Ph.D. in Mathematics, University of Minnesota - July 2001
B.A. in Mathematics, High Honors, University of California, Berkeley - May 1996
Discrete Math, Operations Research, and Probability, Logic, Topology
Ramsey theory of infinite relational structures and connections with forcing methods; canonical Ramsey theory for equivalence relations on relational structures; ultrafilters and Tukey and Rudin-Keisler structures; topological Ramsey space theory and applications to combinatorics and to ultrafilters.
- Infinite-dimensional Ramsey theory for homogeneous structures with SDAP^+, 30 pp. Submitted. arxiv:2203.00169
- (with M. Balko, D. Chodounsky, J. Hubicka, M. Konecny, L. Vena, and A. Zucker) Exact big Ramsey degrees via coding trees, 97 pp. Submitted. arXiv:2110.08409
- The Ramsey theory of Henson graphs. Journal of Mathematical Logic, To appear. 78 pp. arXiv:1901.06660
- The Ramsey theory of the universal homogeneous triangle-free graph. Journal of Mathematical Logic, 23 (2023), no. 1, Paper No. 2250018, 88 pp.
- (with S. Todorcevic) A new class of Ramsey-classification theorems and their application in the Tukey theory of ultrafilters, Part 1. Transactions of the American Mathematical Society, 366 (2014), no. 3, 1659–1684.