Courses:
Talks:
Can you color the plane with three colors so that every equilateral triangle with sides of length 1 has one vertex of each color? In this talk I answer this question and describe several generalizations. Some of these have implications for the foundations of quantum mechanics (the Bell-Kochen-Specker theorem); I explain these using only linear algebra and some elementary number theory, without assuming any knowledge of quantum mechanics. Recent comments about these observations invoke Euclid's Postulates; I conclude with a brief discussion of this connection.
Quantum computers, if they existed, would be able to solve certain problems faster than is possible on a classical computer running the best algorithms known. In this talk I illustrate how such efficient quantum algorithms work by discussing the game of "20 questions". I explain the optimal classical strategies for such games, and then show how to do much better quantum mechanically. No knowledge of quantum mechanics is required; I describe the basic facts which are needed during the talk.