# Math

## Research Interests

Stationary random measures, point processes, point-shifts, random walks, probability, measure theory.

## Publications

*Coupling and Unimodularity in Stationary Settings*, (Ph.D. Thesis)

, *Doeblin Trees*, (preprint)

, *Exact Coupling of Random Walks on Polish Groups*, Journal of Theoretical Probability (2018)

, *Point-shifts of Point Processes on Topological Groups*, (preprint)

, *Resolving the one-dimensional autonomous flow-free explosion problem*, SIAM Undergrad. Res. Online (2014)

, *Resolving the one-dimensional autonomous flow-free explosion problem*, Carnegie Mellon University (2014)- my Master's thesis, written under the guidance of Gautam Iyer

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## Talks Given

*Doeblin Trees*, University of Texas (2019)

, *Markov Eternal Family Trees*, University of Texas (2017)

, *Propp and Wilson Coupling from the Past*, University of Texas (2017)- Reference:
*Perfect simulation and backward coupling*
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, - Reference:
*Exact Coupling of Random Walks on Polish Groups*, University of Texas (2017)

, *On the Liouville Property of Stationary Random Graphs*, University of Texas (2017)

, *Threshold Dynamics with Applications to Image Processing*, University of Texas (2016)

, *An Introduction to Stationary Random Measures on Topological Groups with Focus on Point-shift Foliations*, University of Texas (2016)- .pdf (reference on point-shifts)
- .pdf (reference on stationary random measures on topological groups)

, *An Elementary Proof of Rademacher's Theorem*, University of Texas (2015)

, *A Brief Introduction to Processes of Flats*, University of Texas (2015)

, *Existence for the Dirichlet Problem in Zaremba Domains*, University of Texas (2015)

, *Arrow's Theorem by Boolean Fourier Analysis*, University of Texas (2015)

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