## Dates and venues

October 8 |
Denver, CO |
Towards bordered HF^{-} with torus boundary |

April 13 |
East Lansing, MI |
A Khovanov stable homotopy type |

April 24 |
Corvalis, OR |
Refinements of the Jones polynomial |

April 24 |
Corvalis, OR |
Some 4-dimensional questions in 3-dimensional topology |

May 25 |
Athens, GA |
Introduction to Heegaard Floer homology |

May 26 |
Athens, GA |
Computing involutive HF-hat |

June 2 |
Eugene, OR |
The unknotting number |

June 13 |
Sabhal Mòr Ostaig, Isle of Skye, UK |
Bordered involutive Floer homology |

## Abstracts

**October 8, AMS Special Session on Floer Theoretic Invariants of 3-manifolds and Knots**.

*Towards bordered HF ^{-} with torus boundary*

Abstract. We will outline work in progress towards extending bordered Floer homology to the "minus" variant of Heegaard Floer homology. This is joint work with Peter Ozsváth and Dylan Thurston.

**April 13, Michigan State Geometry & Topology Seminar**.

*A Khovanov stable homotopy type*

Abstract. Khovanov homology is a combinatorially-defined knot invariant which refines the Jones polynomial. After recalling the definition of Khovanov homology we will sketch a construction of a stable homotopy refinement of Khovanov homology. We will conclude with some modest applications and some work in progress. This is joint work with Tyler Lawson and Sucharit Sarkar. Another construction of the Khovanov stable homotopy type was given by Hu-Kriz-Kriz.

**April 24, Oregon State Topology Seminar**.

*Refinements of the Jones polynomial*

Abstract. After recalling the Jones polynomial of a knot, we will sketch the definition of two refinements: Khovanov homology and a Khovanov stable homotopy type. We will then discuss briefly how, following ideas of Lee, Ozsvath-Szabo, and Rasmussen, these can be used to obtain results about surfaces in 4-space bounded by a knot. This is joint work with Tyler Lawson and Sucharit Sarkar. There is related work by Hu-Kriz-Kriz.

**April 24, Oregon State Mathematics Department Colloquium**.

*Some 4-dimensional questions in 3-dimensional topology*

Abstract. In the first three quarters of the talk we will introduce several 4-dimensional questions about knots in 3-space. In the last quarter we will discuss some recent strategies for solving such questions, coming from abstract algebra and partial differential equations. Most of the talk should be broadly accessible.

**May 25, Georgia International Topology Conference**.

*Introduction to Heegaard Floer homology*

Abstract. We will outline some of the formal structure of Heegaard Floer homology, sketch the definitions of some of the Heegaard Floer invariants, and give some misleading examples. Time permitting we will also mention some of its applications.

**May 26, Georgia International Topology Conference**.

*Computing involutive HF-hat*

Abstract. Bordered Heegaard Floer homology is an extension of the Heegaard Floer invariant HF-hat to 3-manifolds with boundary. In the first half of the talk we will recall the basics of bordered Heegaard Floer homology and how it can be used to compute the Heegaard Floer invariant HF-hat. In the second half we will extend this algorithm to compute Hendricks-Manolescu’s involutive HF-hat. The first half of the talk is joint with Peter Ozsváth and Dylan Thurston, and the second half with Kristen Hendricks.

**June 2, UO Basic Notions Seminar**.

*The unknotting number*

Abstract. We will define the unknotting number of a knot and discuss some classical and modern techniques used to study it, some recent results, and some open questions.

**June 13, Low-dimensional topology on Skye**.

*Bordered involutive Floer homology*

Abstract. Hendricks-Manolescu introduced involutive Heegaard Floer homology as a partial analogue of pin-equivariant monopole Floer homology. We will discuss an algorithm for computing involutive HF-hat using bordered Floer homology and a proposed definition of bordered involutive Floer homology. This is joint work with Kristen Hendricks.

Previous years: 2015-2016.