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Current Schedule

This Week

Wednesday September 16 at 4:00 PM in RH 104
Jonathan Hanselman (IU), "Ribbon concordance, fibered predecessors, and satellite knots"

In 2022 Agol showed ribbon concordance gives a partial ordering on knots, confirming a conjecture of Gordon from 1981. Gordon also conjectured that there are no infinite descending chains under this order. We prove that any knot has finitely many fibered predecessors under ribbon concordance; in particular any fibered knot has finitely many predecessors, implying Gordon’s conjecture for fibered knots. This is joint work with Baldwin and Sivek and builds on their recent work showing any knot has finitely many fibered hyperbolic predecessors. The key new input for removing the word “hyperbolic” is a rank inequality for knot Floer homology of satellites, which is of independent interest. We prove this rank inequality using the immersed curve interpretation of bordered Floer homology.

Upcoming Weeks

Wednesday September 23 at 4:00 PM in RH 104
Paul Kirk (IU), "A genus 2 symplectic surface in an exotic CP^2#2 bar CP^2 with"

Abstract:  I'll outline how to construct a minimal symplectic 4-manifold homeomorphic but not diffeomorphic toCP^2 blown up twice (a' la Akhmedov-Park) and show that it contains a genus two symplectic surface with simply connected complement.  As an application, I'll show how to easily fill large regions in the geography/botatny problem for simply connected4-manifolds.

Wednesday September 30 at 4:00 PM in RH 104
Eleftherios Chatzitheodoridis (VCU), “Trees associated with unitary partition complexes”

In a recent paper, Heuts and Moerdijk develop a poset of trees whose classifying space is homotopy equivalent to the n-th partition complex, that is, the classifying space of the poset of partitions of a set with n elements. The latter poset features in work of Arone, Dwyer, and Lesh, and it finds a unitary analog introduced by Arone and Lesh. In joint work with Julie Bergner, Pedro Brunialti Lima de Andrade, and Josh Turner, we develop a topological poset of trees whose classifying space is homotopy equivalent to the n-th unitary partition complex, that is, the classifying space of the topological poset of partitions of n-dimensional complex space in pairwise orthogonal subspaces. Our work builds on the study of unitary partition complexes by Bergner, Joachimi, Lesh, Stojanoska, and Wickelgren, and it also entails some new results in the theory of topological categories that may be of independent interest.

Wednesday October 21 at 4:00 PM in RH 104
Adam Levine (Duke)