I will discuss recent progress on understanding the tmf-based Adams spectral sequence, where tmf = topological modular forms.  The idea is to generalize the work of Mahowald and others in the context of bo-resolutions.  The work I will discuss is joint with Prasit Bhattacharya, Dominic Culver, and J.D. Quigley.

Together with Alex Degtyarev and Vincent Florence we introduced a new link invariant, called slope, of a colored link in an integral homology sphere. In this talk I will define the invariant, highlight some of its most interesting properties as well as its relationship to Conway polynomials and to the  Kojima–Yamasaki eta-function. The stress in this talk will be on our latest computational progress: a formula to calculate the slope from a C-complex.

In this session we will host a Q&A with current researchers who have recently gone through successful applications as well as more senior staff who have been on interview panels and hiring committees for postdoctoral positions in mathematics. The session will be a chance to get varied perspectives on the application process and find out about the different types of academic positions to apply for.

The panel members will be Candy Bowtell, Luci Basualdo Bonatto, Mohit Dalwadi, Ben Fehrman and Frances Kirwan. 

Most of the talk will be about the Farrell-Jones conjecture from the point of view of an outsider. I'll try to explain what the conjecture is about, why one wants to know it, and how to prove it in some cases. The motivation for the talk is my recent work with Fujiwara and Wigglesworth where we prove this conjecture for (virtually torsion-free hyperbolic)-by-cyclic groups. If there is time I will outline the proof of this result.