# [QSMS Monthly Seminar] Closed orbits and Beatty sequences

by qsms posted Jun 24, 2021
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일정시작 2021-06-25 2021-06-25 #036eb7

Date: 6월24일 금요일, 2021년

Place: 129동

Title: Closed orbits and Beatty sequences

Speaker: 강정수 교수

Abstract:

A long-standing open question in Hamiltonian dynamics asks whether every strictly convex hypersurface in R^{2n} carries at least n closed orbits. This was answered affirmatively in the non-degenerate case by Long and Zhu in 2002. The aim of this talk is to outline their proof and to highlight its connection to partitioning the set positive integers.

Title: On the $\tilde{H}$-cobordism group of $S^1 \times S^2$'s

Speaker: 이동수 박사

Abstract:

Kawauchi defined a group structure on the set of homology S1 × S2’s under an equivalence relation called $\tidle{H}$-cobordism. This group receives a homomorphism from the knot concordance group, given by the operation of zero-surgery. In this talk, we review knot concordance invariants derived from knot Floer complex, and apply them to show that the kernel of the zero-surgery homomorphism contains an infinite rank subgroup generated by topologically slice knots.

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