Seminar Report

The iTHEMS Math seminar entitled "Knotted 2-spheres in the 4-space and Yang-Mills gauge theory," by Dr. Masaki Taniguchi, was held on 27 May.

In the first part, the speaker reviewed that classical knot theory and history of knot. Especially, he introduced that one and two dimensional knot theory, and gave many examples. For one dimensional knot theory, he explained the fundamental problem of knot theory, i.e., the problem of classifying 1-knots up to equivalent. As an example, he introduced a knot invariant coming from 3-colorings. For two dimensional knot theory, he explained the problem of how we write diagrams of 2-knots in four dimensional Euclidean space. Then he introduced the motion picture.

In the second part, the speaker focuses on a problem considered in differential topology. First, he explained that the fundamental problem in differential topology. Next, he introduced gauge theory and some examples. Finally, as the main result of the talk, he explained his theorem about the difference between continuous and smooth two dimensional knots. He then introduced that the proof uses Yang-Mills gauge theory for 4-manifolds obtained by the surgery of 2-knots.

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