Today was the first day of the Third Mile High Conference on Nonassociative Mathematics at University of Denver. Looks like a good group of people, only a few of whom I know. Yay for making connections.

Had lunch with Aleš Drápal today; I don't believe that we'd ever actually met before, though he immediately knew who I was, as I expected. The world is still small.

Neither he nor I are actively working on LD-related research at the moment, though finite LDs form nice test examples for computational packages; he mentioned that he has some unpublished theorems relating to the "levels" of homomorphisms between Laver tables. He also mentioned a direction of possible research that he had mostly abandoned, but where there might be results of manageable difficulty for a person or collaboration with the right crossover knowledge:

Let \( \mathbf{A} = \langle A; * \) be a LD-groupoid (probably finite and monogenerated). It is known that in some cases, such as when \( \mathbf{A} \) is a Laver Table, we can define an associative composition \( \circ \) on \( A \) satisfying

To future me, who wants to play around with this problem: start with Aleš' paper in Semigroup Forum 51, "On the semigroup structure of cyclic left distributive algebras".

Had lunch with Aleš Drápal today; I don't believe that we'd ever actually met before, though he immediately knew who I was, as I expected. The world is still small.

Neither he nor I are actively working on LD-related research at the moment, though finite LDs form nice test examples for computational packages; he mentioned that he has some unpublished theorems relating to the "levels" of homomorphisms between Laver tables. He also mentioned a direction of possible research that he had mostly abandoned, but where there might be results of manageable difficulty for a person or collaboration with the right crossover knowledge:

Let \( \mathbf{A} = \langle A; * \) be a LD-groupoid (probably finite and monogenerated). It is known that in some cases, such as when \( \mathbf{A} \) is a Laver Table, we can define an associative composition \( \circ \) on \( A \) satisfying

- \( ( a \circ b ) * c = a * (b * c) \)
- \( a \circ b = (a * b) \circ a \)
- \( a * (b \circ c) = ( a * b ) \circ (a * c) \)

To future me, who wants to play around with this problem: start with Aleš' paper in Semigroup Forum 51, "On the semigroup structure of cyclic left distributive algebras".

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