the 3rd Asia-Pacific Conference of Physics pp.339-363 (Single)
39.	1988	Article	Linear representations of braid groups and classical Yang-Baxter equations Contemp. Math. Amer. Math. Soc. 78,pp.339-363 (Single)
40.	1987	Article	Hecke algebra representations of braid groups and classical Yang-Baxter equations Advanced Studies in Pure Math. 16,pp.255-269 (Single)
41.	1987	Article	Monodromy representations of braid groups and Yang-Baxter equations Ann. Inst. Fourier 37(4),pp.139-160 (Single)
42.	1987	Article	One-parameter family of linear representations of Artin's braid groups Advanced Studies in Pure Math. 12,pp.189-200 (Single)
43.	1986	Article	Homology of a local system on the complement of hyperplanes 62,pp.144-147 (Single)
44.	1985	Article	Serie de Poincare-Koszul associee aux groupes de tresses pures Invent. Math. 82,pp.57-75 (Single)
45.	1983	Article	On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces Nagoya Math. J. 92,pp.21-37 (Single)
46.	1982	Article	Differential forms and the fundamental group of the complement of hypersurfaces Proc. Symp. in Pure Math. 40(1),pp.655-662 (Single)
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■ Conference Presentations

1.	2023/03/07	Formal connections and the category of braid cobordisms (Building-up Differential Homotopy Theory 2023 in Aizu)
2.	2022/03/15	Temperley-Lieb-Jones category and the space of conformal blocks (Low dimensional topology and Number theory XIII)
3.	2021/06/02	Quantum computation and homological representations of braid groups (Workshop on "Computational Knot Theory")
4.	2021/03/19	Monodromy representations in higher categories and iterated integrals (Colloquium, Graduate School of Mathematical Sciences, the University of Tokyo)
5.	2019/12	Higher holonomy maps and iterated integrals (Hyperplane Arrangements and Singularities)
6.	2019/11	Mathematical forms - geometric models, lattices and crystals (Design Innovation from Nature Symposium)
7.	2019/07	Higher holonomy functors (Loops in Leeds)
8.	2019/02	Higher category extensions of holonomy maps and iterated integrals (Higher structures in algebra, geometry and quantum field theory)
9.	2017/06	Higher category extensions of holonomy maps for hyperplane arrangements (Arrangements and beyond: Combinatorics, geometry, topology and applications)
10.	2017/06	Representations of the category of braid cobordisms (2017 KIAS Research Station Busan)
11.	2015/07	Holonomy of braids and its 2-category extension (Integrability in Algebra, Geometry and Physics: New Trends)
12.	2013/11	Discriminantal arrangements and fusion rules in WZW model (Hyperplane arrangements and characteristic classes)
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■ Academic Qualifications

1.

1979/04～1981/03

〔Master Course〕 Mathematics, School of Science, School of Science, the University of Tokyo, Completed, Ph,D

■ Career History

1.	1995/04～2020/03	The University of Tokyo Graduate School of Mathematical Sciences Professor
2.	1992/04～1995/03	The University of Tokyo Graduate School of Mathematical Sciences Associate Professor
3.	1990/04～1992/03	Kyushu University Faculty of Science Associate Professor
4.	1988/04～1990/03	Nagoya University Lecturer
5.	1981/06～1988/04	Nagoya University Research Assistant

■ Teaching Activities

● Textbook and Other Teaching Materials of your own
1.	2020/04～2021/09	Curvature and Topology - From Geometry of Surfaces to the Shape of Space

■ Academic Associations Membership

1.

Mathematical Society of Japan

■ researchmap Researcher Code

R000000564

■ Research Topics, Consignment Studies & KAKENHI Researches

1.

2021/04～2025/03

Geometric quantum representations of discrete groups and generalization to higher categories (Key Word : discrete group, quantum representation, iterated integral, higher category)

■ Web Sites

https://www.ms.u-tokyo.ac.jp/~kohno/

■ Email Addresses

■ Award History

1.

2013/09

Mathematical Society of Japan MSJ Geometry Prize

■ Current Specialized Field

Geometry (Key Word：topology, mathematical physics, braid groups, quantum groups, topological field theory,)

■ KAKENHI Researcher Number

80144111