Natasha DobrinenUniversity of Denver |
An article on being a mathematician |

** Association for Symbolic Logic.**

As of January 1, 2018, I am Chair of the ASL Committee on Logic in North America and a member of the ASL Council. Past service includes a 3-year term on the Committee on Logic in North America, and a two-year term on the ASL Web Advisory Committee.

**
Advising and Postdoctoral 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 Currently I am advising Devin Groh at DU, and am co-advising Sonia Navarro Flores (with Michael Hrusak) on her PhD thesis at UNAM.

From Fall 2013 - Spring 2015 was 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 - Spring 2018, I mentored DU postdoctoral scholar Daniel Hathaway. From October 2018 - September 2019 I will be a research mentor to visiting scholar Dr. Kaiyun Wang from the College of Mathematics and Information Science, Shaanxi Normal University.

**Invited Talks, Workshops, Tutorials, and Panels.** For slides from 2015-2017, see Invited Talks Page.

Oberwolfach Workshop on Set Theory, Oberwolfach, Germany, April 5-11, 2020.

Carlos di Prisco Birthday Meeting, Bogota, Colombia, November 27-29, 2019.

Fall Southeast AMS Sectional Meeting, Special Session on Cech-Stone compactification of semigroups: Algebra, Topology, Dynamics, and Combinatorics, University of Florida at Gainesville, November 2-3, 2019.

National Academies of Sciences, Engineering, and Medicine. "Mathematical Frontiers" Webinar Series. I will be one of two panelists on the topic of Logic and Foundations, on September 10, 2019.

15th International Luminy Workshop in Set Theory, Luminy, France, September 23-27, 2019.

Casa Matematica Oaxaca, Workshop on Reverse Mathematics of Combinatorial Principles, September 15-20, 2019.

AMS Sectional Meeting, Special Session on "Topology and Descriptive Set Theory," Madison, WI, September 14-15, 2019.

Casa Matematica Oaxaca, Set theory of the reals, August 4-9, 2019. (unfortunately unable to attend, due to a prior commitment)

Midsummer Combinatorial Workshop XXIV, July 29 - August 2, 2019, Prague, Czech Republic. Ramsey theory on infinite graphs

Logic Fest in the Windy City, May 30 - June 2, 2019. Tutorial: Ramsey theory on trees and applications to infinite graphs

50 Years of Set Theory in Toronto, May 13-17, 2019. Strong coding trees and applications to Ramsey theory on infinite graphs

Spring Topology and Dynamical Systems Conference, March 14-16, 2019. Special Session on Set Theoretic Topology, "Borel colorings of the Rado graph". (unable to attend because of flights cancelled due to a blizzard in Denver)

Notre Dame Logic Seminar, March 5, 2019.

Miami University, February 25 - March 1, 2019. Colloquium talk.

University of Florida, February 18-23, 2019. A talk in the Colloquium, and a talk in the Logic Seminar.

Arctic Set Theory Workshop 4, Kilpisjaervi, Finland, January 21-26, 2019. Ramsey theory of the Henson graphs.

ASL Winter Meeting, at the Joint Mathematics Meetings, Baltimore, January 18-19, 2019, (plenary). Ramsey theory of the Henson graphs.

University of Oxford, Analytic Topology in Mathematics and Computer Science Seminar, January 16, 2019. Ramsey theory and infinite graphs.

University of Vienna, at the invitation of Vera Fischer, January 7-12, 2019. I gave a Mini-course on Infinitary Ramsey Theory (slides and video available here), and a lecture on the Ramsey theory of Henson graphs.

Centro de Ciencias Matematicas, December 2-8, 2018, "The Halpern-Lauchli Theorem at uncountable cardinals". (chalk talk)

Unifying Themes in Ramsey Theory, Banff International Research Station, November 18-23, 2018. (chalk talk)

Notre Dame Logic Seminar, September 4, 2018. Ramsey theory of homogeneous structures

Generalised Baire Spaces, Amsterdam, The Netherlands, August 22-24, 2018. Perfect tree forcings for singular cardinals

Ramsey Theory in Logic, Combinatorics and Complexity, Bertinoro International Center for Informatics, Italy, July 15 - 20, 2018. Bertinoro talk

SETTOP, Novi Sad, Serbia, July 2-5, 2018, (plenary). (similar to Bertinoro talk)

Logic Seminar, University of Illinois, Urbana-Champaign, May 21, 2018. (chalk talk)

Association for Symbolic Logic North American Annual Meeting, May 16-19, 2018, Special Session on Set Theory. (chalk talk)

Logic Seminar, University of Illinois, Chicago, April 24, 2018. (similar to JMM talk)

52nd Spring Topology and Dynamical Systems Conference, Auburn University, March 14-17, 2018, Special Session on Set-theoretic topology. Applications of high dimensional Ellentuck spaces

ASL-AMS Special Session on Ramsey theory, set theory and logic, Joint Mathematics Meeting, San Diego, January 10-11, 2018. JMM talk

** Other conferences I will be attending in 2019.**

British Combinatorial Conference, July 29 - August 2, 2019, Birmingham, UK. Contributed talk on "Ramsey theory on infinite graphs". This will be an overview of several papers. slides

European Set Theory Conference, July 1-5, 2019, Vienna, Austria. Contributed talk on "Barren extensions." This is joint work with Dan Hathaway extending results of Henle, Mathias, and Woodin to a large collection of sigma-closed forcings adding new ultrafilters with weak partition properties. slides

ASL Annual North American Meeting, May 20-23, 2019, CUNY, New York. Contributed talk on "Borel colorings of a space of Rado graphs". This work extends the Galvin-Prikry theorem for Borel partitions of the Baire space to Borel partitions of a topological space where each point represents a Rado graph. slides

** Research.**
I work in Set Theory, Ramsey Theory, Topology, and related areas. See my Research Page for more information.

