My research interests are in topology and my advisor is David Gay. Most recently I have been thinking about trisections of 4-manifolds, group trisections, and Lagrangian cobordisms between Legendrian knots. For a layperson’s “explainer” on some of the context in which my research sits, check out this awesome Quanta article (in which I was quoted!).
Publications & Preprints
- “A group-theoretic framework for low-dimensional topology”
- Joint work with Robion Kirby, Michael Klug, Vincent Longo, Benjamin Ruppik. In this project, which began at the Summer Trisectors Workshop in 2020, we detail how to recover a bridge trisected surface in a 4-manifold from its group trisection.
- “Constructions of Lagrangian cobordisms”
- Joint with my group from the WiSCon workshop in 2019: Noémie Legout, Caitlin Leverson, Maÿlis Limouzineau, Ziva Myer, Yu Pan, Samantha Pezzimenti, Lara Simone Suárez, and Lisa Traynor.
- “Good Reduction of Preperiodic Points”
- During my senior year at St. Louis University I completed an independent research project on dynamical systems under the guidance of Benjamin Hutz.
- “A Generalization of Mordell to Ternary Quadratic Forms”
- In the summer of 2015 I participated in WADE Into Research, a number theory REU. My group studied ternary quadratic forms, and our work led to a paper and several presentations. Joint with Gabriel Durham, Katherine Thompson, and Tiffany Treece.
Recent Talks
- “Group Trisections and Smoothly Knotted Surfaces,” Spring Topology and Dynamical Systems Conference, March 2022
- “Triple Knot Grid Diagrams,” Western Hemisphere Virtual Symplectic Seminar, February 2022
- “Triple Knot Grid Diagrams,” Binghamton University Geometry and Topology Seminar, February 2022
- “Triple Knot Grid Diagrams,” UGA Graduate Student Seminar, February 2022
- “Triple Knot Grid Diagrams,” Rice University Topology Seminar, December 2021
- “Triple Knot Grid Diagrams,” Geometric Topology Grad and Postdoc Seminar, November 2021
- “Triple Knot Grid Diagrams,” AMS Southeastern Sectional Meeting, November 2021
- “Group Trisections and Smoothly Knotted Surfaces,” AMS Central Sectional Meeting, October 2021
- “Distinguish Knotted Surfaces With This One Weird Trick,” UGA Graduate Student Summer Conference, August 2021
- “Triple Knot Grid Diagrams,” Tech Topology Summer School (lightning talk), July 2021
- “Group Trisections and Smoothly Knotted Surfaces,” Young Topologists Meeting, July 2021
- “Group Trisections and Smoothly Knotted Surfaces,” Graduate Student Conference in Algebra, Geometry, and Topology, May 2021
- “Group Trisections and Smoothly Knotted Surfaces,” Graduate Student Topology and Geometry Conference, April 2021
- “Group Trisections and Smoothly Knotted Surfaces,” AIM 4-Dimensional Topology Research Community (lightning talk), March 2021
- “Visualizing the 4th Dimension,” UGA Math Graduate Visitation Day, March 2021
- “Group Trisections and Smoothly Knotted Surfaces,” Virtual Trisectors Meeting (with Vincent Longo and Benjamin Ruppik), February 2021
- “Group Trisections and Smoothly Knotted Surfaces,” UGA Topology Seminar, February 2021
- “Group Trisections and Smoothly Knotted Surfaces,” Tech Topology Conference (lightning talk), December 2020
- “Intro to Trisections Redux,” UGA Topology Student Seminar, October 2020
- “Intro to Trisections,” UGA Graduate Student Seminar, October 2020
- “The Worst Definition of Linking Number,” UGA Graduate Student Summer Conference, July 2020
- “My Favorite Proof Concerning Legendrian Knots,” Geometric Topology Grad and Postdoc Seminar, March 2020
- “A Short History of Me (feat. Legendrian Knots),” MPIM Oberseminar, January 2020
- “Configuration Space Integrals for Links,” Geometric Topology Grad and Postdoc Seminar, December 2019
- “Linking Numbers and Gauss Integrals,” MPIM Configuration Spaces Seminar (with Jason Joseph), October 2019
- “Lagrangian Cobordisms Between Legendrians,” Geometric Topology Grad and Postdoc Seminar, July 2019
- “Chekanov’s DGA in the Front Projection,” UGA Topology Student Seminar, November 2018
- “Differential Graded Algebras of Legendrian Knots,” UGA Graduate Student Summer Conference, July 2018
- “Knot Floer Homology and Legendrian Knots,” UGA Topology Student Seminar, April 2018
- “Zeeman’s Collapsibility Conjecture,” UGA Topology Student Seminar, October 2017
Recent & Upcoming Travel
- Topology in Dimension 4.5 (at BIRS), November 2022
- 4-Manifolds: From Above and Below (at CIRM), September 2022
- SYNC Early Career Workshop, August 2022
- Summer Trisectors Workshop, June 2022
- New Developments in Four Dimensions, June 2022
- Georgia Topology Conference, May 2022
- University of Virginia Geometry Seminar, May 2022
- Braids in Low-Dimensional Topology (at ICERM), April 2022
- Joint Mathematics Meeting (virtual), April 2022
- Graduate Student Topology and Geometry Conference, April 2022
- Spring Topology and Dynamical Systems Conference, March 2022
- Rice University Topology Seminar, December 2021
- AMS Southeastern Sectional Meeting (virtual), November 2021
- AMS Central Sectional Meeting (virtual), October 2021
- Tech Topology Summer School (virtual), July 2021
- Park City Mathematics Institute Graduate Summer School: Illustrating Mathematics (virtual), July 2021
- Young Topologists Meeting (virtual), July 2021
- Nearly Carbon Neutral Geometric Topology Conference (virtual), June 2021
- Georgia Topology Conference (virtual), June 2021
- Summer Trisectors Workshop (virtual), June 2021
- Graduate Student Conference in Algebra, Geometry, and Topology (virtual), May 2021
- paraDIGMS (Diversity in Graduate Mathematical Sciences) (virtual), April 2021
- Graduate Student Topology and Geometry Conference (virtual), April 2021
- Winter Trisectors Workshop (virtual), December 2020
- Tech Topology Conference (virtual), December 2020
- Graduate Online Anything Topology Series (virtual), April, June, July 2020
- Virtual Summer Trisectors Workshop (virtual), June 2020
- Nearly Carbon Neutral Geometric Topology Conference (virtual), June 2020
- Winter Braids X, February 2020
- Symplectic Geometry, Contact Geometry and Interactions (CAST), February 2020
- Women in Symplectic and Contact Geometry and Topology (at ICERM), July 2019
- Park City Mathematics Institute Graduate Summer School, July 2019
- Spring Trisectors Meeting, April 2019
- Nebraska Conference for Undergraduate Women in Mathematics, January 2019
- Virginia Topology Conference, December 2018
- Tech Topology Conference, December 2018
- Topology Students Workshop, June 2018
- Critical Issues in Mathematics Education (at MSRI), February 2018
- Tech Topology Conference, December 2017
- Joint Mathematics Meeting, January 2017
I co-organized GOATS, a virtual mini-conference series for graduate students in topology and geometry, held on April 25, June 6, and July 18. See details here.
Here are some postcards I made for NGNCT 2021.
Sarah Blackwell 
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