Research

Publications
Research Interests
  • Theoretical Neuroscience
  • Dynamical Systems
  • Network Science
  • Mathematical Biology
  • Numerical Methods
  • Image Processing and Compressive Sensing
Selected Presentations
  • SIAM Conference on Life Sciences 2018: A Signal Processing Perspective on the Role of Receptive Field Structure in Encoding Natural Scenes and Illusory Images
  • International Conference on Applied Mathematics and Computational Neuroscience 2018: Reconstruction of Sparse Connectivity in Neuronal Networks Using Compressive Sensing of Network Dynamics
  • AMS Spring Central Sectional Meeting 2018: The Role of Neuronal Network Structure in Encoding Natural and Non-Natural Scenes
  • Organization for Computational Neuroscience Annual Meeting 2017: The Role of the Receptive Field Structure in Neuronal Compressive Sensing Signal Processing
  • SIAM Conference on Applications of Dynamical Systems 2017: The Role of Localization and Center-Surround Structure in Compressive Sensory Signal Processing
  • SIAM Conference on Nonlinear Waves and Coherent Structures 2016: Improved Compressive Sensing Signal Reconstruction via Localized Random Sampling
  • SIAM Conference on Applied Mathematics Education 2016: Musings on Mathematical Modeling: Reflections on an Upper-Level Undergraduate Course
  • SIAM Conference on Life Sciences 2016: Compressive Sensing Reconstruction of Feed-Forward Connectivity in Pulse-Coupled Nonlinear Neuronal Networks
  • Bryn Mawr–Haverford College Colloquium 2016: Compressed Coding in Sensory Systems: From Sparse Stimuli to Network Structure
  • SIAM Conference on Applications of Dynamical Systems 2015: Reconstruction of Structural Connectivity in Neuronal Networks Using Compressive Sensing of Network Dynamics
  • RPI Mathematical Sciences Colloquium 2015: Sparsity, Compression, and Complexity: Fundamental Organizing Features in the Brain
  • IMACS 2015: Efficient Reconstruction of Structural Connectivity From Neuronal Dynamics
  • JMM 2015: Reconstruction of Structural Connectivity in Sparsely-Connected Neuronal Networks Using Compressive Sensing
  • Courant Computational Biology Colloquium 2014: A Novel Characterization of Amalgamated Networks in Natural Systems Using Sparse and Low-Rank Optimization
  • SIAM Conference on Life Sciences 2014: Novel Characterization of Brain Networks Through Low-Rank Network Decomposition
  • Sino-French International Workshop on Computational Neuroscience 2014: Compressive Sensing in Sensory Systems
  • Peking University Invited Lecture 2014: Input Data Recovery Via Compressive Sensing of Time-Evolving Networks
  • RPI Mathematical Sciences Colloquium 2014: A Novel Characterization of Amalgamated Networks in Natural Systems
  • NYUAD Annual Research Conference 2014: Sparsity and Compressed Coding in Sensory Systems
  • Courant Biomathematics Colloquium 2013: Sparsity and Compressed Coding in Sensory Systems
  • IMACS 2013: Data Compression in Sensory Processing
  • JMM 2013: Is Our Sensing Compressed?
  • SIAM Conference on Life Sciences 2012: Data Compression and Sparsity in the Retina
  • AIMS Conference on Dynamical Systems 2012: Compressed Sensing in Retinal Image Processing
  • Applied Math Days 2012: Compressed Sensing in Retinal Image Processing
  • New York Conference on Applied Mathematics 2011: Neuronal Dynamics Subject to Additional Slow Ionic Currents
  • SIAM Annual Meeting 2010: A Comparison of Bifurcations for Neuronal Models with Slow Ionic Currents
Organized Conference Sessions
  • SIAM Conference on Life Sciences 2018: Information Processing in Neuronal Networks
  • SIAM Conference on Applications of Dynamical Systems 2017: The Dynamics and Function of Neuronal Networks
  • SIAM Conference on Nonlinear Waves and Coherent Structures 2016: Coherent Structures and Nonlinear Dynamics in Neuronal Networks
  • SIAM Conference on Life Sciences 2016: The Dynamics and Structure of Neuronal Networks
  • SIAM Conference on Applications of Dynamical Systems 2015: The Dynamics and Computation of Neuronal Networks
  • JMM 2015: AMS Session on Mathematical Biology IV
  • SIAM Conference on Life Sciences 2014: Dynamics and Connectivity of Complex Networks in the Brain
About My Research
    My research interests in applied mathematics give me the opportunity to study a wide array of fascinating scientific problems. A central thread of my work is characterizing the relationship between the structure of a network and its function, particularly in the context of high dimensional systems with nonlinear dynamics. Currently, I mostly find myself involved in the exciting field of theoretical neuroscience. Though the brain is a fundamental component of human existence, it still remains one of the most mysterious and captivating biological systems. My research uses new mathematical approaches to investigate the neuronal computations underlying sensory processing and the role of neuronal network connectivity in facilitating brain function. While much of my work is motivated by experimental findings, mathematical techniques prove invaluable in exploring novel theories currently impossible to verify experimentally and also crucial in the interpretation of neuroscientific data. Interestingly, much of this research has raised important theoretical questions in other fields. So, I also investigate intriguing problems in the realms of network science and signal processing. This flexibility to explore diverse research topics is one of the features uniquely remarkable about being an applied mathematician.

    Additional insights regarding my research are highlighted in a two-part interview published in The Daily Gazette.

    If you are an undergraduate student at Swarthmore interested in applying mathematics to understand the mechanisms underlying computation in the brain, please feel free to contact me. Preferred prerequisites include a background in differential equations and computer science.