Department of Mathematics
Recent and Upcoming Invited Talks, Tutorials, and Panels.
Association for Symbolic Logic 2017 North American Meeting, Boise, March 20-23, 2017, Special Session in Set Theory and its Applications to Analysis and Topology. The universal triangle-free graph has finite big Ramsey degrees
2017 Spring Topology and Dynamical Systems Conference, New Jersey City University, March 8-11, 2017, Special Session in Set-Theoretic Topology. Banach spaces from high dimensional Ellentuck spaces
Arctic Set Theory Workshop 3, Kilpisjaervi, Finland, January 25 - 30, 2017. On the finite big Ramsey degrees for the triangle-free graph: A progress report
Seventh Indian Conference on Logic and its Applications - 2017, Indian Institute of Technology Kanpur, January 5 - 7, 2017. Ramsey Theory on Trees and Applications
RIMS Workshop on Infinite Combinatorics and Forcing Theory, Research Institute for Mathematical Sciences, Kyoto University, Japan, November 28 - December 1, 2016. I gave a tutorial on Ramsey theory in forcing. Ramsey Theory in Forcing: Tutorial 1 Ramsey Theory in Forcing: Tutorial 2 Forcing in Ramsey Theory: Tutorial 3
Set Theory and its Applications in Topology, Casa Matematica Oaxaca, Mexico, September 11 - 16, 2016. Topological Ramsey spaces in creature forcing
BEST 2016, San Diego, California, June 14 - 17, 2016. Ramsey spaces coding universal triangle-free graphs and applications to Ramsey degrees
SEALS. University of Florida, February 27-28, 2016. Ultrafilters with complete combinatorics over L(R)
Association for Symbolic Logic Winter Meeting, at the Joint Mathematics Meeting, Seattle, Washington, January 6 - 9, 2016. Inner topological Ramsey spaces
1st Pan Pacific International Conference on Topology and Applications. Min Nan Normal University, Zhangzhou, China, November 25 - 30, 2015. Tukey theory of ultrafilters
The Emmy Noether Society. Cambridge University, United Kingdom, November 17, 2015. Canonical equivalence relations (chalk talk)
The 5th European Set Theory Conference, Isaac Newton Institute, Cambridge, United Kingdom, August 24 - 28, 2015. Infinite dimensional Ellentuck spaces: video of chalk talk
30th Summer Conference on Topology and Its Applications, Galway, Ireland, June 23 - 26, 2015. I also served on a 1-hour career panel on June 22 during a workshop for graduate students and early career researchers.
49th Spring Topology and Dynamics Conference 2015, Bowling Green State University, Ohio, May 14 - 16, 2015. Canonical cofinal maps on ultrafilters and properties inherited under Tukey reducibility
Forcing and Its Applications Retrospective Workshop, Fields Institute, Toronto, Canada, March 29 - April 2, 2015. Higher dimensional Ellentuck spaces
Miniworkshop at the Kurt Goedel Research Center for Mathematical Logic, University of Vienna, Austria, February 20, 2015. High and higher dimensional Ellentuck spaces and initial segments in the Rudin-Keisler and Tukey types of non-p-pointsArctic Set Theory 2, Kilpisjarvi Research Center, Finland, February 12 - 17, 2015.
Oberwolfach Workshop on Set Theory, Oberwolfach, Germany, January 12 - 19, 2014. Progress in Ramsey Theory
Papers since 2015 published or accepted.
Natasha Dobrinen and Daniel Hathaway. "The Halpern-Lauchli Theorem at a measurable cardinal." Journal of Symbolic Logic. 16 pp. (to appear).
Natasha Dobrinen. "Creature forcing and Topological Ramsey spaces." Topology and Its Applications, special issue in honor of Alan Dow's 60th birthday. 213 (2016), 110--126.
Natasha Dobrinen. "Infinite-dimensional Ellentuck spaces and Ramsey-classification theorems." Journal of Mathematical Logic. 16 (2016), no.1, 1650003, 37pp.
Natasha Dobrinen, Claude Laflamme, and Norbert Sauer. "Rainbow Ramsey simple structures." Discrete Mathematics. 339 (2016), no. 11, 2848--2855.
Natasha Dobrinen, Jose G. Mijares, and Timothy Trujillo. "Topological Ramsey spaces from Fraisse classes, Ramsey-classification theorems, and initial structures in the Tukey types of p-points." To appear in Archive for Mathematical Logic, special issue in honor of James E. Baumgartner. 35pp.
Natasha Dobrinen and Jose G. Mijares. "Topological Ramsey spaces and metrically Baire sets." Journal of Combinatorial Theory, Series A. 135 (2015) 161--180.
Andreas Blass, Natasha Dobrinen, and Dilip Raghavan. "Then next best thing to a P-point." Journal of Symolic Logic. 80 (2015), no. 3, 866--900.
