Topology of Lie groups | Operator theory | Hilbert space | Theorems in topology | K-theory
In mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H. It states that the space GL(H) of invertible bounded endomorphisms of H is such that all maps from any finite complex Y to GL(H) are homotopic to a constant, for the norm topology on operators. A significant corollary, also referred to as Kuiper's theorem, is that this group is weakly contractible, ie. all its homotopy groups are trivial. This result has important uses in topological K-theory. (Wikipedia).
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Calculus 5.3 The Fundamental Theorem of Calculus
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Multivariable Calculus | The Squeeze Theorem
We calculate a limit using a multivariable version of the squeeze theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
Regularity of the limit set of embedded Poincaré Disks - Vincent Borelli
Workshop on the h-principle and beyond Topic: Regularity of the limit set of embedded Poincaré Disks Speaker: Vincent Borelli Affiliation: University of Lyon Date: November 4, 2021 Abstract: Let f be an embedding of a non compact manifold into an Euclidean space and p_n be a divergent se
From playlist Mathematics
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Maxim Kazarian - 1/3 Mathematical Physics of Hurwitz numbers
Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num
From playlist Physique mathématique des nombres de Hurwitz pour débutants
Dimitri Zvonkine - On two ELSV formulas
The ELSV formula (discovered by Ekedahl, Lando, Shapiro and Vainshtein) is an equality between two numbers. The first one is a Hurwitz number that can be defined as the number of factorizations of a given permutation into transpositions. The second is the integral of a characteristic class
From playlist 4th Itzykson Colloquium - Moduli Spaces and Quantum Curves
After years of searching, Clyde Tombaugh discovered tiny Pluto on February 18th, 1930, Little did he realize this was just one icy object in a vast belt of material known as the Kuiper Belt. Mike Brown explains, "The Kuiper Belt is a collection of bodies outside the orbit of Neptune that,
From playlist Pluto
Life Beyond Neptune: The Kuiper Belt & Scattered Disc
The solar system is enormous, and includes the Kuiper Belt and the Scattered Disc, both of which turn out to be really weird in some pretty awesome ways. We want to learn more about you and your opinions! If you have time, please take a moment to fill out this survey: https://www.surveymo
From playlist What Fraser's watching
The Oort Cloud: Crash Course Astronomy #22
Now that we’re done with the planets, asteroid belt, and comets, we’re heading to the outskirts of the solar system. Out past Neptune are vast reservoirs of icy bodies that can become comets if they get poked into the inner solar system. The Kuiper Belt is a donut shape aligned with the pl
From playlist Astronomy
The Kuiper Belt and its implications
Kavli Prize Laureate lecture in collaboration with the Kavli Foundation. The early solar system was not always the orderly place it is now. Professor Jane Luu explores the Kuiper Belt, a swarm of icy bodies left over from the formation of the planets, and its implications for our solar sys
From playlist Comets and the Oort Cloud Playlist
The Alsos Project and the Rescue of Max Planck, May 16, 1945
Max Planck is considered to be "the father of quantum physics." Gerard Kuiper is considered to be "the father of modern planetary science." The two met for the only known time during a daring rescue in May, 1945. This is original content based on research by The History Guy. Images in th
From playlist Extraordinary people and personalities
Mapping the Moon for Apollo 11
Distant Lens, an original documentary short from Active Galactic, tells the unbelievable true story of how a scrappy group of planetary scientists at the University of Arizona put their knowledge to the ultimate test to provide NASA with the vital information they needed to send a man to t
From playlist New Releases for July 2019
Massimiliano Mella: Unirational varieties - Part 1
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
Finding Proof of the Kuiper Belt
Visitation of comets from the far reaches of the solar system suggested the existence of the Kuiper Belt. However, the relatively small size of the bodies theorized to exist beyond the planets made finding one an unbelievably difficult challenge. Finally, in 1992, astronomers located a slo
From playlist How the Universe Works
One-on-One Conversation with New Horizons Scientist
Hank interviews Dr. Alex Harrison Parker about New Horizons' Pluto flyby, what's next for the probe, and what we can anticipate learning about the solar system's history! ---------- Dooblydoo thanks go to the following Patreon supporters -- we couldn't make SciShow without them! Shout out
From playlist SciShow Talk Show
Multivariable Calculus | Differentiable implies continuous.
We prove the classic result that if a function is differentiable, then it is continuous. To start, we prove this for a two variable function and then repeat for an n-variable function. http://www.michael-penn.net https://www.researchgate.net/profile/Michael_Penn5 http://www.randolphcolleg
From playlist Multivariable Calculus