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Natasha Dobrinen

Professor

  • Faculty
  • College of Natural Sciences and Mathematics
  • Department of Mathematics

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

  • Banach spaces from high-dimensional Ellentuck spaces
  • A new class of Ramsey-Classification Theorems and their applications in the Tukey theory of ultrafilters, Part 2
  • High-dimensional Ellentuck spaces and initial chains in the Tukey structure of non-p-points
  • Rainbow Ramsey simple structures

Presentations

  • The Ramsey theory of Henson graphs
  • Ramsey theory of the Henson graphs
  • Ramsey theory on trees and applications
  • Ramsey theory, trees and ultrafilters
  • The universal triangle-free graph has finite big Ramsey degrees

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