## Topics in Quantum Groups and Finite-Type Invariants: Mathematics at the Independent University of MoscowBoris L. Feigin, V. A. Vasilʹev, V. Vassiliev This volume presents the first collection of articles consisting entirely of work by faculty and students of the Higher Mathematics College of the Independent University of Moscow (IUM). This unique institution was established to train elite students to become research scientists. Covered in the book are two main topics: quantum groups and low-dimensional topology. The articles were written by participants of the Feigin and Vassiliev seminars, two of the most active seminars at the IUM. |

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affine Lie algebra affine quantum group affine Weyl group arbitrary associative algebra BGG resolutions Bopp cocycle coincides Coind commutative complex component configuration Consider construction CorollAry corresponding cycle defined definition denote derived category DG-algebras diagram differential edges element elliptic curve embedding equal Feigin fiber Figure filtration finite flips formula function functor graded hexagon homomorphism immersion integer isomorphic knot invariants Lemma Lie algebra linear loops manifold Math Mathematics matrix module moduli space morphism Moscow multiplication nontrivial obtained pair polynomials Proof Proposition prove Qn,r quotient resp respect root root datum s-orientation satisfying self-intersection point semi-infinite homology singular knot space of knots spectral sequence Sr(V stratum subalgebra subgroup subspace summand Suppose symmetric symmetric matrix Theorem triangular decompositions trivial Tutte decomposition Tutte invariant Tutte relation twisted values Vassiliev vector space vertex vertices weighted graphs weighted Tutte zero