Topology of Lie groups | Operator theory | Hilbert space | Theorems in topology | K-theory

Kuiper's theorem

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).

Video thumbnail

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

Video thumbnail

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)

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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)

Video thumbnail

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

Video thumbnail

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

Video thumbnail

What Is The Kuiper Belt?

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Related pages

Michael Atiyah | Topological space | Homeomorphism | Homotopy group | Unitary group | Classifying space for U(n) | Strong operator topology | Fredholm operator | Unit sphere | CW complex | Bounded operator | Banach space | Adrien Douady | Classifying space | Homotopy theory | General linear group | Connected space | Mathematics | Circle group | Vector bundle | Weakly contractible | Brouwer fixed-point theorem | Hilbert space | Homogeneous space | Bott periodicity theorem | Maximal compact subgroup | Mathematical folklore | Contractible space | Topological K-theory