PhD in Pure Mathematics - Number Theory in Cambridge United States | Massachusetts Institute of Technology

Since antiquity, integers and prime numbers have captivated human curiosity. In modern times, the discipline has experienced remarkable progress. Wiles' 1995 proof of Fermat's Last Theorem sparked ongoing mathematical developments, including Khare and Wintenberger's recent confirmation of Serre's conjecture linking mod p Galois representations to modular forms. As one of the Clay Millennium Problems, the Riemann hypothesis belongs to analytic number theory - a field using calculus and complex analysis to study integers. Notable breakthroughs include Green and Tao's demonstration of infinitely long arithmetic progressions containing primes. The expansive Langlands Program proposes deep connections between number theory and representation theory. Practical applications emerge in computer science, particularly cryptography.

Our research group focuses on multiple areas: Galois representations, Shimura varieties, automorphic forms, lattice theory, computational methods, rational points on algebraic varieties, and K3 surface arithmetic.