Number Theory | Lagrange's Theorem of Polynomials
We prove Lagrange's Theorem of Polynomials which is related to the number of solutions to polynomial congruences modulo a prime.
From playlist Number Theory
Camille Horbez: Automorphisms of hyperbolic groups and growth
Abstract: Let G be a torsion-free hyperbolic group, let S be a finite generating set of G, and let f be an automorphism of G. We want to understand the possible growth types for the word length of fn(g), where g is an element of G. Growth was completely described by Thurston when G is the
From playlist Topology
Harald Helfgott - 1/4 Growth in groups and applications
Harald Helfgott - Growth in groups and applications
From playlist École d'été 2014 - Théorie analytique des nombres
Mikhail Gromov - 3/4 Old, New and Unknown around Scalar Curvature
Geometry of scalar curvature, that is comparable in scope to symplectic geometry, mediates between two worlds: the domain of rigidity, one sees in convexity and the realm of softness, characteristic of topology, such as the cobordism theory. The aim of this course is threefold: 1. An ove
From playlist Mikhail Gromov - Old, New and Unknown around Scalar Curvature
Number Theory | Hensel's Lemma
We prove Hensel's Lemma, which is related to finding solutions to polynomial congruences modulo powers of primes. http://www.michael-penn.net Thumbnail Image: By Unknown - Universität Marburg, Public Domain, https://commons.wikimedia.org/w/index.php?curid=9378696
From playlist Number Theory
Adam Piggott & Murray Elder Double Header: Geodesics in Groups
Double header seminar by two SMRI domestic visitors: Adam Piggott (Australian National University) ‘Stubborn conjectures concerning rewriting systems, geodesic normal forms and geodetic graphs’ & Murray Elder (University of Technology Sydney) ‘Which groups have polynomial geodesic growth
From playlist SMRI Seminars
Asymptotic invariants of locally symmetric spaces – Tsachik Gelander – ICM2018
Lie Theory and Generalizations Invited Lecture 7.4 Asymptotic invariants of locally symmetric spaces Tsachik Gelander Abstract: The complexity of a locally symmetric space M is controlled by its volume. This phenomena can be measured by studying the growth of topological, geometric, alge
From playlist Lie Theory and Generalizations
Panagiotis Papasoglu - Asymptotic dimension of graphs of polynomial growth and systolic inequalities
Asymptotic dimension and n-Uryson width are useful notions of dimension in coarse and systolic geometry respectively. I will explain how using similar techniques one obtains: 1. Sharp estimates for the asymptotic dimension of graphs of polynomial growth 2. A new proof of a theorem of Guth
From playlist Geometry in non-positive curvature and Kähler groups
Visual Group Theory, Lecture 6.3: Polynomials and irreducibility
Visual Group Theory, Lecture 6.3: Polynomials and irreducibility A complex number is algebraic over Q (the rationals) if it is the root of a polynomial with rational coefficients. It is clear that every number that can be written with arithmetic and radicals is rational. Galois' big achie
From playlist Visual Group Theory
Mikhael Gromov - 2/4 Mathematical Structures arising from Genetics and Molecular Biology
Cours des professeurs permanents de l'IHÉS - Mikhael GROMOV (IHÉS) À l'Institut Henri Poincaré (IHP) Paris le 4 octobre 2013
From playlist Mikhael Gromov - Mathematical Structures arising from Genetics and Molecular Biology
Field Theory - Subgroups of Units - Lecture 13
In this video we show that any finite subgroup of K^{\times} is cyclic. This is an amazing proof using the fundamental theorem of abelian groups and the way polynomials factor. This has big applications: --that the nth roots of unity in any field are a cyclic group. --that the group of
From playlist Field Theory
24. Structure of set addition IV: proof of Freiman's theorem
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX This lecture concludes the proof of Freiman's theorem on
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Quantitative propagation for solutions of elliptic equations – A. Logunov & E. Malinnikova – ICM2018
Partial Differential Equations | Geometry Invited Lecture 10.11 | 5.12 Quantitative propagation of smallness for solutions of elliptic equations Alexander Logunov & Eugenia Malinnikova Abstract: Let u be a solution to an elliptic equation div(A∇u)=0 with Lipschitz coefficients in ℝⁿ. Ass
From playlist Geometry
Gromov–Witten Invariants and the Virasoro Conjecture (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
Alessandro Chiodo - Towards a global mirror symmetry (Part 3)
Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathematics and physics in the last twenty years; we will review here a number of results going from the enumerative geometry of curves to homological algebra. These advances justify the i
From playlist École d’été 2011 - Modules de courbes et théorie de Gromov-Witten
Universality of Resurgence in Quantization Theories - 13 June 2018
http://crm.sns.it/event/433 Universality of Resurgence in Quantization Theories Recent mathematical progress in the modern theory of resurgent asymptotic analysis (using trans-series and alien calculus) has recently begun to be applied systematically to many current problems of interest,
From playlist Centro di Ricerca Matematica Ennio De Giorgi
High dimensional expanders – Alexander Lubotzky – ICM2018
Plenary Lecture 13 High dimensional expanders Alexander Lubotzky Abstract: Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways. In the last decad
From playlist Plenary Lectures
Multiplicative Subgroup of a Field is Cyclic
We prove an initially unintuitive fact about subgroups under multiplication of fields. To do so, we prove a classic result that polynomials of degree n have at most n roots.
From playlist Abstract Algebra
Mikhail Gromov: Powerspace and the bulk problem
This lecture was given by the 2009 Abel Laurate Mikhail Leonidovich Gromov at The University of Oslo, May 20, 2009 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations.
From playlist Mikhail L. Gromov