Compactness of Sequences of Warped Product Length Spaces, B. Allen, B. Sanchez, and Y. Torres, Journal of Topology and Analysis (2025) (arxiv) (ref)
Bryan Sanchez and Yahaira Torres took my MAT 320 Analysis I class in the Fall of 2023 and my MAT 321 Analysis II class in the Spring of 2024. They worked with myself in the Summer of 2024 and produced the paper cited above. They gave a talk on this research to the Lehman College mathematics department on October 23, 2024.
Harry Pacheco was chosen to work with myself as part of the inaugural 2024-2025 Lehman College CUNY Immersive Research Experience (CIRE). We are studying the textbook An Invitation to Model Theory by Jonathan Kirby and will produce a research article exploring Complete Ordered Fields versus Real Closed Fields as a way of contrasting first order versus second order logic.
Preston Blake, Bernardo Falcao, Lewis Luis, Harry Pacheco, and Bryan Sanchez will be working on research with me during the Summer of 2025 exploring sequences of metrics conformal to the Euclidean metric. The goal is to understand the minimal hypotheses necessary on a sequence to conclude Lipschitz bounds and to provide examples showing the sharpness of the conditions imposed. The goal will be to write up our findings by the end of the summer, submit for publication, and present to the Lehman math department.
Bernardo Falcao is doing his Lehman Scholars Program Honors thesis with me where we are reading and discussing Gödel's Proof by Ernest Nagel and James R. Newman. Bernardo will write his capstone paper on the effort to establish foundations for math in the early twentieth century.
CDT Reilly Dosh, Topological Data Analysis Applied to Time-Series Data, Fall 2016 and Spring 2017, Co-advised with Dr. Dungan
CDT Zachary Riggenbach, Geometric Analysis Applied to the Physics of Microdroplets, Fall 2017 and Spring 2018, Co-advised with LTC Watts and MAJ Hood
SCUDEM Differential Equations Modeling Competition Oct. 9-14, 2017
MCM/ICM Modeling Competition February 8-12 2018