Research

The main focus of my research has been asymptotic problems arising from Branching Processes, Branching Diffusions and related Dynamical Systems. The central theme in most of my work is the use of spectral theory in addition with techniques from probability, stochastic differential equations, parabolic partial differential equations, homogenization theory and dynamical systems to obtain the asymptotics of these stochastic processes that are valid up-to the domain of large deviations.

Publications

Preprints:

• P. Hebbar, L. Koralov "Distribution of particles at and near the front in supercritical branching Brownian motion with compactly supported branching" (2025).

• L. Ajax, B. Durham, P. Hebbar, C. Johnston, M. Zhang "Inhomogeneous Branching Random Walks: Incorporating Genealogy and Density Effects" (2025) * in collaboration with undergraduate students. 

Published Journal Articles

• P. Hebbar, K. Fernando, Higher order asymptotics for large deviations -- Part II,  Stochastics and Dynamics, Vol. 21, No. 05, 2150025, (2021)

• P. Hebbar, L. Koralov, J. Nolen,  Asymptotic behavior of branching diffusion processes in periodic media, Electronic Journal of Probability, vol. 25, paper no. 126, 40 pp doi:10.1214/20-EJP527 (2020)

•  P. Hebbar, K. Fernando, Higher order asymptotics for large deviations -- Part I, Asymptotic Analysis, vol. Pre-press, pp. 1-39, (2020). doi:10.3233/ASY-201602.

• D.Dolgopyat, P. Hebbar, L. Koralov, M. Perlman, "Multi-type branching processes with time-dependent branching rates", Journal of Applied Probability, 55(3), 701-727. doi:10.1017/jpr.2018.46, (2018)

Ph.D Dissertation

• Branching diffusion processes in periodic media, Thesis, August 2019.

Book Reviews

•  Hebbar P. "Testing the waters of differential equations", Physics Today, Volume 73, Issue 7, Page 54 (2020). doi.org/10.1063/PT.3.4525

Talks, Conferences

• • 2025 Progress in Discrete and Continuous Probability Conference, Schenectady, July 23rd, 2025.

  • Emerging Connections between Reaction-Diffusion, Branching Processes, and Biology (Conference) Banff, Canada, May 18th -23rd 2025.

  • Colloquium, Carleton College, Northfield MN, April 30th 2024.

  • Probability and Analysis Seminar, Iowa State University, Ames IA, March 29th, 2023.

  • Probability and Statistics Seminar, Lehigh University, Bethlehem, March 24th, 2023.

  • Probability Seminar, Louisiana State University, March 20th, 2023.

  • Workshop on Reaction Diffusion Equations, University of Maryland, College Park, March 9th, 2023.

  • 2022 Union College Mathematics Conference, Session on Stochastic Analysis and Applications, Schenectady, June 4th, 2022.

  • Colloquium, Rutgers University - Camden, November 12th, 2021.

  • Colloquium, North Carolina Central University (NCCU), October 26th, 2021.

  • Computational & Applied Mathematics Seminar, University of North Carolina Charlotte (UNCC), October 15th, 2021.

  • SURE: Speakers and Undergraduate Research Engagement, Virginia Tech, USA, October 11th, 2021.

  • CRM-ISM Probability Seminar, Centre de Recherches Mathematiques (CRM) Montreal, Canada, November 4th, 2020.

  • Probability and Statistical Physics Seminar, University of Chicago, October 23nd, 2020.

  • Probability Seminar, University of Virginia, USA, February 5th, 2020.

  • National Webinar on Galton-Watson Processes, MES Garware College, Pune, India, October 5th, 2020. (slides, video excerpt)

  • Probability  Seminar, Duke University, USA, September 26th, 2019.

  •  Conference -- Perturbation Techniques in Stochastic Analysis and Its Applications, CIRM, France, March 14th 2019.

  • Probability Seminar , University of Washington, USA (March 4th 2019).

  • Probability/Math Finance Seminar , Carnegie Mellon University, USA (January 28th 2019).

  • Probability Seminar , Boston University, USA (January 24th 2019).

  • Probability Seminar, Pennsylvania State University, USA (January 11th 2019).

  • Poster talk at the Seminar on Stochastic Processes , Brown University, Providence, USA (May 10, 2018). 

  • GWU-SIAM Conference on Applied Mathematics, George Washington University, Washington D.C, USA (April 29, 2017). 

  • "Multi-type branching processes with time-dependent branching rates" , Workshop on Dynamical Systems and Related Topics, University of Maryland, College Park, USA (March 31 - April 2, 2017) (slides).