A differentiable stack is the analogue in differential geometry of an algebraic stack in algebraic geometry. It can be described either as a stack over differentiable manifolds which admits an atlas, or as a Lie groupoid up to Morita equivalence. Differentiable stacks are particularly useful to handle spaces with singularities (i.e. orbifolds, leaf spaces, quotients), which appear naturally in differential geometry but are not differentiable manifolds. For instance, differentiable stacks have applications in foliation theory, Poisson geometry and twisted K-theory. (Wikipedia).
Multivariable Calculus | Differentiability
We give the definition of differentiability for a multivariable function and provide a few examples. http://www.michael-penn.net https://www.researchgate.net/profile/Michael_Penn5 http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
Stack Data Structure - Algorithm
This is an explanation of the dynamic data structure known as a stack. It includes an explanation of how a stack works, along with pseudocode for implementing the push and pop operations with a static array variable.
From playlist Data Structures
301.5C Definition and "Stack Notation" for Permutations
What are permutations? They're *bijective functions* from a finite set to itself. They form a group under function composition, and we use "stack notation" to denote them in this video.
From playlist Modern Algebra - Chapter 16 (permutations)
Definition of Differentiability
Discussion of definition of differentiability, focussing on hybrid (piecewise) functions.
From playlist Further Calculus - MAM Unit 3
Data structures: Introduction to stack
See complete series on data structures here: http://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P In this lesson, we have described stack data structure as abstract data type. Lesson on Dynamic memory allocation: http://www.youtube.com/watch?v=_8-ht2AKyH4 For practic
From playlist Data structures
Fibered Categories, Descent Data and The Definition of a Stack. (This was the first video I made.)
From playlist Stacks
Algebraic Spaces and Stacks: Representabilty
We define what it means for a functor to be representable. We define what it means for a category to be representable.
From playlist Stacks
When is a curve differentiable?
► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course 0:00 // What is the definition of differentiability? 0:29 // Is a curve differentiable where it’s discontinuous? 1:31 // Differentiability implies continuity 2:12 // Continuity doesn
From playlist Popular Questions
On the notion of λ-connection - Carlos Simpson
Geometry and Arithmetic: 61st Birthday of Pierre Deligne Carlos Simpson University of Nice October 18, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a four-day confe
From playlist Pierre Deligne 61st Birthday
David Ben-Zvi - Between Coherent and Constructible Local Langlands Correspondences
(Joint with Harrison Chen, David Helm and David Nadler.) Refined forms of the local Langlands correspondence seek to relate representations of reductive groups over local fields with sheaves on stacks of Langlands parameters. But what kind of sheaves? Conjectures in the spirit of Kazhdan
From playlist 2022 Summer School on the Langlands program
Akhil Mathew - Remarks on p-adic logarithmic cohomology theories
Correction: The affiliation of Lei Fu is Tsinghua University. Many p-adic cohomology theories (e.g., de Rham, crystalline, prismatic) are known to have logarithmic analogs. I will explain how the theory of the “infinite root stack” (introduced by Talpo-Vistoli) gives an alternate approach
From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021
M. Olsson - Hochschild and cyclic homology of log schemes
I will discuss an approach to extending the notions of Hochschild and cyclic homology from schemes to log schemes. The approach is based on a more general theory for morphisms of algebraic stacks.
From playlist Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday
Some directions in derived geometry - Gabriele Vezzosi
Gabriele Vezzosi March 10, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu
From playlist Mathematics
Fourier transform for Class D-modules - David Ben Zvi
Locally Symmetric Spaces Seminar Topic: Fourier transform for Class D-modules Speaker: David Ben Zvi Affiliation: University of Texas at Austin; Member, School of Mathematics Date: Febuary 13, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Gromov–Witten Invariants and the Virasoro Conjecture - II (Remote Talk) by Ezra Getzler
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
EXTREMELY LOW TEMPERATURES! - Using TECs
I explain why stacking TECs is not done to increase their cooling efficiency, but can be used to achieve very low temperatures. Construction and testing of the freezer is coming up in the next video. Stay tuned! Previous videos: https://youtu.be/YWUhwmmZa7A https://youtu.be/cw8ipUYodkE
From playlist Cooling
Charles Rezk: Elliptic cohomology and elliptic curves (Part 3)
The lecture was held within the framework of the Felix Klein Lectures at Hausdorff Center for Mathematics on the 8. June 2015
From playlist HIM Lectures 2015
Continuity vs Partial Derivatives vs Differentiability | My Favorite Multivariable Function
In single variable calculus, a differentiable function is necessarily continuous (and thus conversely a discontinuous function is not differentiable). In multivariable calculus, you might expect a similar relationship with partial derivatives and continuity, but it turns out this is not th
State Space Representation of Differential Equations
In this video we show how to represent differential equations (either linear or non-linear) in state space form. This is useful as it allows us to combine an arbiter number of higher order differential equations into a single set of first order, coupled, matrix equations. Topics and tim
From playlist Ordinary Differential Equations