Theorems in algebraic topology | Homological algebra
In algebraic topology, universal coefficient theorems establish relationships between homology groups (or cohomology groups) with different coefficients. For instance, for every topological space X, its integral homology groups: Hi(X; Z) completely determine its homology groups with coefficients in A, for any abelian group A: Hi(X; A) Here Hi might be the simplicial homology, or more generally the singular homology: the result itself is a pure piece of homological algebra about chain complexes of free abelian groups. The form of the result is that other coefficients A may be used, at the cost of using a Tor functor. For example it is common to take A to be Z/2Z, so that coefficients are modulo 2. This becomes straightforward in the absence of 2-torsion in the homology. Quite generally, the result indicates the relationship that holds between the Betti numbers bi of X and the Betti numbers bi,F with coefficients in a field F. These can differ, but only when the characteristic of F is a prime number p for which there is some p-torsion in the homology. (Wikipedia).
Tutorial - Detrmining the Leading coefficient and degree of a polynomial with a fraction ex 14
👉 Learn how to find the degree and the leading coefficient of a polynomial expression. The degree of a polynomial expression is the the highest power (exponent) of the individual terms that make up the polynomial. For terms with more that one variable, the power (exponent) of the term is t
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👉 Learn how to find the degree and the leading coefficient of a polynomial expression. The degree of a polynomial expression is the the highest power (exponent) of the individual terms that make up the polynomial. For terms with more that one variable, the power (exponent) of the term is t
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From playlist Find the leading coefficient and degree of a polynomial | expression
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👉 Learn how to find the degree and the leading coefficient of a polynomial expression. The degree of a polynomial expression is the the highest power (exponent) of the individual terms that make up the polynomial. For terms with more that one variable, the power (exponent) of the term is t
From playlist Find the leading coefficient and degree of a polynomial | equation
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
A (truly) universal polynomial differential equation Lee A. Rubel proved in 1981 that there exists a universal fourth-order algebraic differential equation P(y,y',y'',y''')=0 (1) and provided an explicit example. It is universal in the sense that for any continuous function f from R to
From playlist DART X
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Iwasawa Main Conjecture for Universal Families by Xin Wan
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
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Macroscopically minimal hypersurfaces - Hannah Alpert
Variational Methods in Geometry Seminar Topic: Macroscopically minimal hypersurfaces Speaker: Hannah Alpert Affiliation: Ohio State University Date: March 12, 2019 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
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Computer Science/Discrete Mathematics Seminar I Topic: Common Linear Patterns Are Rare Speaker: Nina KamÄŤev Affiliation: University of Zagreb Date: April 03, 2023Â Several classical results in Ramsey theory (including famous theorems of Schur, van der Waerden, Rado) deal with finding mon
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The Ramanujan Conjecture and some diophantine equations - Peter Sarnak
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Joint IAS/Princeton University Number Theory Seminar Topic: Local (\ell = p) Galois Deformation Rings Speaker: Ashwin Iyengar Affiliation: Johns Hopkins University Date: February 10, 2022 I will present joint work with V. Paškūnas and G. Böckle concerning deformation rings for mod p Galo
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Stochastic Homogenization (Lecture 3) by Andrey Piatnitski
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Geometry of the moduli space of curves – Rahul Pandharipande – ICM2018
Plenary Lecture 3 Geometry of the moduli space of curves Rahul Pandharipande Abstract: The moduli space of curves, first appearing in the work of Riemann in the 19th century, plays an important role in geometry. After an introduction to the moduli space, I will discuss recent directions
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From playlist Find the leading coefficient and degree of a polynomial | equation
CTNT 2022 - The unbounded denominators conjecture (by Yunqing Tang)
This video is one of the special guess talks or conference talks that took place during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. Note: not every special guest lecture or conference lecture was recorded. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - Conference lectures and special guest lectures