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Research Interests

Last modified: August 16, 2018

I am a mathematician. I am currently working on problems in two somewhat related research areas. On the theoretical side, my area of research is algebraic combinatorics. On the applied side, I am also working on combinatorial aspects of cryptography. This latter work is funded by the National Science Foundation.

As of August 2018, my research in combinatorics is supported through a grant from the United States National Science Foundation. This generous support is gratefully acknowledged.

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Combinatorial Aspects of Cryptography

My interests in cryptography deal mainly with combinatorial and other mathematical structures lying beneath various cryptographic protocols. On the algorithmic side, I work on these issues with Dr. Berk Sunar in the Department of Electrical and Computer Engineering at WPI.

I currently supervise two graduate students working on these problems.

Some topics of interest:

In the optimal years, I help organize a Cryptography Seminar which brings world leaders in these research areas to WPI each term.

Algebraic Combinatorics

I work mostly with association schemes. These can be viewed as a generalization of groups or as a generalization of distance-regular graphs. I am also interested in error-correcting codes and combinatorial designs. The theory of association schemes (and distance-regular graphs) provides an algebraic approach to codes and designs and this approach has been very successful over the past thirty years.

My most recent work aims to build a theory of cometric association schemes and to investigate applications related to these.

Applications that compel me, aside from cybersecurity, include quantum information theory, error-correcting codes, quasi-Monte Carlo methods, and other strange designs.

Delsarte's Thesis

The thesis of Philippe Delsarte played an important role in establishing a connection between association schemes and the subjects of error-correcting codes and combinatorial designs. It was published in 1973 as an entire volume of Philips Research Reports Supplements.

Here are my papers on these subjects.

My other research interests include: theoretical computer science; telecommunications; graph theory; pure mathematics.

A recent curriculum vita can be found here in PostScript.

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