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Search results “Algebraic geometry in coding theory and cryptography”
Cryptography for Everyone: John Voight at TEDxUVM
 
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(NOTE: This new upload has improved audio; the initial upload had 267 views) JOHN VOIGHT John Voight is an assistant professor of mathematics and computer science. His research interests include computational and algorithmic aspects of number theory and arithmetic algebraic geometry, with applications in cryptography and coding theory. About TEDx In the spirit of ideas worth spreading, TEDx is a program of local, self-organized events that bring people together to share a TED-like experience. At a TEDx event, TEDTalks video and live speakers combine to spark deep discussion and connection in a small group. These local, self-organized events are branded TEDx, where x = independently organized TED event. The TED Conference provides general guidance for the TEDx program, but individual TEDx events are self-organized.* (*Subject to certain rules and regulations)
Views: 2057 TEDx Talks
Cryptographic Problems in Algebraic Geometry Lecture
 
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AGNES is a series of weekend workshops in algebraic geometry. One of our goals is to introduce graduate students to a broad spectrum of current research in algebraic geometry. AGNES is held twice a year at participating universities in the Northeast. Lecture presented by Kristin Lauter.
Views: 1506 Brown University
Algebraic geometric codes and their applications - Gil Cohen
 
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Computer Science/Discrete Mathematics Seminar Topic: Algebraic geometric codes and their applications Speaker: Gil Cohen Affiliation: Princeton University For more videos, visit http://video.ias.edu
Geometry and Number Theory By Kevin Charles Atienza | Indian Programming Camp 2016
 
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You may download the slides referred in the video here: https://docs.google.com/presentation/d/1242hfrxTJ1PpHlKymZHExis9PeH5OBi9UtZL8cKX04M/edit?usp=sharing The lecture was conducted on the Day 3 of the training camp. More details about the series of lectures and assignments given on Day 3 can be found here: https://blog.codechef.com/2016/07/17/snackdown-training-camp-day-3/
Views: 7069 CodeChef
Cryptography: From Mathematical Magic to Secure Communication
 
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Dan Boneh, Stanford University Theoretically Speaking Series http://simons.berkeley.edu/events/theoretically-speaking-dan-boneh Theoretically Speaking is produced by the Simons Institute for the Theory of Computing, with sponsorship from the Mathematical Sciences Research Institute (MSRI) and Berkeley City College. These presentations are supported in part by an award from the Simons Foundation.
Views: 13210 Simons Institute
Alena Pirutka: Algebraic cycles on varieties over finite fields
 
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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, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area Let X be a projective variety over a field k. Chow groups are defined as the quotient of a free group generated by irreducible subvarieties (of fixed dimension) by some equivalence relation (called rational equivalence). These groups carry many information on X but are in general very difficult to study. On the other hand, one can associate to X several cohomology groups which are "linear" objects and hence are rather simple to understand. One then construct maps called "cycle class maps" from Chow groups to several cohomological theories. In this talk, we focus on the case of a variety X over a finite field. In this case, Tate conjecture claims the surjectivity of the cycle class map with rational coefficients; this conjecture is still widely open. In case of integral coefficients, we speak about the integral version of the conjecture and we know several counterexamples for the surjectivity. In this talk, we present a survey of some well-known results on this subject and discuss other properties of algebraic cycles which are either proved or expected to be true. We also discuss several involved methods. Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' » the May 18, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
Theory and Algorithm research group
 
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This video explores the Theory and Algorithm research group at the university of Bristol through an interview with the head of the group, Dr Raphael Clifford.
Views: 100 AzitaGhassemi Media
Cryptography research group
 
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This video explores the Cryptography research group at the University of Bristol through an interview with the head of the group, Prof. Nigel Smart.
Applied Number Theory
 
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Learn more at: http://www.springer.com/978-3-319-22320-9. First book that covers all four areas: cryptography, coding theory, quasi-Monte Carlo methods, pseudo-random numbers. Contains material for courses on number theory, cryptography, coding theory and quasi-Monte Carlo methods. Builds a bridge from basic number theory to recent research in applied number theory.
Views: 115 SpringerVideos
Cyclic Groups  (Abstract Algebra)
 
