• Speaker: Peter Johnson, UVA
• Title: A zero surgery obstruction from involutive Heegaard Floer homology
• Date: 09/14/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

A fundamental result in 3-manifold topology due to Lickorish and Wallace says that every closed oriented connected 3-manifold can be realized as surgery on a link in the 3-sphere. One may therefore ask: which 3-manifolds can be obtained by surgery on a link with a single component, i.e. a knot, in the 3-sphere? More specifically, one can ask: which 3-manifolds are obtained by zero surgery on a knot in the 3-sphere? In this talk, we give a brief outline of some known results to this question in the context of small Seifert fibered spaces. We then sketch a new method, using involutive Heegaard Floer homology, to show that certain 3-manifolds cannot be obtained by zero surgery on a knot in the three sphere. In particular, we produce a new infinite family of weight 1 irreducible small Seifert fibered spaces with first homology Z which cannot be obtained by zero surgery on a knot in the 3-sphere, extending a result of Hedden, Kim, Mark and Park.

• Speaker: Peng Zhou, Berkeley
• Title: Homological Mirror Symmetry for A_n-type cluster varieties
• Date: 09/28/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

The A_n type cluster variety, denoted by X_n, is the affine scheme associated to the upper cluster algebra of the A_n quiver (of n unfrozen vertices and one frozen vertex). The dual of X_n is denoted as Y_n, and is isomorphic but not canonically to X_n. For example, the variety X_1 is given by the equation {x y = 1 + q} where x, y are in \C and q is in \C^*. We prove that the homological mirror symmetry (HMS) conjecture for X_n, Y_n: the coherent sheaf category of Coh(X_n) is equivalent to the wrapped Fukaya category WFuk(Y_n), generalizing the known case for n=1 and 2. This is based on a recent work of Gammage-Le on HMS for truncated cluster variety, by putting back the 'truncated' part. This is work in progress, and is joint with Linhui Shen and Zhe Sun.

• Speaker: Ka Ho Wong, Texas A&M University
• Title: Asymptotics of the relative Reshetikhin-Turaev invariants
• Date: 10/12/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

In a series of joint works with Tian Yang, we made a volume conjecture and an asymptotic expansion conjecture for the relative Reshetikhin-Turaev invariants for a closed oriented 3-manifold with a colored framed link inside it. We propose that their asymptotic behavior is related to the volume, the Chern-Simons invariant and the adjoint twisted Reidemeister torsion associated with the hyperbolic cone metric on the manifold with singular locus the link and cone angles determined by the coloring. In this talk, I will first discuss how our volume conjecture can be understood as an interpolation between the Kashaev-Murakami-Murakami volume conjecture of the colored Jones polynomials and the Chen-Yang volume conjecture of the Reshetikhin-Turaev invariants. Then I will describe how the adjoint twisted Reidemeister torsion shows up in the asymptotic expansion of the invariants. Especially, we find new explicit formulas for the adjoint twisted Reidemeister torsion for the fundamental shadow link complements and for the 3-manifold obtained by doing hyperbolic Dehn-filling on those link complements. Those formulas cover a very large class of hyperbolic 3-manifold and appear naturally in the asymptotic expansion of quantum invariants. Finally, I will summarize the recent progress of the asymptotic expansion conjecture of the fundamental shadow link pairs.

• Speaker: Break day, no talk
• Title: TBA
• Date: 10/26/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: Honghao Gao (gaohongh@msu.edu)

TBA

• Speaker: Mike Wong, Dartmouth
• Title: TBA
• Date: 11/09/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

TBA

• Speaker: Vijay Higgins, MSU
• Title: TBA
• Date: 11/23/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

TBA

• Speaker: Yu-Shen Lin, Boston University
• Title: TBA
• Date: 12/14/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

TBA