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K-State Today

October 13, 2021

Math department hosts Women Lecture Series colloquium Oct. 14

Submitted by Reta McDermott

Juanita Pinzon-Caicedo, assistant professor at the University of Notre Dame, will present the colloquium "Instantons and Knot Concordance" as part of the Mathematics Department Women Lecture Series in celebration of the 50th anniversary of the Association for Women in Mathematics from 2:30-3:20 p.m. Thursday, Oct. 14, in 122 Cardwell Hall. The lecture will also be streamed live

The abstract for the lecture: Knot concordance can be regarded as the study of knots as boundaries of surfaces embedded in spaces of dimension 4. Specifically, two knots K_0 and K_1 are said to be smoothly concordant if there is a smooth embedding of the annulus S^1 × [0, 1] into the "cylinder" S^3 × [0, 1] that restricts to the given knots at each end. Smooth concordance is an equivalence relation, and the set C of smooth concordance classes of knots is an abelian group with connected sum as the binary operation. The algebraic structure of C, the concordance class of the unknot, and the set of knots that are topologically slice but not smoothly slice are much studied objects in low-dimensional topology. Gauge theoretical results on the nonexistence of certain definite smooth 4-manifolds can be used to better understand these objects. In particular, the study of anti-self-dual connections on 4-manifolds can be used to show that the group of topologically slice knots up to smooth concordance contains a subgroup isomorphic to Z^\infty.

The math department is a part of K-State’s College of Arts and Sciences. To learn more about opportunities in Math at K-State, visit the math department website.