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, 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. My research so far can be divided into three separate projects (that have produced the following three papers).

My advisor is Dr. Leonid Koralov .### Publications

- 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

- P. Hebbar, L. Koralov, J. Nolen, The asymptotics of solutions to parabolic PDEs with periodic coefficients, with applications to branching in periodic media, preprint.

- P. Hebbar, K. Fernando, Higher order asymptotics for large deviations, arXiv:1811.06793 [math.PR].

- "Higher Order Asymptotics for Large Deviations", Conference -- Perturbation Techniques in Stochastic Analysis and Its Applications , CIRM, France (March 14th 2019).
- "Higher Order Asymptotics for Large Deviations", Probability Seminar , University of Washington, USA (March 4th 2019).
- "Higher Order Asymptotics for Large Deviations", Probability/Math Finance Seminar , Carnegie Mellon University, USA (January 28th 2019).
- "Higher Order Asymptotics for Large Deviations", Probability Seminar , Boston University, USA (January 24th 2019).
- "Higher Order Asymptotics for Large Deviations", Probability Seminar, Pennsylvania State University, USA (January 11th 2019).
- "Asymptotics of some classes of SDE's in the Large Deviation Domain", Poster talk at the Seminar on Stochastic Processes , Brown University, Providence, USA (May 10, 2018).
- "Multi-type branching processes with time-dependent branching rates", 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"(pdf) , Workshop on Dynamical Systems and Related Topics, University of Maryland, College Park, USA (March 31 - April 2, 2017).