source: Wikipedia

Topological data analysis (TDA) is a subfield of algebraic topology whose application to areas of study outside mathematics is becoming more and more common. Two such areas of interest to me are neuroscience and computer science. In neuroscience, TDA has been applied to EEG signals, fMRI data and connectomes to study both implicit and explicit topological structures of brain states and function. In computer science, specifically in the fields of machine learning and networks, TDA has been used to both take the topology of the input data into account in order to inform models, as well as to incorporate topological information directly into the design of models. TDA helps us extract topological features from the data and use this information to better understand and learn from the data, and along with statistical tools and approaches, we can discuss the significance of such features. My research will focus on answering important structural questions about how both biological and artificial neural networks function through the study of topological features and their statistical significance.

Past Presentations on Existing Literature

1. Using Topological Data Analysis for Insights into Biological and Artificial Neural Networks
2. Topological Data Analysis (TDA) and Bayesian Classification of Brain States
3. Modeling Stochastic Processes in Ecology
4. Pirotta et al: State-space modelling of the flight behaviour of a soaring bird provides new insights to migratory strategies
5. The Effects of Being Caught: How Fisheries Affect Oceanic Whitetip Sharks
6. The (Markov) Hidden Connection: Quantifying Neuronal Spikes and Forest Fires (with Jacob Pennington)
7. Cui et al.: Paxos Made Transparent: presenting CRANE, an SMR system to replicate general server programs