Natasha Dobrinen's Research


Research Interests

My research interests mainly fall under the broad category of Logic and Foundations of Mathematics. I do research in Set Theory, Ramsey Theory, Boolean Algebras, and Measure Theory. I have investigated relationships between random reals, eventually dominating functions, measure, generalized weak distributive laws, infinitary two-player games, and complete embeddings of the Cohen algebra into complete Boolean algebras. Currently, I am working in Ramsey theory, the structure of the Tukey types of ultrafilters on countable base sets and in Boolean algebras in general, and problems involving both.


Grants

National Science Foundation Grant DMS-142470. "Conference on Infinitary Ramsey Theory, May 24-28, 2014". $10,200.

National Science Foundation Grant DMS-1301665. "Ramsey Theory, Set Theory, and Tukey Order." September 1, 2013 - August 31, 2016. $114,368.

Support for Travel and Living Expenses to participate in the Fields Institute Thematic Program in Forcing and Its Applications, National Science Foundation, July 2012 - December 2012. $5000.

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.)

Association for Women in Mathematics/National Science Foundation Mentoring Travel Grant. November/December 2010 (Paris). $2800.

University of Denver Faculty Research Fund grant. "Subtle Measurements on Large Spaces." July/August 2010 (Paris). $3000.

National Science Foundation grant to start the BLAST Conference series (Co-PI) (University of Denver). $27,390.


Papers

Natasha Dobrinen. "Generalized weak distributive laws in Boolean algebras and issues related to a problem of von Neumann" thesis.pdf

Natasha Dobrinen. "Games and general distributive laws in Boolean algebras," Proc. Amer. Math. Soc. 131 (2003) 309-318. Distributive_laws.pdf

Natasha Dobrinen. "Errata to `Games and general distributive laws in Boolean algebras'," Proc. Amer. Math. Soc. 131 (2003) 2967-2968. Distributive_laws_errata

Natasha Dobrinen. "Complete embeddings of the Cohen algebra into three families of c.c.c., non-measurable Boolean algebras," Pacific Jour. Math. 214(2) (2004) 201-222. Cohen_algebras.pdf

Natasha Dobrinen and Stephen G. Simpson. "Almost everywhere domination," Jour. of Symbolic Logic 69(3) (2004) 914-922. Almost everywhere domination.pdf

Natasha Dobrinen and Sy-David Friedman. "Co-stationarity of the ground model," Jour. Symbolic Logic 71(3) (2006) 1029-1043. co-stationarity.pdf

James Cummings and Natasha Dobrinen. "The hyper-weak distributive law and a related game in Boolean algebras," Annals of Pure and Applied Logic 149 (2007), no. 1-3, 14--24 hyper-weak.pdf.

Natasha Dobrinen. "More ubiquitous undetermined games and other results on uncountable length games in Boolean algebras," Note di Matematica 27 (2007), suppl. 1, 65--83. unctbl_games.pdf.

Natasha Dobrinen. "Co-stationarity of the ground model and new $\omega$-seqences," Proc. Amer. Math. Soc. 136 (2008), no.5, 1815--1821. new_omega_seq.pdf.

Natasha Dobrinen. "$\kappa$-stationary subsets of $\mathcal{P}_{\kappa^+}\lambda$, infinitary games, and distributive laws in Boolean algebras," Journal of Symbolic Logic 73 (2008), no. 1, 238--260. games_kstat.pdf.

Natasha Dobrinen and Sy-David Friedman. "Internal consistency and co-stationarity of the ground model," Journal of Symbolic Logic 73 (2008), no. 2, 512--521. Internal Consistency Costationarity.pdf.

Natasha Dobrinen and Sy-DavidFriedman. "Homogeneous iteration and measure one covering relative to HOD," Archive for Mathematical Logic 47 (2008), no. 7-8, 711--718. Homogeneous Iterations

Natasha Dobrinen and Sy-David Friedman. "The consistency strength of the tree property at the double successor of a measurable," Fundamenta Mathematicae 208 (2010), 123--153. treeproperty.pdf.

Natasha Dobrinen and Stevo Todorcevic. "Tukey types of ultrafilters," Illinois Journal of Mathematics 55(3) (2011), 907--951. (This paper now has an official publication date of 2011, even though it is appearing in 2013 due to the journal's backlog.) Here is a revised and improved version: tukey.pdf.

Natasha Dobrinen. "Continuous cofinal maps on ultrafilters," (2010) 23 pp, submitted. continuous_maps.pdf

Natasha Dobrinen and Stevo Todorcevic. "A new class of Ramsey-Classification Theorems and their applications in the Tukey theory of ultrafilters, Part 1," Transactions of the American Mathematical Society, 366 (2014), no. 3, 1659--1684. A Ramsey Classification Theorem

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, 34 pp, to appear. Ramsey-Classification Theorems

"Natasha Dobrinen and Stevo Todorcevic. "A new class of Ramsey-classification Theorems and their applications in the Tukey theory of ultrafilters, Parts 1 and 2," (Extended Abstract from poster at the Erdos Centennary conference, Budapest, July 2013), Electronic Notes in Discrete Mathematics, 43 (2013) 107--112.

Andreas Blass, Natasha Dobrinen, and Dilip Raghavan. "The next best thing to a p-point," (2013) 35 pp, submitted. Next best thing

Natasha Dobrinen. "Survey on the Tukey theory of ultrafilters," Mathematical Institutes of the Serbian Academy of Sciences," (2013) 28 pp, to appear. Tukey Survey

Natasha Dobrinen. "High dimensional Ellentuck spaces and initial chains in the Tukey structure of non-p-points," (2014) 28 pp, submitted. Generalized Ellentuck Spaces

Natasha Dobrinen, Jose Mijares, and Timothy Trujillo. "Topological Ramsey spaces from Fraisse classes, Ramsey-classification theorems, and initial structures in the Tukey types of p-points," (2014) 31 pp, Invited submission to Archive for Mathematical Logic special volume in honor of James E. Baumgartner.

Jennifer Brown and Natasha Dobrinen. "Spectra of Tukey types of ultrafilters on Boolean algebras," (2014) 18 pp, submitted. Tukey spectra in Boolean algebras

Natasha Dobrinen and Jose Mijares. "Topological Ramsey spaces and metrically Baire sets," (2014) 17pp, submitted. Metrically Baire Sets

Please note: If there are any problems with the links to papers, the latter ones may be found at the Mathematics Department Preprint Series http://www.du.edu/nsm/departments/mathematics/research/preprintseries.html


Book Reviews

Herbert B. Enderton. "A Mathematical Introduction to Logic," Bull. Symbolic Logic. 9(3) (2003) 406--407.

Steven Givant and Paul Halmos. "Introduction to Boolean Algebras," Bull. Symbolic Logic 16(2) (2010) 281--282.

"Appalachian Set Theory, 2006-2012," James Cummings and Ernest Schimmerling, Editors. Bull. Symbolic Logic. 4pp, To appear.


"For the Lord God is my strength and song, and He has become my salvation." Isaiah 12:2