Anabelian Geometry - Absolute Anabelian Geometry and the Reconstruction of the Base Field
This video describes one of the key features of absolute anabelian geometry. One is able to interpret the map Pi_X \to G_K just from Pi_X itself! https://twitter.com/dupuytaylor
From playlist Anabelian Geometry
Anabelian Geometry - The Section Injection
Tamagawa's 1999 IMRN paper has a nice proof. Read this paper. Twitter: https://twitter.com/dupuytaylor
From playlist Anabelian Geometry
Anabelian Geometry - part 0 - Overview of the Papers
Here we describe what papers are involved here. There are two notable mentions which we have not described. Twitter: @DupuyTaylor
From playlist Anabelian Geometry
Anabelian Geometry - Inertia and Decomposition Groups (Part 1)
We discuss the statements about the recovery of inertia and decomposition groups of cusps. We will give proofs in the number field case of some statements. Proofs for finite extensions of QQ_p appear later. Twitter: @DupuyTaylor
From playlist Anabelian Geometry
Anabelian Geometry - Kummer Classes
To functions f we associate cohomology classes. Using galois sections we can evaluate these functions. Recovering the Kummer classes of the jacobi theta function
From playlist Anabelian Geometry
Introduction to the terms locus, focus, directrix, line of symmetry, vertex, maximum and minimum
From playlist Geometry
Inertia and Decomposition Groups (part 3)
Here we do the local case. Twitter: @DupuyTaylor
From playlist Anabelian Geometry
Divine Proportions: Rational Trigonometry to Universal Geometry
I discuss my book Divine Proportions: Rational Trigonometry to Universal Geometry, which gives a novel way of thinking not only about trigonometry, but also Euclidean geometry. It also lays the ground work for a more rational and logical approach to other geometries, including hyperbolic g
From playlist MathSeminars
David Roberts, Hurwitz Belyi maps
VaNTAGe seminar, October 12, 2021 License: CC-BY-NC-SA
From playlist Belyi maps and Hurwitz spaces
Toy Ind3 - Part 03 - Anabelian Geometry and the Case of a Single Log Link
Here we briefly discuss Corollary 1.10 of Absolute Anabelian Geometry 3. This result is used in the Definition 1.1 of IUT3 which is the case of a log-link. Using this setup we are able to give a structure result (omitted in the body of IUT) that is key to deriving the log-shell upper bound
From playlist Toy Ind3
CTNT 2022 - Grothendieck’s section set and the Lawrence–Venkatesh method (by Alex Betts)
This video is one of the special guess talks or conference talks that took place during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. Note: not every special guest lecture or conference lecture was recorded. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - Conference lectures and special guest lectures
Math Talk! Taylor Dupuy, professor of mathematics, (differential) algebraic geometry and IUTT.
A conversation with Dr. Dupuy about differential algebraic geometry, the abc-conjecture and IUTT, the field with one element, Clifford algebras, and more! Dr. Dupuy's channel: https://www.youtube.com/channel/UCHWnZ1NtJ4WvE5AHmNVXziw Homepage: https://www.uvm.edu/~tdupuy/ AWS: https://
From playlist Math Talk!
Introduction to Projective Geometry (Part 1)
The first video in a series on projective geometry. We discuss the motivation for studying projective planes, and list the axioms of affine planes.
From playlist Introduction to Projective Geometry
The circle and projective homogeneous coordinates (cont.) | Universal Hyperbolic Geometry 7b
Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine
From playlist Universal Hyperbolic Geometry
Hyperbola 3D Animation | Objective conic hyperbola | Digital Learning
Hyperbola 3D Animation In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other an
From playlist Maths Topics
The p-adic Logarithm - Part 03 - Log Shells
Here are the "log-shells" which originated (I think) in Mochizuki's Topics in Absolute Anabelian Geometry 3. They can be interpreted using absolute Galois groups of local fields and appear in Mochizuki's inequality.
From playlist p-adic log