Bulent Tosun
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 – Dan Rutherford (Ball State University)
ZoomTitle: Normal rulings, augmentations, and the colored HOMFLY-PT polynomial Abstract: Normal rulings are certain decompositions of front diagrams of Legendrian links in $R^3$ that were discovered independently by Chekanov & Pushkar and Fuchs in the context of generating families and augmentations of the Legendrian DG-algebra respectively. They can be used to define combinatorial invariants of
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,
Colloquium – Ralf Schiffler (University of Connecticut)
ZoomTitle: An Introduction to Cluster Algebras Abstract: Cluster algebras are commutative algebras with a special combinatorial structure. They were introduced in 2002 by Sergey Fomin and Andrei Zelevinsky in the context of canonical bases in Lie theory and have quickly developed deep connections to other areas of mathematics and physics, including combinatorics, representation theory, hyperbolic geometry, elementary
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
Colloquium – Lisa Traynor (Bryn Mawr)
ZoomTitle: Legendrian Torus and Cable Links Abstract: In contact topology, an important problem is to understand Legendrian submanifolds; these submanifolds are always tangent to the plane field given by the contact structure. In fact, every smooth knot type will have an infinite number of different Legendrian representatives. A basic problem is to give the “Legendrian
Colloquium – Peter Johnson (University of Virginia)
ZoomTitle: A zero surgery obstruction from involutive Heegaard Floer homology Abstract: A fundamental result in 3-manifold topology due to Lickorish and Wallace says that every closed, oriented, connected 3-manifold can be obtained by surgery on a link in the 3-sphere. One may therefore ask: which 3-manifolds can be obtained by surgery on a link with
Colloquium – Gordana Todorov (Northeastern University)
ZoomTitle: Friezes, Quiver Representations and Cluster Theory Abstract: After cluster algebras were introduced by Fomin and Zelevinsky, there were many new connections found among many fields of mathematics: combinatorics, representation theory, quiver representations, non-commutative algebra, poisson theory and much more. Friezes were introduced by Conway and Coxeter as a very combinatorial notion. Since the introduction of cluster