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Linear algebra, real and complex analysis, topology, differential geometry, probability, combinatorics, and number theory.
Structural connections linking subfields, mathematical foundations, and courses across disciplines.
Institute for Advanced Study · Jonathan Pila, Jacob Tsimerman & Thomas Scanlon
This course explores advanced topics in algebraic geometry, including Hodge theory and o-minimality, which are fundamental to modern research in topology and geometry, particularly in understanding complex manifolds.
Michael J. Hopkins · Harvard University
This lecture celebrates a giant in algebraic topology, directly extending the subfield's core concepts by exploring advanced topics like manifolds, homotopy theory, and rational homotopy theory, central to Sullivan's work.