Search Results

While I do not have direct experience with using it myself, I believe there are several packages out there for GAP that might do the trick for you, especially the HAP package. See especially 6: Homolo …

Lackenby discussed the unknotting number (and mentions some explicit knots for which we do not know the unknotting number!) in Lackenby, Marc, Elementary knot theory, Woodhouse, N. M. J. (ed.), Lectur …

The full text of the article can be found scanned here.

An excellent and very recent comparative analysis (which addresses your first two bullet points) on the development of infinitesimal calculus has been done by Jacques Bair, Alexandre Borovik, Vladimir …

Is the conjugacy problem for two-relator groups known to be undecidable? The word problem for two-relator groups is a famous open problem (appearing e.g. as Question 9.29 in the Kourovka notebook), an …

As mentioned in the comments, this is still considered an open problem. I thought I'd flesh out a few aspects. A solution was claimed in 1992 by Juhasz, but it seems to have failed to convince experts …

Here is a connection that I recently noticed, but I haven't quite been able to make sense of. It might follow from well-known facts; apologies, if so. This is quite far from my area. First, in "Yang-M …

I asked Christian Choffrut and Dominique Perrin this question today. They essentially told me the following: certainly, the name tropical comes in honour of the Brazilian mathematician Imre Simon; and …

In my recent paper (arXiv:2401.08146), I give a new presentation for $\operatorname{SL}_2(\mathbf{Z}[\frac{1}{2}])$. This group is generated by the two matrices $$ A = \begin{pmatrix}1 & 0 \\ 1 & 1\en …

How about a very recent political appointment? Eric Lander co-chaired Obama's "Council of Advisors on Science and Technology", and was very recently appointed to President Biden's director of the Offi …

An article you probably want to look at is E. S. Chibrikov, "The Right-Normed Basis for a Free Lie Superalgebra and Lyndon–Shirshov Words", Algebra Logika 45 (2006), issue 4, pp. 458--483. This contai …

The thesis can be found here.

Polycyclic groups are LERF, by Mal'cev 1948. In particular, all nilpotent and all abelian groups are LERF. As mentioned in the comments, as not all one-relator groups are residually finite, not all on …

The Blocks of Finite Groups wiki, which aims to classify the Morita equivalence classes of blocks with a given defect group. This is in part to understand Donovan's Conjecture better.

This is not, perhaps, a very large area, nor a complete "ending", but it was an interesting development in early semigroup theory that I think bears writing down. Some background, first. A semigroup $ …