Beijing International Center for Mathematical Research Campuses

The Beijing International Center for Mathematical Research (BICMR) at Peking University offers advanced programs in pure and applied mathematics, focusing on cutting-edge research and graduate-level education. As a hub for international collaboration, BICMR emphasizes interdisciplinary approaches, integrating mathematics with physics, computer science, and economics.

Main courses cover foundational and specialized topics. Core graduate seminars include Algebraic Geometry, where students explore schemes, sheaves, and moduli spaces through rigorous proofs and applications to string theory. Number Theory courses delve into analytic methods, elliptic curves, and the Riemann Hypothesis, with hands-on projects in computational number theory using tools like SageMath.

• Differential Geometry: Studies manifolds, curvature, and Riemannian metrics, with applications to general relativity and machine learning.
• Partial Differential Equations (PDEs): Advanced analysis of elliptic, parabolic, and hyperbolic equations, including numerical solutions via finite element methods.
• Probability and Stochastic Processes: Covers martingales, Brownian motion, and stochastic differential equations, essential for financial mathematics and data science.
• Topology and Algebraic Topology: Introduces homotopy theory, cohomology, and knot theory, bridging pure math with quantum field theory.
• Mathematical Physics: Focuses on quantum mechanics, statistical mechanics, and integrable systems, fostering collaborations with physicists.

BICMR also offers workshops on Combinatorics and Graph Theory, emphasizing extremal problems and random graphs. Applied courses include Optimization and Control Theory, teaching linear programming, convex optimization, and optimal control for engineering applications. Data-driven mathematics courses integrate statistics, machine learning algorithms, and big data analysis, preparing students for AI research.

The curriculum promotes research output through thesis supervision and international exchanges. Students engage in seminars with global experts, attend conferences, and contribute to publications. BICMR's programs cultivate problem-solving skills, theoretical depth, and practical applications, producing leaders in academia and industry. With a diverse faculty from top institutions worldwide, the center ensures a vibrant learning environment. Elective modules allow customization, such as cryptography based on number theory or bioinformatics using dynamical systems. Overall, BICMR's offerings span from abstract algebra to computational modeling, totaling over 300 instructional hours per semester, equipping scholars for groundbreaking contributions in mathematics.