About

My research interests include dynamical systems, mathematical and computational neuroscience, multiple timescale dynamics, network dynamics and homeostasis. I am particularly interested in modeling and analyzing intrinsic neural dynamics in central pattern generators, brain rhythms associated with cognition, and sensory feedback control in complex adaptive biological systems, using geometric singular perturbation theory, bifurcation analysis, mathematical modeling and numerical simulations. In addition,  I also explore the role that network structure plays in determining what dynamics are possible within a system. 

Applications of interest include neural control of breathing and disorders such as opioid-induced respiratory depression, motor control in food-swallowing behavior in the sea slug Aplysia, neuromodulation, role of astrocytes in chemosensory control of respiration, speech perception, and homeostasis in biochemical networks.   

Upcoming Activities and Talks

• October 29, 2024, invited talk at Mathematical Biology and Deep Learning Seminar, Beijing Institute of Mathematical Sciences and Applications (BIMSA)

• November 5, 2024, invited talk at Centre for Mathematical Medicine and Biology Seminar, University of Nottingham, UK

• November 15, 2024, invited talk at Mathematics Colloquium, the Florida State University, Tallahassee, Florida

• November 19, 2024, invited talk at Applied Mathematics Seminar, UMass Amherst, Amherst, MA

• May 11-15, 2025, SIAM Conference on Applications of Dynamical Systems, Denver, Colorado

• July 21-25, 2025,  Mathematical Congress of the Americas, Miami, Florida

Selected Past Activities

• August 8-9, 2024

  • Co-organized Mathematical Biosciences Workshop at Penn State, University Park, PA (with W. Hao, H. Jain and G. Rempala)

  • Talk at Mathematical Biosciences Workshop

• August 5-6, 2024, Swartz Foundation Meeting, University of Washington, Seattle, WA

• June 30 - July 5, 2024, SMB Annual Meeting, Seoul, Republic of Korea

  • Co-organized a minisymposium "Neuronal network dynamics unveiled with analysis" (with C. Ly)

  • Talk at SMB Annual Meeting

• Sep 18-22 2023, invited talk at ICERM Workshop on Mathematical Challenges in Neuronal Network Dynamics

• Aug 7-11th 2023, AIM SQuaRE for research collaboration in Caltech, Pasadena, CA 

• July 16-21th 2023, co-organized a two-part minisymposium "Uncovering activity patterns, oscillations and other key dynamics of neuronal (and other) networks" at the SMB Annual Meeting (with C. Ly, J. Best, and P. Pyzza)

• July 13-15th 2023, co-organized a 3-day workshop Dynamical Systems in the Life Sciences (with H. Jain and G. Rempala)

• June 2nd 2023, talk at the Institute for Mathematical Sciences at Renmin University of China, Beijing, China

• May 14-18th 2023, talk in the minisymposium on Phase-Based Reduction of Limit Cycle Oscillators at the SIAM Conference on Applications of Dynamical Systems

• July 2022,  MS talk titled "Homeostasis in Input-Output Networks, with Applications to Biological Systems" at SIAM Conference on the Life Sciences

• June 2021, MS talk titled "Timing and shape responses of limit cycle with hard boundaries: application to neuromechanical control problems" at International Conference on Mathematical Neuroscience

• June 2021, SMB Annual Meeting 

Co-organized a two-part minisymposium titled "Biological Rhythms and Motor Control" (with P. Thomas)

MS talk titled "Shape and timing: using variational analysis to dissect motor robustness"

• May 2021 SIAM Conference on Applications of Dynamical Systems

Co-organized a three-part minisymposium titled "Homeostasis in Networks" (with M. Golubitsky)

• June 5, 2020 SIAM Conference on the Life Sciences 

     MS talk titled "Complex Bursting Patterns in an Embryonic Respiratory Neuron Model"  

     Co-organized CAMBAM Zoomposium titled "Multiple Timescales in Neuronal and Other Systems" (with J Rubin) 

     -->Recordings available on the CRM YouTube channel: https://www.youtube.com/watch?v=eODSNQoCbL0