# Graduate Colloquium Spring 2010

Jack Baskin Engineering Room 301A

Tea is served at 3:50 p.m.

For further information please contact contact Zhe Xu at zhexu71@gmail.com

**April 15, 2010**

**The Canonical Induction Formula on Trivial Source Modules**

**The Canonical Induction Formula on Trivial Source Modules**

**Michael Miller**

In 1946 Brauer proved that given a finite group G the induction map is a surjection from the ring of linear virtual characters to the ring of virtual characters. Robert Boltje showed there is a natural section (way to map backwards) for Brauer's induction map when he defined the Canonical Induction Formula (1989). We will look at the C.I.F. on the ring of isomorphism classes of trivial source modules and state a conjecture about one of its properties in this setting.

**May 27, 2010**

**On a Fundamental Question Involving Area Minimizing Surfaces**

**On a Fundamental Question Involving Area Minimizing Surfaces**

**Professor Tony Tromba, UCSC Department of Mathematics**

I will present a version of my lecture at the Swiss Academy's Basel Symposium honoring the life and work of Leonhard Euler on the occasion of his 300TH birthday. We shall consider methods of how to extend Euler and Lagrange's results connecting partial differential equations with the Calculus of Variations and their applications to least area surfaces and Plateau's Problem.