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
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
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, ... 1
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Imprimitive irreducible representations of finite quasisimple groups by Gerhard Hiss
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Zinovy Reichstein: The rationality problem for forms of moduli spaces of stable marked curves
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
Mathieu ANEL - Toposes are commutative rings
Abstract: In this talk, we shall develop the point of view comparing (higher) toposes to commutative rings. We shall then see how the corresponding integral and differential calculus are related respectively to Verdier duality and Goodwillie calculus of functors.
From playlist Topos à l'IHES
Aurel PAGE - Cohomology of arithmetic groups and number theory: geometric, ... 1
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Francis Brown - 2/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)
In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of
From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, ... 2
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-
From playlist Abstract Algebra
Richard Hain - 4/4 Universal mixed elliptic motives
Prof. Richard HAIN (Duke University, Durham, USA) Universal mixed elliptic motives are certain local systems over a modular curve that are endowed with additional structure, such as that of a variation of mixed Hodge structure. They form a tannakian category. The coordinate ring of its fu
From playlist Richard Hain - Universal mixed elliptic motives
Richard Hain - 3/4 Universal mixed elliptic motives
Prof. Richard HAIN (Duke University, Durham, USA) Universal mixed elliptic motives are certain local systems over a modular curve that are endowed with additional structure, such as that of a variation of mixed Hodge structure. They form a tannakian category. The coordinate ring of its fu
From playlist Richard Hain - Universal mixed elliptic motives
Off-shell Partition Functions in 3d Gravity - Lorenz Eberhardt
IAS Physics Group Meeting Topic: Off-shell Partition Functions in 3d Gravity Speaker: Lorenz Eberhardt Affiliation: Member, School of Natural Sciences, IAS Date: May 25, 2022 I will discuss partition functions in three-dimensional quantum gravity with negative cosmological constant in ca
From playlist Physics Group Meeting
Peter PATZT - High dimensional cohomology of SL_n(Z) and its principal congruence subgroups 4
Group cohomology of arithmetic groups is ubiquitous in the study of arithmetic K-theory and algebraic number theory. Rationally, SL_n(Z) and its finite index subgroups don't have cohomology above dimension n choose 2. Using Borel-Serre duality, one has access to the high dimensions. Church
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Cohomology and arithmetic of some mapping spaces - Oishee Banerjee
Members' Colloquium Topic: Cohomology and arithmetic of some mapping spaces Speaker: Oishee Banerjee Affiliation: Member, School of Mathematics Date: Date: April 10, 2023 How do we describe the topology of the space of all nonconstant holomorphic (respectively, algebraic) maps F: X--- g
From playlist Mathematics
https://www.math.ias.edu/files/media/agenda.pdf More videos on http://video.ias.edu
From playlist Mathematics
Normal Subgroups and Quotient Groups (aka Factor Groups) - Abstract Algebra
Normal subgroups are a powerful tool for creating factor groups (also called quotient groups). In this video we introduce the concept of a coset, talk about which subgroups are “normal” subgroups, and show when the collection of cosets can be treated as a group of their own. As a motivat
From playlist Abstract Algebra
Frédéric Barbaresco : Sympletic and Poly-Sypectic Model of Souriau Lie-Groups Thermodynamics : ...
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 30, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
Francis Brown - 1/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)
In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of
From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)
Peter PATZT - High dimensional cohomology of SL_n(Z) and its principal congruence subgroups 1
Group cohomology of arithmetic groups is ubiquitous in the study of arithmetic K-theory and algebraic number theory. Rationally, SL_n(Z) and its finite index subgroups don't have cohomology above dimension n choose 2. Using Borel-Serre duality, one has access to the high dimensions. Church
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory