Monica Marie VanDieren

Research and papers Teaching Talks C.V. Outreach

Contact Information E-mail:  mylastname at rmu dot edu Office:   John Jay 318 Office Phone: (412) 397-4278 Office Hours Summer 2008: By appointment Anagram:  I AM ONE DRIVEN AMERICAN

My research is in model theory, a branch of mathematical logic. I am particularly interested in the classification theory of non-elementary classes and applications of this program to number theory and geometry. I am involved in the development of a stability theory for tame abstract elementary classes and am active in the drive to prove Shelah's Categoricity Conjecture which is perhaps the most difficult problem in model theory having a great potential for applications in other branches of mathematics. My work is partially supported by NSF grant DMS 0801313.

In July of 2006 there was a workshop at the American Institute of Mathematics dedicated to Shelah's Categoricity Conjecture. An account of my experience of co-organizing this workshop appears in the Fall 2006 American Institute of Mathematics newsletter.

Recently I had the honor of serving as the opponent for the doctoral public examination of Meeri Kesälä at the University of Helsinki. The defense in Finland is based on a long tradition and is unlike the informal thesis defenses in the U.S. After the candidate presents her research, the opponent speaks on how the candidate's work relates to other work done in the field. Then, the candidate and the opponent engage in a long dialogue or debate in which the opponent challenges the candidate's work. In the long night of celebrations that followed the defense, I even met a member of the Finnish Parliament.

1. The equality S1=D=R, with Rami Grossberg, Alexei Kolesnikov and Ivan Tomasic. Mathematical Logic Quarterly, 49, (2003), pp.115-128. Download the pdf file from the publisher, Wiley InterScience .
2. Categoricity in Abstract Elementary Classes with No Maximal Models. Annals of Pure and Applied Logic, 141, Issues 1-2 , August 2006, Pages 108-147.
3. Shelah's Categoricity Conjecture from a successor for tame abstract elementary classes, with Rami Grossberg. Journal of Symbolic Logic, 71, (2006) 2, 553-568. pdf.
4. Upward Stability Transfer Theorem for Tame Abstract Elementary Classes, with John Baldwin and David Kueker. Notre Dame Journal of Formal Logic, 47, no. 2 (2006) 291-298. pdf.
5. Galois-stability in Tame Abstract Elementary Classes, with Rami Grossberg. Journal of Mathematical Logic, 6, no. 1 (2006) 25-49. pdf.
6. Categoricity from One Successor Cardinal in Tame Abstract Elementary Classes, with Rami Grossberg Journal of Mathematical Logic, 6, no. 2 (2006) 181-201. pdf.
7. Categoricity and No Vaughtian Pairs.(13 pages). Submitted.
8. Uniqueness of Limit Models in Classes with Amalgamation, with Rami Grossberg and Andrés Villaveces. (18 pages). Submitted.
9. A Stochastically Independent Example, with Rami Grossberg. In preparation.