The Topology Seminar will meet on Fridays, usually alternating with the AGC seminar, 3:00 p.m. – 4:00 p.m. in room MB 124 (Mathematics Building). Below you find the information for the topology talks. Everybody who is interested is invited to join. Please send email to email@example.com for more information.
August 25: All participants
Title: Conjectures and Planning
September 1: Jens Harlander
Title: The Geometric Realization Problem
Abstract: Homology can be thought of as an algebraic shadow of geometry and topology. How coarse is that image? Surprisingly, not as much information gets lost as is to be expected, especially in higher dimensions. Dimension 2 however remains problematic. In my talk I will introduce the geometric realization problem and survey what is known.
September 15: Uwe Kaiser
Title: A Survey of the Volume Conjecture in Knot Theory
Abstract: In 1996 Kashaev conjectured that the growth rate of a sequence of knot invariants, which he recently defined, is up to a constant equal to the hyperbolic volume of a hyperbolic knot. In 2001 Jun Murakami and Hitoshi Murakami proved that the conjecture could be stated in terms of evaluations of colored Jones polynomials at roots of unity, and can be extended to all knots. The conjecture is important because it relates the geometry/topology of 3-manifolds with its quantum invariants. Meanwhile many generalizations of the conjecture have been formulated. But even the original conjecture has been proven for only few hyperbolic knots. The talk will trace back the history of Kashaev’s invariant to Euler’s dilogarithm function and also mention recent attempts at its proof.
September 29: Jens Harlander
Title: Groups, Homology, and Bias
Abstract: In my talk I will review basics on homology of complexes and groups. I
will state and maybe even prove a famous observation of Hopf: the second
homology of a complex, modulo spherical elements, depends only on the
fundamental group of the complex. This is used in the construction of the
bias invariants that can distinguish 2-complexes with the same fundamental
October 27: Kayla Neal
Title: Geodesics in Link Complements
Abstract: I will discuss cell decomposition of hyperbolic links, constructing generators of the fundamental group, and belt sum composition of links. I will also discuss results related to geodesics in link complement of the Whitehead knot and the Borromean Rings.
November 10: Michelle Pyles
Title: An Introduction to the Cap Set Problem: the game SET and Tic-Tac-Toe
Abstract: I will introduce the Cap Set Problem using the game SET and walk through the proofs for a 2-cap,3-cap and (time permitting) 4-cap in the finite field F3. I will also briefly discuss the current findings and the connection to the realm of combinatorics.
November 17: tba
Please go to the AGC seminar homepage for further information.