# Ravi Montenegro

### Course Web Pages

- All of my course web pages are now maintained on Blackboard.

### Graduate Coordinator

I am the graduate coordinator for the mathematics department. If you have any questions about our program then please feel free to contact me.

### Research

My research is in Mixing times of finite Markov chains (random walks), analysis of randomized algorithms, geometric bounds on eigenvalues, and geometric isoperimetric inequalities.

What is the "Mixing time of a random walk"? Roughly speaking it is the number of steps required for a random process to get completely lost. Perhaps the most intuitive example is the question "How many shuffles does it take to mix a deck of cards when shuffling by ______ method?" Many algorithms can be characterized as implementing a random walk, or an approximation of a random walk. Such algorithms can show up in unexpected places. For instance, we have recently given the first rigorous proofs that two methods for code-breaking -- Pollard's Rho and Kangaroo methods for Discrete Logarithm -- are indeed as fast as Computer Scientists have believed. This shows that a clever cryptographer using a Discrete Log based cryptosystem cannot choose a special group on which these methods will break the code more slowly than expected.

For more particulars please see my research papers (publications, dissertation, etc.).

### Contact Info:

- Office : Olney 428-E
- Office Phone : 978-934-2442
- Mailing address :

*Ravi Montenegro*

*Department of Mathematical Sciences*

*University of Massachusetts Lowell*

*1 University Avenue*

*Lowell, MA 01854*

Ravi Montenegro (ravi_montenegro@uml.edu)