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Graduate Mathematics summaries
Every long episode from Graduate Mathematics, read in minutes: the key takeaways, the chapters, and a digest of the whole conversation.
Peter Sarnak, Summation formulae in spectral theory and number theory [2021]
Peter Sarnak discusses spectral theory and number theory, focusing on summation formulas like Poisson, Selberg trace, and explicit formulas that connect spectral data with primes and zeros.
Tangles, Bangles and Knots with John Conway [2012]
John Conway explores the mathematical concepts of tangles, bangles, and knots, revealing their complex structures and relationships.
Fractran: A Ridiculous Logical Language with John Conway [2012]
John Conway explores Fractran, a logical language illustrating the power of simple fraction-based programs to simulate computation and undecidability theories.
Peter Scholze (Universität Bonn) - Condensed Mathematics (2019)
Condensed Mathematics by Peter Scholze explores complex mathematical structures through simplified frameworks that yield profound insights.
Thin groups as monodromy groups, Part II - Jordan Ellenberg (University of Wisconsin-Madison)
This video on thin groups as monodromy groups explores the dichotomy between finite index and thin cases, emphasizing deformation dynamics.
Thin groups as monodromy groups, Part I - Jordan Ellenberg (University of Wisconsin-Madison)
In this talk on thin groups, Jordan Ellenberg discusses their relevance in algebraic geometry and monodromy groups, highlighting their applications and implications.
Apollonian circle packings via spectral methods - Hee Oh (Yale University)
Apollonian circle packings use advanced spectral methods to explore geometric configurations through modern proofs and transformations.
Finding L-Functions out of Nothing - David Farmer [2011]
David Farmer advocates studying L-functions as autonomous objects, emphasizing their axiomatic properties and computational reconstruction from functional equations.
Scott Aaronson - Complexity and computability with closed timelike curves [2018]
Exploring computability and complexity with closed timelike curves (CTCs) reveals limitations, showing CTCs enable PSPACE computation but do not solve the halting problem.
Sasaki geometry and positive curvature - Song Sun [2012]
This talk explores the connection between Sasaki geometry and positive curvature in manifolds, showing how Sasaki structures can be used to understand Kähler manifolds and their deformations.
The Hilbert--Einstein functional and the Sasaki-Futaki invariant - Eveline Legendre [2016]
This talk introduces the Hilbert--Einstein functional and its relation to Sasaki--Einstein manifolds and constant scalar curvature metrics.
Compactness of conformally compact Einstein manifolds in dimension 4 - Sun-Yung Chang [2016]
This talk explores the compactness of conformally compact Einstein manifolds in dimension 4, focusing on conditions that ensure a sequence of such manifolds remains bounded. It introduces the Fefferman-Graham metric and related analytic tools to establish this compactness.
Alex Kontorovich - On the Strong Density Conjecture for Apollonian Circle Packings [2012]
The Strong Density Conjecture for Apollonian circle packings posits that most integers satisfying local conditions will appear as curvatures. Progress involves using unipotent elements and congruence subgroups to establish density.