Department of

February 2014 March 2014 April 2014 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 1 1 2 3 4 5 2 3 4 5 6 7 8 2 3 4 5 6 7 8 6 7 8 9 10 11 12 9 10 11 12 13 14 15 9 10 11 12 13 14 15 13 14 15 16 17 18 19 16 17 18 19 20 21 22 16 17 18 19 20 21 22 20 21 22 23 24 25 26 23 24 25 26 27 28 23 24 25 26 27 28 29 27 28 29 30 30 31

Monday, March 10, 2014

**Abstract:** Motivic homotopy theory was introduced by V. Voevodsky as part of his work on the Milnor conjecture. It provides a way of using topological methods as a way to study algebraic varieties over a field. We discuss a new connection between motivic homotopy theory and the study of invariants of manifolds with symmetry. This builds on the classical Galois correspondence and in the case of a real closed field it leads to a surprising generalization of the Fundamental Theorem of Galois theory. This is joint work with K. Ormsby.