I prove that every finite-dimensional Poisson manifold X admits a canonical deformation
quantization. Informally, it means that the set of equivalence classes of associative algebras …

With hundreds of worked examples, exercises and illustrations, this detailed exposition of
the theory of Vassiliev knot invariants opens the field to students with little or no knowledge …

Over the last fifteen years, the face of knot theory has changed due to various new theories
and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to …

The workshop and seminars on “Invariants of knots and 3-manifolds” was held at Research
Institute for Mathematical Sciences, Kyoto University in September 2001. There were 25 …

In temporal gauge A0= 0 the 3d Chern–Simons theory acquires quadratic action and an
ultralocal propagator. This directly implies a 2d R-matrix representation for the correlators of …

A celebrated theorem of Kapranov states that the Atiyah class of the tangent bundle of a
complex manifold X makes TX− 1 into a Lie algebra object in D+(X), the bounded below …

Using elementary equalities between various cables of the unknot and the Hopf link, we
prove the Wheels and Wheeling conjectures, which give, respectively, the exact Kontsevich …

In 1999, Rozansky conjectured the existence of a rational presentation of the Kontsevich
integral of a knot. Roughly speaking, this rational presentation of the Kontsevich integral …

Path integrals do not really exist, but it is very useful to dream that they do and figure out the
consequences. Apart from describing much of the physical world as we now know it, these …

Characteristic numbers of compact hyper-Kähler manifolds are expressed in graph-
theoretical form, considering them as a special case of the curvature invariants introduced …