Education
Ph.D. University of California, Riverside, 2024.
Topic: Conicality of Morse Limit Sets and Stability
M.S. Ball State University, Mathematics, 2018
Topic: Generalized covering space theory
B.S. University of California, Davis, Mathematics, 2016
Publications
J. Garcia, Y. Qing, E. Vest, "Topological and Dynamic Properties of the Sublinearly Morse Boundary and the Quasi-Redirecting Boundary." (2024)
Preprint available (arXiv:2408.10105 .)
J. Garcia, "Characterizations of Stability via Morse Limit Sets." (2023)
Preprint available (arXiv:2309.09135 .) Accepted for Publication in Algebraic & Geometric Topology, expected publication date in early 2026.
J. Garcia, "Conicallity of Morse Limit Sets and Stability." (2024)
PhD Dissertation, Univsersity of California Riverside, https://escholarship.org/uc/item/84w4v2jb
H. Fischer, J.D. Garcia, "Fibrations, unique path lifting, and continuous monodromy,"
Topology and its Applications (2019), https://doi.org/10.1016/j.topol.2019.107047 (arXiv link here: arXiv:1902.00081.)
J. Garcia, "Some aspects of generalized covering space theory,"
Master's Thesis, Ball State University, (2018), https://cardinalscholar.bsu.edu/handle/123456789/201134
Presentations and Talks
"Characterizations of Stability via Morse Limit Sets", JMM, January 8-11th, 2025.
"Characterizations of Stability via Morse Limit Sets", Geometry and Topology Seminar, UMass Amherst, November 2024.
"Characterizations of Stability via Morse Limit Sets", Fall Eastern Sectional Meeting, October 19-20th, 2024.
"Characterizations of Stability via Morse Limit Sets", 58th Spring Topology and Dynamics Conference, March 7th, 2024.
"Characterizations of Stability via Morse Limit Sets", Tufts Geometric Group Theory Seminar, February, 2024.
"Conicality and Stability in Finitely Generated Groups", Poster Presentation at GAGTA, July 19th, 2023.
"An Introduction to Hierarchically Hyperbolic Spaces", Riverside Workshop on Geometric Group Theory, March 26th, 2023.
"Conicality and Stability in Finitely Generated Groups", Poster Presentation at Young Geometric Group Theory XI, Feb 15th, 2023.
"Big mapping class groups with hyperbolic actions: classification and application", Workshop on Big Mapping Class Groups at Boston College, Aug 3rd, 2022.
"An Informal Description of Hierarchically Hyperbolic Spaces", UCR Topology Seminar, Riverside, California, April 23rd, 2022.
"An Introduction to Boundaries at Infinity", UCR Topology Seminar, Riverside, California, January 26, 2022.
"Equivalent Characterizations for Convex Cocompactness in Proper Metric Spaces", Graduate Student Seminar, Riverside, California, October 29, 2021.
"Aspects of Generalized Covering Space Theory", Underrepresented Students in Topology and Algebra Research Symposium, Virtual, April 30 2021.
"The Milnor-Schwartz Lemma and You: Why we care about Geometric Group Theory", Graduate Student Seminar, Riverside, California, November 20, 2020.
"Generalized Covering Space Theory and Fibrations", UCR Topology Seminar, Riverside, California, October 28, 2020.
"Some Aspects of Generalized Covering Space Theory", Master's Thesis Presentation, Muncie, Indiana, March 1, 2018.
Invited Conferences
58th Spring Topology and Dynamics Conference, Christopher Newport University, March 2025.
AMS Fall Eastern Sectional Meeting, University at Albany, October 2024.
Riverside Workshop on Geometric Group Theory, Riverside, California, March 2023.
World of GroupCraft II, virtual, September 2022.
USTARS, virtually at ICERM, April 2021.
Organized Events
Conference: WiMiN (Women in Mathematics in New England), September 20, 2025.
Panel Discussion for Project NExT: Understanding Service at Your Institution and Beyond: Navigating and Meeting Service
Expectations at Mathfest 2025, Sacramento.
Conference: WiMiN (Women in Mathematics in New England), September 21, 2024.
Conference: WiMiN (Women in Mathematics in New England), September 23, 2023.
Attended Conferences
MAA Mathfest, Sacramento, August 2025. Attended with the graduating cohort of Project NExT.
JMM, Seattle, January 2025.
MAA Mathfest, Indianapolis, August 2024. Attended with the incoming cohort of Project NExT.
