The 'probabilistic method' is a fundamental tool in combinatorics. The basic idea is as follows: to prove that an object (for example, graph) with certain properties exists, it suffices to prove that if the object is chosen at random, then it has the desir ...
After introducing the foundations of classical and quantum information theory, and quantum measurement, the course will address the theory and practice of digital quantum computing, covering fundamental and advanced topics such as recent quantum algorithms ...
The course aims to introduce the basic concepts and results of integer optimization with special emphasis on algorithmic problems on lattices that have proved to be important in theoretical computer science and cryptography during the past 30 years. ...
The classical distinction between polynomial time solvable and NP-hard problems is often too coarse. This course covers techniques for proving more fine-grained lower and upper bounds on complexity of computational problems. ...
Probabilistic proof system (eg PCPs and IPs) have had a tremendous impact on the theoretical computer science, and have also found practical uses. They underlie delegation of computation protocols and hardness of approximation. This course covers the found ...
This course introduces statistical field theory, and uses concepts related to phase transitions to discuss a variety of complex systems (random walks and polymers, disordered systems, combinatorial optimisation, information theory and error correcting cod ...