This will be a talk for the CUNY Set Theory Seminar, January 31, 2014, 10:00 am.
Abstract. I will demonstrate that a large cardinal need not exhibit its large cardinal nature in HOD. I will begin with the example of a measurable cardinal that is not measurable in HOD. After this, I will describe how to force a more extreme divergence. For example, among other possibilities, it is relatively consistent that there is a supercompact cardinal that is not weakly compact in HOD. This is very recent joint work with Cheng Yong.