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Cyclic groups are the building blocks of abelian groups. There are finite and infinite cyclic groups. In this video we will define cyclic groups, give a list of all cyclic groups, talk about the name “cyclic,” and see why they are so essential in abstract algebra. If​ ​you​’d​ ​like​ ​to​ ​help​ ​us​ ​make​ ​videos more quickly,​ ​you​ ​can​ ​support​ ​us​ on ​Patreon​ at https://www.patreon.com/socratica We​ ​also​ ​welcome​ ​Bitcoin​ ​donations!​ ​​ ​Our​ ​Bitcoin​ ​address​ ​is: 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank​ ​you!! ************** We recommend the following textbooks: Dummit & Foote, Abstract Algebra 3rd Edition http://amzn.to/2oOBd5S Milne, Algebra Course Notes (available free online) http://www.jmilne.org/math/CourseNotes/index.html ************** Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W You​ ​can​ ​also​ ​follow​ ​Socratica​ ​on: -​ ​Twitter:​ ​@socratica -​ ​Instagram:​ ​@SocraticaStudios -​ ​Facebook:​ ​@SocraticaStudios ******** Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison
Views: 105196 Socratica
Introduction to Geometric (Clifford) Algebra.
 
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Introduction to Geometric (Clifford) algebra. Interpretation of products of unit vectors, rules for reducing products of unit vectors, and the axioms that justify those rules.
Views: 2258 Peeter Joot
Coding theory
 
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Coding theory is the study of the properties of codes and their fitness for a specific application. Codes are used for data compression, cryptography, error-correction and more recently also for network coding. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction of errors in the transmitted data. This video is targeted to blind users. Attribution: Article text available under CC-BY-SA Creative Commons image source in video
Views: 239 Audiopedia
Introduction to Grobner Bases - Prof. Bernd Sturmfels
 
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Using Grobner bases to perform Gaussian elimination on non-linear systems, apply the Euclidean algorithm to multivariate systems and run the Simplex algorithm in a minimisation problem.
Views: 3024 logicmonkeyuk
The Mathematics of Lattices II
 
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Vinod Vaikuntanathan, Massachusetts Institute of Technology Cryptography Boot Camp http://simons.berkeley.edu/talks/vinod-vaikuntanathan-2015-05-18b
Views: 2630 Simons Institute
Light-cone lattice, quantum affine algebras, and the modular double | Joerg Teschner | EIMI
 
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Light-cone lattice, quantum affine algebras, and the modular double | Курс: Mathematical Physics: Past, Present and Future | Лектор: Joerg Teschner | Организатор: -еждународный математический институт им. Л. Эйлера Смотрите это видео на Лекториуме: https://lektorium.tv/lecture/23193 Подписывайтесь на канал: https://www.lektorium.tv/ZJA Следите за новостями: https://vk.com/openlektorium https://www.facebook.com/openlektorium
Views: 364 Лекториум
Ernst-Ulrich Gekeler: Algebraic curves with many rational points over non-prime finite fields
 
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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, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area We construct curves over finite fields with properties similar to those of classical elliptic or Drinfeld modular curves (as far as elliptic points, cusps, ramification, ... are concerned), but whose coverings have Galois groups of type GL(r) over finite rings (r≥3) instead of GL(2). In the case where the finite field is non-prime, there results an abundance of series or towers with a large ratio "number of rational points/genus". The construction relies on higher-rank Drinfeld modular varieties and the supersingular trick and uses mainly rigid-analytic techniques. Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' the May 19, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
Felipe Voloch:  Maps between curves and diophantine obstructions
 