** In January 2019, I finished writing a proof that the universal homogeneous k-clique-free graphs have finite big Ramsey degrees.** This paper is available on the arxiv.
The first paper on the Ramsey theory universal homogeneous triangle-free graph received some good preliminary reviews from Annals of Mathematics (available here), calling this "a remarkable achievment" and "the first major advance towards the Ramsey theory of Fraisse limits that have forbidden configurations", further writing that "Many top names in combinatorics worked on this problem for years, so it can be definitely confirmed that the problem is hard and important." As the assessments were not unanimous, that paper is currently submitted elsewhere.
My approach is opening up a large class of homogeneous structures with forbidden configurations to investigations of their canonical partitions, and connections with topological dynamics via this work of Andy Zucker. It also has provided means for extending the Galvin-Prikry theorem on the Baire space to a topological space of copies of the Rado graph, opening up the possibility of more extensions of Ramsey theory where the objects being colored are infinite structures, and the colorings are definable in some manner.

**Papers since 2016 published or accepted.**

Natasha Dobrinen and Daniel Hathaway. "Forcing and the Halpern-Lauchli Theorem." Journal of Symbolic Logic (to appear).

Natasha Dobrinen. "Continuous and other finitely generated cofinal maps on ultrafilters." Fundamenta Mathematicae (to appear).

Natasha Dobrinen. "Topological Ramsey spaces dense in forcings." Proceedings of the 2016 SEALS Conference (to appear).

Alvaro Arias, Natasha Dobrinen, Gabriel Giron-Garnica, Jose G. Mijares. "Banach spaces from barriers in high dimensional Ellentuck spaces." Journal of Logic and Analysis, 10 (2018), no. 5, 42pp.

Natasha Dobrinen and Daniel Hathaway. "The Halpern-Lauchli Theorem at a measurable cardinal." Journal of Symbolic Logic, 82 (2017), no. 4, 1560--1575.

Natasha Dobrinen. "Forcing in Ramsey theory." RIMS Kokyuroku 2042, (2017) 17--33.

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." Archive for Mathematical Logic, special issue in honor of James E. Baumgartner. 55 (2017), no. 7-8, 733--782.

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.

**Grants and Awards.**

My research is currently supported by National Science Foundation Grant DMS-1600781. "Ramsey Theory, Set Theory, and Tukey Order." September 1, 2016 - August 31, 2019. $129,995.

I received a third National Science Foundation Grant DMS-1901753 on "Logic, Ramsey Theory, and Relational Structures," which will start September 1, 2019. $158,476.

I won the Excellence in Research Award, University of Denver, Division of Natural Sciences and Mathematics, 2015-2016.

See Grants and Awards for the listing of these and previous grants and awards.**
Teaching.**

In Fall 2018 I taught Calculus 1 (MATH 1951) and Set Theory (MATH 3050). In Winter 2019 I focused solely on research. In Spring 2019 I am teaching a graduate course in Set Theory and Infinite Combinatorics (MATH4700). This course is new, focusing on Ramsey Theory and forcing, drawing from Todorcevic's book "Introduction to Ramsey Spaces," Kunen's "Set Theory," and various research articles. The intent is to develop background in this area and introduce students to current research topics. I am also teaching Perspectives in Art (MATH1150).

**
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. I also run quarterly mentoring meetings for the women graduate students in math.

**
Conference Organizing.**

Lynn Yengulalp and I are the Program Committe for the Special Session in Set-theoretic Topology at the 54th Spring Topology and Dynamical Systems Conference, Murray State University, March 18-21, 2020.

I am chairing the Program Committee for the ASL Winter Meeting at the Joint Mathematics Meeting, Denver, January 15-18, 2020.

I am on the Program Committee for the BEST conference series, 2018-2023.

Nick Galatos and I (Chair) organized BLAST 2018. This 10-year anniversary conference was held at the University of Denver, August 6-10, 2018.

Dan Hathaway and I organized a special session on Set Theory of the Reals (including Ramsey Theory) at the AMS Western Sectional Meeting 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, which started in 2008 when Professor Nikolaos Galatos and myself co-founded and co-chaired BLAST 08. BLAST is an interdisciplinary conference focused on Boolean algebras, Logic, Lattices, algebraic Logic, universal Algebra, Set theory, and Topology (Set-theoretic, point free, and general). 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. BLAST conferences are good for graduate students, early career mathematicians, and anyone interested in expanding their research to include neighboring areas. We are grateful for National Science Foundation funding for the BLAST Conference Series.

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 was run by Dan Hathaway and Timothy Trujillo from 2015-2018.

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.

last updated June 14, 2019.