Braids Reunion Workshop, ICERM, July 2024.
Advances in Hierarchical Hyperbolicity Workshop, Bannf International Research Station, May 2024.
Riverside Workshop on Geometric Group Theory, Riverside, California, May 2024.
JMM, San Francisco, January 2024.
FARM: Group Theory 2023, Fairfield University, Connecticut, December 2023.
Geometric and Asymptotic Group Theory with Applications (GAGTA), Vienna, Austria, July 2023.
Young Geometric Group Theory XI, Münster, Germany, Feburary 2023.
Joint Mathematical Meetings, Boston, Mass, January 2023.
SACNAS National Diversity in STEM, San Juan Puerto Rico, October 2022.
Workshop on Big MCGs at Boston College, August 2022.
MSRI Summer School on Metric Geometry and Analysis, Oxford, United Kingdom, July 2022.
Hyperbolic Groups and their Generalizations, Paris, June 2022.
Cornell Topology Festival, Ithaca, New York, May 2022.
Groups Acting on Fractals, CIRM in Marseille, France, April 2022.
A week at infinity, virtual, March 2022.
Young Geometric Group Theory X, virtually at Newcastle, July 2021.
Artin Groups, CAT(0) Geometry, and Related Topics, Columbus, Ohio, July 2021.
Beyond Hyperbolicity, Columbus, Ohio, June 2021.
Arches Topology Conference, Hurricane, Utah, April 2019.
Awards
Dissertation Year Program Award, Summer 2023.
Vernon A. Kramer Memorial Service Award, Spring 2022.
Jones Junior Fellow in Pure Mathematics, Fall 2020.
Outreach
Putnam exam proctor and session coordinator at Smith college, 2023-2025.
Vice President of the AMS Graduate Student Chapter for University of California, Riverside, 2021 - 2023.
Student Organizer of the UCR Topology Seminar, 2021-2022.
Graduate Recruitment Ambassador for University of California, Riverside, 2020 - 2022.
Teaching Experience, Lecturer at Smith College
MTH 370tp “Topology.” Fall 2025.
MTH 111 “Calculus 1.” Fall 2023, Fall and Spring 2024, Spring 2025
MTH 102 “Elementary Functions.” Fall 2023, Fall 2024, Fall 2025
Teaching Experience, Primary Instructor at University of California, Riverside
Topology Qualifying Exam Preparation Seminar. Summer 2021 and Summer 2022.
Math 198 "Exploring (g,f)-colorability of knots". Spring 2022. I lead a group of four students in an undergraduate research project exploring the strength of a new knot invariant called (g,f)-colorings.
Math 194 “Introduction to Geometric Group Theory”. Spring 2021. I developed a reading course for undergraduates interested in Topology. At the end of the term, the students presented a proof of the Milnor-Schwarz Lemma.
Math 31 "Applied Linear Algebra." Summer 2020.
Math 6A "Introduction to Functions / Precalculus." Spring 2023.
Teaching Experience, Primary Instructor at Ball State University
Math 125 "Quantitative Reasoning". Fall 2017, Spring 2018, Fall 2018.
Teaching Experience, Graduate Teaching Assistant
Math 144 "Introduction to Set Theory". Winter 2021 at University of California, Riverside.
Math 133 "Geometry". Spring 2021 at University of California, Riverside.
Math 131 "Linear Algebra I". Summer 2022, Spring 2020, Winter 2020, Fall 2019, Summer 2019, and Winter 2019 at University of California, Riverside.
Math 46 "Introduction to Differential Equations". Fall 2022 at University of California, Riverside.
Math 31 "Applied Linear Algebra". Fall 2020, Winter 2020, and Spring 2019 at University of California, Riverside.
Math 22 "Calculus for Business". Fall 2019, Spring 2019 at University of California, Riverside.
Math 10A "Calculus: Several Variables". Summer 2019 and Winter 2023 at University of California, Riverside.
Math 10B "Calculus: Several Variables". Winter 2021 at University of California, Riverside.
Math 9C "First Year Calculus". Winter 2020 at University of California, Riverside.
Math 9A "First Year Calculus". Fall 2022, Spring 2020, Summer 2019, and Fall 2018 at University of California, Riverside.
Math 6B "Introduction to College Mathematics for the Sciences II". Winter 2023 at University of California, Riverside.
Math 4 "Intro to College Math". Winter 2019, Fall 2018 at University of California, Riverside.