Left: Adrian Ocneanu in his office at Harvard in 2017.
Right: This photo taken in 1999 shows Adrian holding Misner-Thorne-Wheeler in one hand, and some models in the other hand. He was celebrating the fact that he realized intertwiners, and coefficients like the 6j symbols, are made of a network of small permutohedra, in frames subject to Riemann curvature, namely gravity-like conditions.
In 2017, Professor Adrian Ocneanu, visiting from Penn State's mathematics department, taught a course introducing completely new work in higher representation theory. Cross-listed in Harvard's physics and mathematics departments, the course will cover the construction of higher (category) simple Lie groups, their roots, weights and representations, and Dynkin and Young diagrams - all encoded by discrete Riemann curvature.
Transcriptions of the course lectures are posted on this website. Videos can be obtained from A. Ocneanu.
Relevant papers and talks
A. Ocneanu, The classification of subgroups of quantum SU(N). In: Bariloche (Argentine), pp. 26, 2000.
A. Ocneanu, Chirality for operator algebras. In: H. Araki, Y. Kawahigashi and H. Kosaki (eds.): Subfactors. pp. 39-63. World Scientiﬁc Publ., 1994.
A. Ocneanu, Operator algebras, topology and subgroups of quantum symmetry— construction of subgroups of quantum groups. In: Taniguchi Conference on Mathematics Nara 1998, 235–263, Adv. Stud. Pure Math., 31, Math. Soc. Japan, Tokyo, 2001.
A. Ocneanu, Paths on Coxeter diagrams: From platonic solids and singularities to minimal models and subfactors, (Notes by S. Goto) in “Lectures on operator theory”, Fields Inst. Monographs 13, Amer. Math. Soc., Providence, 1999.
A. Ocneanu, Quantized groups, string algebras and Galois theory for algebras. In: Operator algebras and applications, Vol. 2, pp. 119-172, Cambridge Univ. Press, 1988.
A. Ocneanu, Quantum Subgroups and Higher McKay Correspondences. Talk given at workshop "Generalized McKay Correspondences and Representation Theory", MSRI, Berkeley, 2006.