# Graham Leach-Krouse

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PhD: Univeristy of Notre Dame - 2013

### PhD: Univeristy of Notre Dame - 2013

Advisors: Starchenko & Budur

Research Area:

Year Started: 2009

### Research Interests:

Graham's is currently interested in generalizing some of the results in the paper Model Theory of Diﬀerence Fields II: Periodic Ideals and the Trichotomy in All Characteristics. There, several results are presented on the model companion AFCA of the theory of diﬀerence domains (integral domains with an injective endomorphism), obtained by adding a generic automorphism to ACF. The question will be how well these results transfer over to the general situation in which an arbitrary “nice” theory (perhaps strongly minimal) replaces ACF , and in which the theory Tσ obtained by adding generic automorphisms to T is the model companion of T∀σ , the theory obtained by adding an injective endomorphism to the universal part of T.

### Meetings and Workshops attended:

- Conference in Honor of Harvey Friedman, May 14-17, 2009.
- Midwest PhilMath Workshop October 9-11, 2009.
- Midwest Model Theory Meeting, Nov 7-8, 2009.
- National ASL Meeting March 17-20, 2010.

### Talks Given:

Two Fundamental Theorems in the Model Theory of Qp — Talk on quantiﬁer elimination over Th(Qp ) in MacIntyre’s Language, and the Ax-Kochen-Ershov Theorem.