Courses

Rigorous introduction to computability and complexity theory, covering Turing machines, diagonalization, NP-completeness, space complexity, Savitch's theorem, and the polynomial hierarchy.

Intensive PhD-level complexity theory sequence examining circuit complexity, randomized computation, interactive proofs, PCP theorem foundations, pseudorandomness, and hardness amplification.

Research-level course developing Fourier analysis over the Boolean hypercube, hypercontractivity, noise stability, invariance principles, and applications to hardness of approximation and social choice.

Mathematical development of quantum circuits, entanglement, quantum query complexity, phase estimation, Shor's factoring algorithm, quantum channels, and quantum error correction.

Stream ciphers, DES, AES and finite-field arithmetic, block cipher modes, RSA, Diffie-Hellman key exchange, elliptic curve cryptography, hash functions, and digital signatures.

Michael Sipser's definitive course on finite automata, context-free grammars, Turing machines, decidability, reducibility, time and space complexity, NP-completeness, and interactive proofs.

Foundational MIT algorithms course covering asymptotic complexity, divide-and-conquer, hashing, balanced search trees, graph search, shortest paths, and dynamic programming.

Discrete mathematical foundations for theoretical computer science: proof techniques, well-ordering, number theory, RSA cryptography, graph theory, recurrences, generating functions, and discrete probability.

MIT's upper-level algorithms sequence advancing into divide-and-conquer FFT, amortized analysis, randomized algorithms, network flow, linear programming, NP-completeness, and approximation.

Persistent data structures, retroactive structures, geometric range queries, dynamic optimality, splay trees, van Emde Boas trees, fusion trees, cache-oblivious structures, and succinct representations.

Simons Institute research symposium investigating the algorithmic and complexity-theoretic foundations of non-convex optimization, overparameterized generalization, and statistical-computational gaps.

Essential mathematical machinery for theoretical computer science research: asymptotic tail bounds, spectral graph theory, expanders, linear and semidefinite programming duality, and Fourier analysis.

Interdisciplinary lectures exploring emergence, scaling laws, algorithmic information, network dynamics, biological computation, and collective intelligence across physical and social systems.