文章 发现 ms@ms.lt +370 607 27 665 My work is in the Public Domain for all to share freely. 读物 书 影片 维基百科 Software Upload Ideas to Understand What is a perspective? Fiber bundles, vector bundles. 影片: Daniel Chan. Vector bundles Algebraic geometry. Sheaves. Classical algebraic geometry 影片: Algebraic varieties Max Planck Grothendieck. Elements of Algebraic Geometry I 影片: Algebraic Geometry in the Time of Co-Vid 影片: Taylor Dupuy. Stacks. Dimension 维基百科: N-sphere Representation of topos Notes: Olivia Caramello. An Introduction to Grothendieck toposes 影片: Part 2 of 4 What is composition of perspectives? Alexander Campbell. An Exegesis of Yoneda Structures. Adjoint functors Yoneda Lemma and Lenses String diagrams Higher category theory Emily Riehl. ∞-Category Theory for Undergraduates. What is a division of everything? Chain complexes, homology and cohomology Short and long exact sequences 维基百科: Exact sequence - examples: Integers modulo two {$0\rightarrow L^2 \xrightarrow{grad} \mathbb{H}^3 \xrightarrow{curl} \mathbb{H}^3 \xrightarrow{div} L^2 \rightarrow 0$} 维基百科: Gradient, 维基百科: Curl, 维基百科: Divergence Infinite three-cycle Understand the canonical way of transforming a short exact sequence to a long exact sequence. See: 维基百科: Derived functor 维基百科: Zig-zag lemma 维基百科: Mayer–Vietoris_sequence Supplement: The Long Exact Homology Sequence and Applications What is the eight-cycle? Topology in Condensed Matter Quadratic forms Clifford algebras Wedderburn theorem on division algebras 维基百科: Hopf fibration Understand it. 维基百科: Hopf invariant and Adams's theorem. What is the eightfold way? What is a geometry? 影片: Introduction to Complex Analysis Terrence Tao courses Complex analysis, real analysis, linear algebra, random matrices, topology, probability. 维基百科: Linear fractional transformation 维基百科: Modular group 维基百科: Modular form 书: Ramūnas Garunkštis. Modulinių formų įvadas. Geometries Differences between affine, projective, conformal, symplectic geometry. Classical Lie groups. What is going beyond oneself? Study finite fields and interpret {$F^{1^n}$}. Study points at infinity and how they relate to coordinate systems. What is the foursome? Universality MIT Course. Random Matrix Theory and Its Applications. What are the four geometries? Relate quaternions and Mobius transformations. 影片: 3 Blue 1 Brown. Visualizing quaternions (4d numbers) with stereographic projection Hopf algebras and real forms Grinberg, Reiner. Hopf algebras in combinatorics. 影片: Federico Ardila. Hopf Algebras and Combinatorics, Index and Overview by Sara Billey Lie theory What is duality? Representation theory 影片: Representation Theory Max Planck What is measurement? Quantum physics What is entropy? Ergodic theory 影片: Ergodic theory Max Planck - Tatjana Eisner Walks How to think of sequences, hierarchies and networks? 影片: John Baez. Mathematics in the 21st Century How to think of automata? Daniel Murfet's references on computation
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