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 A new book: the representation theory of finite monoids
 The uniform word problem for finite semigroups
 The first order theory of two endomorphisms of a finite dimensional vector space is undecidable
 Equalizers of free monoid morphisms, supports of rational power series and a question of Pin
 Isomorphism of oriented matroids from a semigroup viewpoint
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A new book: the representation theory of finite monoids
I am writing a book with Springer on the representation theory of finite monoids. A preliminary version is here. Comments and feedback are welcome.
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The uniform word problem for finite semigroups
The goal of this post is to prove the following theorem of Gurevich. Stronger results have been proven by Mark Sapir and can be found in his survey with Olga Kharlampovich. The version stated here lets one prove the results … Continue reading
The first order theory of two endomorphisms of a finite dimensional vector space is undecidable
I was asked by Melvvyn Nathanson to give a talk last year at his summer number theory seminar at the CUNY grad center about problems of wild type and in what sense they are wild. Many books, papers and lecture … Continue reading
Equalizers of free monoid morphisms, supports of rational power series and a question of Pin
In this mathoverflow question, J.E. Pin asked if it is decidable whether the support of a rational power series in noncommuting variables is a regular language. I pointed out that the answer is no and will elaborate here because it … Continue reading
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Isomorphism of oriented matroids from a semigroup viewpoint
This is in some sense a sequel to this post. Basically, I want to show that the somewhat awkward, in my opinion, definition of isomorphism of oriented matroids found, for example, here can be interpreted as isomorphism of underlying unary … Continue reading
Hyperplane face semigroups and zonotopes
Hyperplane face semigroups have attracted interest in recent years due to applications to Markov chains, descent algebras and buildings. Here I’ll describe an alternative way to think about hyperplane face semigroups from the zonotope view point.
Endomorphism monoids of finite topological spaces
This post is inspired by this Mathoverflow question. The question asks when a transformation monoid on a set can be the monoid of all continuous maps for some topology on . The OP observes that the monoid must contain all … Continue reading