Ravi Montenegro

Spring 2013 Classes

Summer 2013 Classes

Graduate Coordinator

From July 2013 - June 2014 I will be on sabbatical at Kyushu University and the University of Auckland. During that period Professor Steven Pennell will be acting Graduate Coordinator. You are still welcome to contact me, but Professor Pennell will make admissions decisions for new applicants.

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:

[UMass Lowell] [UMass Lowell Math Department]
Ravi Montenegro (ravi_montenegro@uml.edu)