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.
I am currently focusing on neurons located in Layer 1 (L1) of the auditory cortex, namely inhibitory L1 NDNF interneurons, where inhibitory neurons suppress activity caused by excitatory neurons. NDNF neurons are under-studied; typically studies focus on neurons in Layer 2/3 of the cortex. This is despite evidence that NDNF neurons play an important role in top-down regulation and are strongly enhanced when an animal is aroused (Hartung et. al., 2024). Thus, we investigate these neurons by building a rate-based model that incorporates them with their unique weak cross-connections between two separate populations of NDNF neurons. Our findings suggest that, depending on synaptic strengths, the sign of the spike correlation between these two populations can be altered. Further, we compare these network changes with NDNF's major inhibitory competitor: SST interneurons.
My first major project 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 developed 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
Correlated Variability in Recurrent Networks of Competing Inhibitory Subtypes, July 2026 (slides)
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)