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3-manifolds algorithm analysis applications asymptotic August 13 boundary bounded calculus coefficients cohomology College Algebra combinatorial complex Computer Science conjecture construction convex course curves defined Department of Mathematics Dept developed differential equations dimension discuss dynamics examples finite formula functions geometry graph Hilbert Hilbert scheme homeomorphism Hopf algebra hyperbolic hyperbolic 3-manifolds integral invariant irreducible isomorphic January 08 January 22 knot lattice Lie algebra linear manifolds maps Math Mathematical Sciences Mathematics and Statistics Mathematics Department matrix matroid method minimal modular forms modules moduli space nonlinear operators polynomials Preliminary report present problem proof properties prove quantum Received April Received August 13 Received December Received January 22 Received March Received October 02 Received September 14 representation ring Schubert polynomials September 14 September 28 sequence solutions space structure subgroup surfaces symmetric symmetric group talk theorem theory topological University vector