Education
Ph.D. University of California, Riverside, in progress, expected Spring 2024
Topic: Stable subgroups and hyperbolic boundary generalizations
M.S. Ball State University, Mathematics, 2018
Topic: Generalized covering space theory
B.S. University of California, Davis, Mathematics, 2016
Publications
J. Garcia, "Characterizations of Stability via Morse Limit Sets." Preprint availible (arXiv:2309.09135 .)
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
"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
Riverside Workshop on Geometric Group Theory, Riverside, California, March 2023.
World of GroupCraft II, virtual, September 2022.
USTARS, virtually at ICERM, April 2021.
Attended Conferences
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
Organizer for WIMIN 2023: Women in Mathematics in New England, September 2023.
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 111 “Calculus 1.” Fall 2023
MTH 102 “Elementary Functions.” Fall 2023
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.