### Algebra/Topology Seminar – Honghao Gao (Michigan State University)

ZoomTitle: Legendrian invariants, Lagrangian fillings and cluster algebras Abstract: Classifications of Legendrian knots and their exact Lagrangian fillings are central questions in low-dimensional contact and symplectic topology. Recent development suggests that one can use cluster seeds to distinguish exact Lagrangian fillings. It requires a filling-to-cluster functoriality over a moduli space of Legendrian invariants. This invariant

### Algebra/Topology Seminar – JungHwan Park (Georgia Institute of Technology)

ZoomTitle: On rationally slice knots Abstract: A knot in the three-sphere is called slice if it bounds a smooth disk in the four-ball. If one only requires the disk to be in a rational homology four-ball, then we say that the knot is rationally slice. We present a rationally slice knot which is not slice even

### Algebra/Topology Seminar – Marco Trombetti (University of Naples Federico II)

ZoomTitle: Abstract Infinite Group Theory in Linear Groups. Abstract: It is a classical result that the commutator subgroup of a group $G$ is finite whenever such is the factor group $G/Z(G)$. In general, this result cannot be reverted: there are (soluble) groups with a finite commutator subgroup but an infinite factor over the centre. However,

### Algebra/Topology Seminar – Ina Petkova (Dartmouth College)

ZoomTitle: A contact invariant from bordered Heegaard Floer homology Abstract: Given a contact structure on a bordered 3-manifold, we describe an invariant which takes values in the bordered sutured Floer homology of the manifold. This invariant satisfies a nice gluing formula, and recovers the Oszvath-Szabo contact class in Heegaard Floer homology. This is joint work

### Algebra/Topology Seminar – Hakan Doga (University of Buffalo)

ZoomTitle: A combinatorial description of the knot concordance invariant epsilon Abstract: Sitting at the intersection of 4-dimensional topology and knot theory, the knot concordance group is an important object in low-dimensional topology whose structure is not yet fully explored and understood. One approach to study knot concordance is to use knot Floer homology, introduced by

### Algebra/Topology Seminar – Eamonn Tweedy (Widener University)

ZoomTitle: The co-rank of three-dimensional homology handlebody groups Abstract: A group G is called very large if G has a non-abelian free quotient. We examine the question of which three-manifolds have very large fundamental group. This question is especially subtle for a three-dimensional homology handlebody of genus g, since the fundamental group of such a

### Algebra/Topology Seminar – Yi Ni (California Institute of Technology)

ZoomTitle: The second term in knot Floer homology Abstract: It is well known that the genus g of a knot is the highest Alexander grading for which the knot Floer homology is nontrivial. In recent years, there is evidence suggesting that the knot Floer homology is also nontrivial in the Alexander grading g-1. In this talk, I

### Algebra/Topology Seminar – Blake Jackson (University of Alabama)

346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Fixed Q under the reverse operation in the RSK correspondence Abstract: The RSK correspondence is a bijection between permutations and pairs of standard Young tableaux with identical shape, where the tableaux are commonly denoted $P$ (insertion) and $Q$ (recording). It has been an open problem to demonstrate where $w^r$ is the reverse permutation

### Algebra/Topology Seminar – Jonathan Simone (Georgia Institute of Technology)

ZoomTitle: The non-orientable 4-ball genus of torus knots Abstract: The non-orientable 4-ball genus of a knot $K$ in $S^3$ is the minimal first Betti number of any smoothly embedded non-orientable surface in $B^4$ bounded by K. This is the non-orientable analog of the 4-ball genus of $K$ (i.e. the minimal genus of any smooth orientable surface

### Algebra/Topology Seminar – Surena Hozoori (Georgia Tech)

ZoomTitle: On Anosovity, divergence and bi-contact surgery Abstract: I will revisit the relation between Anosov 3-flows and invariant volume forms, from a contact geometric point of view. Consequently, I will give a contact geometric characterization of when a flow with dominated splitting is Anosov based on its divergence, as well as a Reeb dynamical interpretation