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Learn Mathematics, earn certificates with free online courses from Harvard, Stanford, MIT, University of Pennsylvania and other top universities around the world. Read reviews to decide if a class is right for you.
Explore methods for proving functional inequalities in hypoelliptic diffusions, including geometric and probabilistic approaches, with applications to Langevin dynamics ergodicity.
Explore the mathematical proof linking Borel resummation of formal power series to Faddeev's quantum dilogarithm in linear difference equations.
Explore mathematical patterns in nature and their applications in neuroscience. Discover how math reveals hidden structures in the world and aids in developing medical solutions for neurological disorders.
Explore rectangular diagrams and Giroux's convex surfaces in topology, delving into advanced mathematical concepts and their applications in quantum mechanics.
Explore self-intersection of curves in surfaces and Drinfeld associators, delving into advanced mathematical concepts and their applications in quantum topology.
Explore noncommutative spectra, their applications to nonrationality questions, and potential generalizations in this advanced mathematics lecture.
Explore complex variations of Hodge structure, focusing on adapting Schmid's analysis to arbitrary polarized variations and examining key results like Hodge norm estimates and limiting mixed Hodge structures.
Explore properties and results of period mapping completions in algebraic geometry, featuring insights from renowned mathematician Philip Griffiths.
Explore holomorphic Lagrangian foliation and Gaiotto's conformal limit in this advanced mathematics lecture by UC Davis professor Motohico Mulase.
Explore the mathematical connection between ribbon graphs and Cohomological Field Theories (CohFT) in this advanced topology lecture by Olivia Dumitrescu from Central Michigan University.
Explore generalizations of classical braid groups with new crossings and relations, focusing on extended representations in virtual and welded braid groups.
Explore the fascinating connection between braids and line arrangements in mathematics, with insights from expert Moshe Cohen in this engaging lecture.
Explore the mathematical concept of braids through dance and movement, blending art and science in this innovative presentation by Nancy Scherich from ICERM.
Explore the fascinating intersection of mathematics and art through the lens of braids, uncovering their significance in both fields and their role in advancing women in mathematics.
Explore Steenbrink spectra in singularity categories, focusing on non-commutative mixed Hodge structures and dimensional properties. Gain insights into natural and mysterious appearances of this concept.
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