Spring 2025 Learning Seminar

Spring 2025 Immersed Curves Learning Seminar

In Spring 2025 we are running an informal learning seminar on immersed curve theory and the unknotting number which meets Wednesdays 10-11 in Hill 425. All are welcome to attend. If it would benefit your attendance to have a day parking pass at Rutgers, please email me. For other questions, contact any of me, Abhishek Mallick, Biji Wong, and Jonathan Hanselman.

The seminar will start with the first paper in the list below, and as time allows may also discuss the other two papers below it:

Jennifer Hom, Tye Lidman, and JungHwan Park. Unkotting number and cabling
Jesse Cohen and Gary Guth. Immersed curves and 4-manifold invariants
Kristen Hendricks and Abhishek Mallick. A note on cables and the involutive concordance invariants

Some notes on the basics of Heegaard Floer theory live here:

Jennifer Hom. Lecture notes on Heegaard Floer homology
Ciprian Manolescu. An introduction to knot Floer homology
Jennifer Hom. A survey on Heegaard Floer homology and concordance

Some references on immersed curves specifically live here:

Jonathan Hanselman, Jacob Rasmussen, and Liam Watson. Bordered Floer homology for manifolds with torus boundary via immersed curves
Jonathan Hanselman, Jacob Rasmussen, and Liam Watson. Heegaard Floer homology for manifolds with torus boundary: properties and examples
Jonathan Hanselman and Liam Watson. Cabling in terms of immersed curves
Jonathan Hanselman. Knot Floer homology as immersed curves
Jonathan Hanselman. Satellite knots and immersed Heegaard Floer homology

Schedule of meetings:

February 12: Basics of immersed curves (Biji Wong)
February 19: Immersed curves and satellites (Jonathan Hanselman)
February 26: The unknotting number in Heegaard Floer homology (Kristen Hendricks)
March 5: Knot-like complexes and their immersed curves (Jay Patwardhan)
March 12 : Involutive Heegaard Floer basics, for later use (Kristen Hendricks
March 19: No seminar (Spring break!)
March 26: No seminar (Princeton Simons Satellite conference)
April 2: Cabling for immersed curves and main proof (Sriram Raghunath)
April 9: Applications Pt I (Aakash Parikh)
April 16: Applications Pt II (Abhishek Mallick)
April 23: HFI and the unknotting number (KH or AM)