## Research Interests

My current mathematical interests are in the intersection of geometry and stochastic analysis. Recently I've beeen working on using coupling to prove functional inequalities. My undergraduate research was in Coarse Geometry. Coarse Geometry is the study of metric spaces from a large scale perspective rather than the small scale perspective as done in topology. Coarse Geometry was found useful in obtaining partial results to the Novikov Conjecture and the Baum–Connes Conjecture.

## Papers

Sayan Banerjee, Maria Gordina, Phanuel Mariano,*Coupling in the Heisenberg group and its applications to gradient estimates*.(2016) arXiv

Phanuel Mariano,

*On the Coarse Geometry of L*,

^{p}**Rose-Hulman Undergraduate Math Journal**Vol. 14 , No. 2 (2013)

## Talks

**UConn Sigma Seminar.**Solving differential equations with probability. Spring 2017**Seminar in Stochastic Processes.**University of Virginia. Functional inequalities of hypoelliptic operators using coupling. Poster. Spring 2017**Fifteenth Northeast Probability Seminar.**Coupling on the Heisenberg group and its applications to gradient estimates. Fall 2016**UConn Analysis Learning Seminar.**Probabilistic Techniques in Analysis. Fall 2016**UConn General Exam.**Gradient Estimates on Manifolds Using Coupling for Diffusion Processes. Spring 2016**UConn Sigma Seminar.**Coarse Geometry. Fall 2014**UConn Math Club Talk.**The volume of the unit ball in*n*dimensions. Spring 2014**JMM – AMS Special Session.**On the Coarse Geometry of*L*: A Course Equivalence. Winter 2013^{p}