Basic Things are Simple

Locally finite basic classical simple Lie superalgebras

In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.

Simple Things We Don’t Know

This is a quite faithful rendering of a Colloquio De Giorgi I had the honor to give at Scuola Normale Superiore on March 21, 2012. The idea was to explain some open problems in arithmetic algebraic geometry which are simple to state but which remain shrouded in mystery. 1. An interactive game: dimension zero Suppose I give you an integer N ≥ 2, and tell you that I am thinking of a monic integer...

Bilattices Are Nice Things

One approach to the paradoxes of self-referential languages is to allow some sentences to lack a truth value (or to have more than one). Then assigning truth values where possible becomes a fixpoint construction and, following Kripke, this is usually carried out over a partially ordered family of three-valued truth-value assignments. Some years ago Matt Ginsberg introduced the notion of bilatti...

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When simple things are meaningful: working memory strength predicts children's cognitive flexibility.

People often perseverate, repeating outdated behaviors despite correctly answering questions about rules they should be following. Children who perseverate are slower to respond to such questions than children who successfully switch to new rules, even after controlling for age and processing speed. Thus, switchers may have stronger working memory strength than perseverators, with stronger rule...