My advisor is Gregory Handy, and my research is based on the intersection of applied mathematics, stochastic processes, and biological systems, particularly in theoretical neuroscience.
So far, my work has focused on investigating the mechanisms shaping neuronal correlations, with an emphasis on how astrocytes and microglia, types of glial cells, impact neuronal interactions by wrapping around, or ensheathing, synapses. Glial cells are supportive cells in the central nervous system with multiple functions, such as pruning synapses, providing structural support, and regulating neurotransmission. We consider two general categories of neurons: excitatory which activate neurons within the network and inhibitory which suppress this activity. Inspired by findings from Haruwaka et al. (2024) that showed anesthesia-induced glial ensheathment of inhibitory synapses leads to neuronal hyperactivity, we are developing a multi-scale model replicating these results and predicting broader effects on neuronal dynamics (Garcia et al., 2025).
Garcia, N., Reitz, S. & Handy, G. Extending Mathematical Frameworks to Investigate Neuronal Dynamics in the Presence of Microglial Ensheathment. Bull Math Biol 87, 63 (2025). https://doi.org/10.1007/s11538-025-01438-w
Glial ensheathment of inhibitory synapses drives hyperactivity and increases correlations, Cosyne (45% acceptance rate), March 2025 (poster)
Unveiling the Impact of Glial Cells on Neuronal Dynamics: Insights from Synaptic Ensheathment, Society for Neuroscience, October 2024 (poster)
A Deep Dive Into Astrocyte Ensheathment, Topics in Mathematical Biology, UMN, April 2024 (slides)
Quasi-Explicit Calibration and Volatility Surfaces, MCFAM Seminar, UMN, November 2023 (slides)
IMA Boot Camp and X Cubed: 3D Volatility Interpolation, IMA Math-to-Industry Boot Camp, July 2023 (slides and white paper)
Algebraic Topology and Combinatorics - A Focus on Monomial Ideals, Summer Research Institute, UMN, August 2022 (slides)
The Stability of Singularity Formation in Nonlinear Wave Equations, Directed Reading Program, UCR, May 2022 (slides)
Simplicial Complexes, Directed Reading Program, UCR, May 2022 (slides)