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Natasha Dobrinen

Professor

What I do

I research the foundations of mathematics and the consequences for infinite structures. My research investigates synergistic interactions between set theory, combinatorics, topology and analysis. Current research focuses include Ramsey theory of infinite structures, the structures of compact spaces, and applications of set-theoretic methods in their analysis.

I teach a wide range of courses from graduate level logic to core math courses for non-majors. I also advise graduate students and mentor postdoctoral scholars.

Professional Biography

Born and raised in the heart of San Francisco, I obtained a BA from Berkeley, with an honors thesis advised by Field's medalist Richard E. Borcherds. I earned a PhD from the University of Minnesota under the supervision of Karel Prikry. My first postdoc was an NSF VIGRE position at Penn State, working with Stephen G. Simpson on recursion theory. After that, I held a three year research position at the Kurt Goedel Research Center for Mathematical Logic in Vienna, headed by Sy-David Friedman. In 2007 I was hired as an Assistant Professor at DU. I became Associate in 2011 and Full Professor in 2016.

Degree(s)

  • Ph.D., Mathematics, University of Minnesota, 2001
  • BA, Mathematics, University of California - Berkeley, 1996

Professional Affiliations

  • American Mathematical Society
  • Association for Symbolic Logic
  • Association for Women in Mathematics
  • European Set Theory Society

Research

I work on the interface of logic, combinatorics, topology and analysis. My research is focused on answering longstanding open problems, developing better methods to approach infinite structures, and making new connections between areas of math which, when seen, help each field progress.

Key Projects

  • Ramsey Theory, Set Theory, and Tukey Order
  • Ramsey Theory, Set Theory and Tukey Order
  • Classification of Turkey types of ultrafilters
  • Conference on Infinitary Ramsey Theory
  • BLAST 08 Conference

Featured Publications

Dobrinen, N. L. (2020). Ramsey theory of the universal homogeneous triangle-free graph. Journal of Mathematical Logic, 20(2), 75 pp.
Dobrinen, N. L., Arias, A., Giron Garnica, G. E., & Mijares Palacios, J. G. (2018). Banach spaces from high-dimensional Ellentuck spaces. Journal of Logic and Analysis, 10(5), 42 pp.
Dobrinen, N. L., & Todorcevic, S. (2015). A new class of Ramsey-Classification Theorems and their applications in the Tukey theory of ultrafilters, Part 2. Transactions of the American Mathematical Society, 367(7), 4627--4659.
Dobrinen, N. L. (2016). High-dimensional Ellentuck spaces and initial chains in the Tukey structure of non-p-points . Journal of Symbolic Logic, 81(1), 237--263.
Dobrinen, N. L., Laflamme, C., & Sauer, N. (2016). Rainbow Ramsey simple structures. Discrete Mathematics, 339(11), 2848--2855.

Presentations

Dobrinen, N. L. (2019). The Ramsey theory of Henson graphs. Association for Symbolic Logic Winter Meeting, at the JMM. Baltimore, MD: ASL .
Dobrinen, N. L. (2018). Ramsey theory of the Henson graphs. Unifying Themes in Ramsey Theory. Banff, Canada: Banff International Research Station.
Dobrinen, N. L. (2017). Ramsey theory on trees and applications. Seventh Indian Conference on Logic and Its Applications. Kanpur, India: Indian Institute of Technology.
Dobrinen, N. L. (2017). Ramsey theory, trees and ultrafilters. Workshop on Ultrafilters, Ramsey theory and dynamics. Lyon, France: Institut Camille Jordan, University of Lyon 1.
Dobrinen, N. L. (2017). The universal triangle-free graph has finite big Ramsey degrees. BLAST . Vanderbilt University .

Awards

  • NSM Excellence in Research Award, 2016, DU, NSM
  • Invitation to Luminy Workshop on Set Theory, CIRM, Luminy
  • Invited Participant in AIM Workshop on Nonstandard methods in combinatorial number theory, American Institute for Mathematics
  • Invitation to Oberwolfach Workshop in Set Theory, Mathematisches Forschungsinstitut Oberwolfach gGmbH
  • HERS Institute Participant, Denver, HERS Institute