Foundations and Algorithms

The Foundations and Algorithms group investigates mathematical underpinnings of computing, with the goal of designing algorithms and computational approaches to problems of engineering, social and natural sciences, medicine and healthcare. The overarching goal of the group is to build a mathematically sound foundation for the design of modern computing systems, and to develop analytic frameworks for their correctness, performance, reliability and security. Current research topics include design of efficient data structures and algorithms, characterizing the complexity of computational problems, exploring the fundamental limits of quantum computers, and design of secure and scalable cryptographic protocols.

Affilated Labs: 
Computer Security Lab

Faculty

Wim van Dam's research focuses on the theory of quantum computation and quantum communication. His main interest is in the development of new quantum algorithms that give an exponential speed-up when compared with traditional, classical algorithms.

Bijective and enumerative combinatorics, algorithms, computational geometry. 

Prof. Gilbert’s principal research contributions have been in algorithms and software for combinatorial and numerical problems. He has done fundamental work in sparse matrix techniques; he was a primary architect and developer of Matlab’s sparse matrix capability and of the SuperLU solver library

The main research contributions of Professor Gonzalez include the development of exact and approximation algorithms, and establishing complexity results for a wide range of problems arising in several different application areas.

My research interests lie in cryptography and its interplay with other areas in computer science, including theory of computing, algorithm design, and security.

The use of geometry and graph theory, as conceptual tools and an algorithmic lens, has proved invaluable in a number of scientific and engineering disciplines.

I work on cryptography: using rigorous mathematical foundations, I develop new techniques to protect privacy and integrity of information. I also explore the connections between cryptography and areas such as complexity theory, information theory, and computer security at large.