Research
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We study mathematical neuroscience, with particular emphasis on:

• Neural rhythms - What paces brain rhythms? Do rhythms serve functional roles?
• Brain diseases - What mechanisms support epilepsy? Can data analysis reveal precursors to Alzheimer's disease?
• Dynamical systems - What dynamical mechanisms govern neural activity?
• Data analysis - How do we quantify interacting rhythms? How do we makes sense of high-density data?
• Collaboration - How do we build successful, interdisciplinary collaborations?

Network analysis & surgical targets for epilepsy An electrode grid placed on the brain's surface records the voltage activity from a sampling of spatial locations. How do we make sense of this multivariate data? One technique is to compute correlations between the time series and infer functional connections between separate locations. Analyzing the resulting functional networks may suggest possible theraputic targets for epilepsy. Paper: Emergent network topology at seizure onset in humans

Purkinje cells & torus canards Usually, we use mathematics to study biological systems. But sometimes our analysis of a biological systems motivates our study of mathematics. For example, Purkinje cells exhibit fast spiking activity whose amplitude envelope modulates slowly in time. We model these slow-fast dynamics as a system of ordinary differential equations representing the voltage and some intrinsic currents of a Purkinje cell. We find in the biophysical model a surprising type of dynamical behavior: torus canards. Paper: New dynamics in cerebellar Purkinje cells: torus canards