Michael Wibmer: Etale difference algebraic groups
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Dihedral Group (Abstract Algebra)
The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo
From playlist Abstract Algebra
The Weil-Deligne group, and Langlands parameters.
In this video exploring the local Langlands conjectures, we dive deeper into the definitions of the Langlands L group, and the definition of the Weil-Deligne group, allowing us to get a better sense of what Langlands parameters are, and their connection to Galois representations.
From playlist The local Langlands correspondence
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Abstract Algebra | The dihedral group
We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
Everett Howe, Deducing information about a curve over a finite field from its Weil polynomial
VaNTAGe Seminar, March 1, 2022 License CC-BY-NC-SA Links to some of the papers and websites mentioned in this talk are listed below Howe 2021: https://arxiv.org/abs/2110.04221 Tate: https://link.springer.com/chapter/10.1007/BFb0058807 Howe 1995: https://www.ams.org/journals/tran/1995-
From playlist Curves and abelian varieties over finite fields
Alvaro Lozano-Robledo, The distribution of ranks of elliptic curves and the minimalist conjecture
VaNTAGe seminar, on Sep 29, 2020 License: CC-BY-NC-SA. An updated version of the slides that corrects a few minor issues can be found at https://math.mit.edu/~drew/vantage/LozanoRobledoSlides.pdf
From playlist Math Talks
Christelle Vincent, Exploring angle rank using the LMFDB
VaNTAGe Seminar, February 15, 2022 License: CC-NC-BY-SA Links to some of the papers mentioned in the talk: Dupuy, Kedlaya, Roe, Vincent: https://arxiv.org/abs/2003.05380 Dupuy, Kedlaya, Zureick-Brown: https://arxiv.org/abs/2112.02455 Zarhin 1979: https://link.springer.com/article/10.100
From playlist Curves and abelian varieties over finite fields
Andrew Sutherland, Arithmetic L-functions and their Sato-Tate distributions
VaNTAGe seminar on April 28, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
David Corwin, Kim's conjecture and effective Faltings
VaNTAGe seminar, on Nov 24, 2020 License: CC-BY-NC-SA.
From playlist ICERM/AGNTC workshop updates
Valentijn Karemaker, Mass formulae for supersingular abelian varieties
VaNTAGe seminar, Jan 18, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk: Oort: https://link.springer.com/chapter/10.1007/978-3-0348-8303-0_13 Honda: https://doi.org/10.2969/jmsj/02010083 Tate: https://link.springer.com/article/10.1007/BF01404549 Tate: https
From playlist Curves and abelian varieties over finite fields
Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators
Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators A Lie group can always be considered as a group of transformations because any group can transform itself! In this lecture we replace the "geometric space" with the Lie group itself to create a new collection of generators. P
From playlist Lie Groups and Lie Algebras
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
Stefano Marseglia, Computing isomorphism classes of abelian varieties over finite fields
VaNTAGe Seminar, February 1, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk: Honda: https://doi.org/10.2969/jmsj/02010083 Tate: https://link.springer.com/article/10.1007/BF01404549 Deligne: https://eudml.org/doc/141987 Hofmann, Sircana: https://arxiv.org/ab
From playlist Curves and abelian varieties over finite fields
VaNTAGe seminar, on Sep 15, 2020 License: CC-BY-NC-SA.
From playlist Rational points on elliptic curves
Weil conjectures 4 Fermat hypersurfaces
This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. T
From playlist Algebraic geometry: extra topics
Karen Vogtmann, Lecture II - 12 February 2015
Karen Vogtmann (U. of Warwick, UK and Cornell University, USA) - Lecture II http://www.crm.sns.it/course/4037/ Automorphism groups of free groups bear similarities to both lattices in Lie groups and to surface mapping class groups. In this minicourse we will explore the cohomology of thes
From playlist Algebraic topology, geometric and combinatorial group theory - 2015
Edgar Costa, From counting points to rational curves on K3 surfaces
VaNTAGe Seminar, Jan 26, 2021
From playlist Arithmetic of K3 Surfaces