Jennifer Brown and Natasha Dobrinen. "Spectra of Tukey types of ultrafilters on Boolean algebras." Algebra Universalis. 75 (2016), no. 4, 419--438.
Natasha Dobrinen. "High dimensional Ellentuck space and initial chains in the Tukey structure of non-p-points." Journal of Symbolic Logic, 81 (2016), no.1, 237--263.
Natasha Dobrinen. "Survey on the Tukey theory of ultrafilters." Zbornik Radova, Serbian Academy of Sciences and Arts, 17(25) (2015) 53--80. Special Issue on Selected Topics in Combinatorial Analysis. (open access)
Natasha Dobrinen and Stevo Todorcevic. "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 (2015), no. 7, 4627--4659.Preprints of these and the rest of my articles can be found here.
National Science Founfation Grant DMS-1600781. "Ramsey Theory, Set Theory, and Tukey Order." September 1, 2016 - August 31, 2019. $129,995.
National Science Foundation Grant DMS-142470. "Ramsey Theory, Set Theory, and Tukey Order". September 1, 2013 - August 31, 2016. $114,368.
Simons Foundation Collaboration Grant #245286. "Classification of Tukey types of ultrafilters." September 1, 2012 - August 31, 2017. $35,000. (Terminated September 1, 2013 due to NSF grant.)Other research and conference grants are listed here.
In Fall 2016 I will be teaching undergraduate Set Theory (MATH 3050) and Calculus 1 (MATH 1951). The Winter 2017 is my mini-sabbatical. In Spring 2017 I will be teaching graduate-level Combinatorial Set Theory (MATH 4050) and Perspectives in Art (MATH 1150).
Association for Women in Mathematics.
The Mathematics Department at DU now has an AWM Student Chapter. The Faculty Sponsor is Professor Mei Yin and I am the Faculty Co-Sponsor.
Dan Hathaway and I will be organizing a special session on Set Theory of the Reals (including Ramsey Theory) at the AMS Western Sectional Meeting to be held at the Unviersity of Denver in October 2016.
The DU Sesquicentennial Ramsey Theory Conference 2014 was held at the University of Denver, May 24 - 28, 2014. The meeting was organized by Jose Mijares and myself. We thank the National Science Foundation and The DU Provost Sesquicentennial Fund for funding to support many participants.
DU is the birthplace of the BLAST Conference Series. The last BLAST was held at University of North Texas in June 8 - 12, 2015 BLAST North Texas. Winter BLAST 2015 was held at New Mexico State Univerisity, Las Cruces. BLAST 2013 was held at Chapman University. BLAST 2011 was at the University of Kansas; BLAST 2010 was held in Boulder; BLAST 09 was held in Las Cruces. BLAST 08 was held in Denver. Co-chairs were Professor Nikolaos Galatos and myself. BLAST 08. BLAST stands for Boolean algebras, Logic, Lattices, algebraic Logic, universal Algebra, Set theory, Set-theoretic Topology, point free Topology, and general Topology. These are logic-related areas of interest to researchers at Chapman University; New Mexico State University, Las Cruces; University of Colorado, Boulder; University of Denver; University of Kansas, Lawrence; University of Missouri, Kansas City; University of Nebraska, Omaha; and University of North Texas. The BLAST series is graduate-student friendly and supports participation of graduate students, post-docs, and young researchers with NSF funded travel and lodging support.
Front Range Logic Saturdays (formerly known as the Maximally Informal Gathering or MIG) is a consortium of logicians from the Boulder, Denver, Golden and Fort Collins areas. We gather on selected Saturdays to share research talks, ideas, and lunch. MIG was started in 2009 by Bart Kastermans and myself. FRLS is currently being run by Dan Hathaway and Timothy Trujillo.
I have also organized various special sessions and served on program committees for conferences of the ASL and the AMS. These are listed in my CV.
From 2008 until May 2014, I was the coordinator and supervisor for the Graduate Colloquium which meets on Fridays at 2pm. See Graduate Colloquium for a list of past and present speakers.
Advising and mentoring.
I was PhD advisor to Timothy Trujillo who earned his PhD in Spring 2014, with thesis: Topological Ramsey spaces, associated ultrafilters, and their applications to the Tukey theory of ultrafilters and Dedekind cuts of nonstandard arithmetic. Dissertation_Trujillo_2014
From Fall 2013 - Spring 2015 I have been a mentor to postdoctoral scholar Jose Mijares. In 2015 I co-advised (with David Meza-Alcantara) Sonia Navarro Flores on her masters thesis at UNAM Morelia, Mexico. From Fall 2015 onward, I am mentor to DU postdoctoral scholar Daniel Hathaway.