One of the most active and successful areas of research within mathematical logic is the study of first order theories that admit a well behaved independence relation. Indeed, this line of research has led to surprising applications to algebraic geometry (e.g. Hrushovski's proof of the Mordell-Lang Conjecture). I will give a (necessarily brief) introduction to mathematical logic in general, model theory in particular, and describe what a simple theory is. Time permitting, I will speak about current research in the field, describing how two apparently different notions of independence coincide in a large class of theories.
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