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)
Convolution Theorem: Fourier Transforms
Free ebook https://bookboon.com/en/partial-differential-equations-ebook Statement and proof of the convolution theorem for Fourier transforms. Such ideas are very important in the solution of partial differential equations.
From playlist Partial differential equations
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Modular forms: Petersson inner product
This lecture is part of an online graduate course on modular forms. We define the Petersson inner product on modular forms and use it to show that the eigenforms of the Hecke algebra span the space of modular forms. For the other lectures in the course see https://www.youtube.com/playli
From playlist Modular forms
Tony Varilly Alvarado, Descent on K3 surfaces: Brauer group computations and challenges
VaNTAGe seminar March 23, 2021 License: CC-BY-NC-SA
From playlist Arithmetic of K3 Surfaces
Persistence of the Brauer-Manin obstruction under field extension - Viray - Workshop 2 - CEB T2 2019
Bianca Viray (University of Washington) / 27.06.2019 Persistence of the Brauer-Manin obstruction under field extension. We consider the question of when an empty Brauer set over the ground field gives rise to an empty Brauer set over an extension. We first consider the case of quartic d
From playlist 2019 - T2 - Reinventing rational points
Bianca Viray, The Brauer group and the Brauer-Manin obstruction on K3 surfaces
VaNTAGe seminar, February 23, 2021
From playlist Arithmetic of K3 Surfaces
From playlist Linear Algebra Ch 8 (updated Jan2021)
Complex numbers and algebra | Math History | NJ Wildberger
Complex numbers of the form a+bi are mostly introduced these days in the context of quadratic equations, but according to Stillwell cubic equations are closer to their historical roots. We show how the cubic equation formula of del Ferro, Tartaglia and Cardano requires some understanding o
From playlist MathHistory: A course in the History of Mathematics
Applications of additive combinatorics to Diophantine equations - Alexei Skorobogatov
Alexei Skorobogatov Imperial College London April 10, 2014 The work of Green, Tao and Ziegler can be used to prove existence and approximation properties for rational solutions of the Diophantine equations that describe representations of a product of norm forms by a product of linear poly
From playlist Mathematics
The André-Oort conjecture follows from the Colmez conjecture - Jacob Tsimerman
Jacob Tsimerman University of Toronto April 9, 2015 The André-Oort conjecture says that any subvariety of a Shimura variety with a Zariski dense set of CM points must itself be a Shimura subvariety. In recent years, this has been the subject of much work. We explain how this conjecture fo
From playlist Mathematics
Hodge theory and derived categories of cubic fourfolds - Richard Thomas
Richard Thomas Imperial College London September 16, 2014 Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the le
From playlist Mathematics
Emmy Noether: breathtaking mathematics - Georgia Benkart
Celebrating Emmy Noether Topic: Emmy Noether: breathtaking mathematics Speaker: Georgia Benkart Affiliation: University of Wisconsin-Madison Date: Friday, May 6 By the mid 1920s, Emmy Noether had made fundamental contributions to commutative algebra and to the theory of invariants.
From playlist Celebrating Emmy Noether
Simplifying with Laws of Exponents Example 1 in Algebra 2
In this video, we show how to simplify an expression using the laws of exponents. @shaunteaches
From playlist Laws of Exponents
Modular forms: Eisenstein series
This lecture is part of an online graduate course on modular forms. We give two ways of looking at modular forms: as functions of lattices in C, or as invariant forms. We use this to give two different ways of constructing Eisenstein series. For the other lectures in the course see http
From playlist Modular forms
Nick Addington - Rational points and derived equivalence - WAGON
For smooth projective varieties over Q, is the existence of a rational point preserved under derived equivalence? First I'll discuss why this question is interesting, and what is known. Then I'll show that the answer is no, giving two counterexamples: an abelian variety and a torsor over i
From playlist WAGON
Purity for the Brauer group of singular schemes - Česnavičius - Workshop 2 - CEB T2 2019
Kęstutis Česnavičius (Université Paris-Sud) / 27.06.2019 Purity for the Brauer group of singular schemes For regular Noetherian schemes, the cohomological Brauer group is insensitive to removing a closed subscheme of codimension ≥ 2. I will discuss the corresponding statement for scheme
From playlist 2019 - T2 - Reinventing rational points
CTNT 2020 - Topology and Diophantine Equations - David Corwin
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Conference Videos
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
Squares represented by a product of three ternary (...) - Harpaz - Workshop 2 - CEB T2 2019
Yonatan Harpaz (Université Paris Nord) / 27.06.2019 Squares represented by a product of three ternary quadratic forms, and a homogeneous variant of a method of Swinnerton-Dyer. Let k be a number field. In this talk we will consider K3 surfaces over k which admit a degree 2 map to the pr
From playlist 2019 - T2 - Reinventing rational points