Binghamton University Graduate Conference in Algebra and Topology

## November 7-8, 2020

Due to the ongoing pandemic, BUGCAT 2020 will be an online-only conference. Details on how to participate will be added to our Online Conference page as we determine the best way to accomodate our participants. We appreciate your patience and look forward to seeing you online in November.

Graduate students of all levels and faculty are invited to register to give a 30 minute talk. Talks may be expository or on current research.

If you would like to submit a talk, please use our Title and Abstract Submission Form. The deadline for submitting a talk is October 14th.

To attend the conference, please register by October 21st.

## Keynote Speakers

Moshe Cohen SUNY New Paltz
Randomness in low-dimensional topology Combinatorialists have been using randomness to study properties of large objects like graphs since the 1960s, but only recently have these methods become more widespread in topology. I will highlight some of these results for manifolds in 2 and 3 dimensions before arriving at the topic of knot theory. After discussing surprising recent work by Malyutin, I will give a summary of older results in this area and tie these into my own work.
Emily Riehl Johns Hopkins University
∞-category theory for undergraduates At its current state of the art, ∞-category theory is challenging to explain even to specialists in closely related mathematical areas. Nevertheless, historical experience suggests that in, say, a century's time, we will routinely teach this material to undergraduates. This talk describes one dream about how this might come about --- under the assumption that 22nd century undergraduates have absorbed the background intuitions of homotopy type theory/univalent foundations.
Ben Steinberg CUNY
A Lyndon’s Identity Theorem for one-relator monoids Magnus solved the word problem for one-relator groups in the early 1930s. This spurred quite a bit of work into the study of one-relator Lie Algebras, rings and monoids. Adian and his school made a number of breakthroughs on the word problem for one-relator monoids in the sixties and seventies, but the problem remains wide open. In 2000 Kobayashi asked whether the word problem for one-relator monoids can be solved using the theory of finite complete rewriting systems. A necessary condition for a monoid to have a finite complete rewriting system is the homological finiteness condition $$FP_{\infty}$$. Kobayashi asked in 2000 whether every one-relator monoid is of type $$FP_{\infty}$$. Note that one-relator groups are of type $$FP_{\infty}$$ as a consequence of Lyndon’s identity theorem. In this talk we sketch some techniques in the the proof that all one-relator monoids are of type $$FP_{\infty}$$. The main technique involves constructing actions of monoids on contractible CW complexes. Adian’s machinery from his work on the word problem is reinterpreted from a more geometric viewpoint to build these complexes. This is joint work with Robert Gray from the University of East Anglia.