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Abstract: Given two algebraic curves X, Y over a finite field we might want to know if there is a rational map from Y to X. This has been looked at from a number of perspectives and we will look at it from the point of view of diophantine geometry by viewing the set of maps as X(K) where K is the function field of Y. We will review some of the known obstructions to the existence of rational points on curves over global fields, apply them to this situation and present some results and conjectures that arise. Recording during the thematic meeting : "Arithmetic, Geometry, Cryptography and Coding Theory" the June 20, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent 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, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area
applications of cryptography - cryptography applications
 
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📌FREE Signals for Crypto Trading Every Day! 🚀100% Profit ➡ https://t.me/CryptoTopX 🔥Hot Airdrop! Get 18 Tokens ($50) Now! ➡ https://goo.gl/g7SgK2 [hindi] what is cryptography ? Classical cryptography - stacey jeffery - qcsys 2011.This talk will introduce a couple of less well known applications of cryptography. Application to cryptography (screencast 3. Spies used to meet in the park to exchange code words now things have moved on - robert miles explains the principle of public/private key cryptography..Also a simple example of how cryptography is applied in web browsers.... His research interests include computational and algorithmic aspects of number theory and arithmetic algebraic geometry with applications in cryptography and coding theory. Interesting primitives/applications of cryptography | o s l bhavana | csauss17. Prime numbers & public key cryptography.Understand the basics of cryptography and the concept of symmetric or private key and asymmetric or public key cryptography. Interesting primitives/applications of cryptography | o s l bhavana | csauss17.Application to cryptography (screencast 3. Public key cryptography - computerphile.
Local Correction of Codes and Euclidean Incidence Geometry - Avi Wigderson
 
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Avi Wigderson Institute for Advanced Study March 5, 2012 A classical theorem in Euclidean geometry asserts that if a set of points has the property that every line through two of them contains a third point, then they must all be on the same line. We prove several approximate versions of this theorem (and related ones), which are motivated from questions about locally correctable codes and matrix rigidity. The proofs use an interesting combination of combinatorial, algebraic and analytic tools. Joint work with Boaz Barak, Zeev Dvir and Amir Yehudayoff For more videos, visit http://video.ias.edu
Lecture 7: Introduction to Galois Fields for the AES by Christof Paar
 
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For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com
Alexander Vardy - What's New and Exciting in Algebraic and Combinatorial Coding Theory?
 
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2006 ISIT Plenary Talk What's New and Exciting in Algebraic and Combinatorial Coding Theory? Alexander Vardy University of California San Diego We will survey the field of algebraic and combinatorial coding theory, in an attempt to answer the question in the title. In particular, we shall revisit classical problems that are yet unsolved, review promising advances in the past decade, elaborate upon recent connections to other areas, and speculate what may lie ahead for the field.
Randomness Extraction: A Survey - David Zuckerman
 
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David Zuckerman University of Texas at Austin; Institute for Advanced Study February 7, 2012 A randomness extractor is an efficient algorithm which extracts high-quality randomness from a low-quality random source. Randomness extractors have important applications in a wide variety of areas, including pseudorandomness, cryptography, expander graphs, coding theory, and inapproximability. In this talk, we survey the field of randomness extraction and discuss connections with other areas. For more videos, visit http://video.ias.edu
Aurore Guillevic: Computing discrete logarithms in GF(pn): practical improvement of ...
 
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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, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area This talk will focus on the last step of the number field sive algorithm used to compute discrete logarithms in finite fields. We consider here non-prime finite fields of very small extension degree: 1≤n≤6. These cases are interesting in pairing-based cryptography: the pairing output is an element in such a finite field. The discrete logarithm in that finite field must be hard enough to prevent from attacks in a given time (e.g. 10 years). Within the CATREL project we aim to compute DL records in finite fields of moderate size (e.g. in GF(pn) of global size from 600 to 800 bits) to estimate more tightly the hardness of DL in fields of cryptographic size (2048 bits at the moment). The best algorithm known to compute discrete logarithms in large finite fields (with small n) is the number field sieve (NFS) [...] Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' the May 20, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
applications of cryptography - applications of symmetric ciphers - applied cryptography
 
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📌FREE Signals for Crypto Trading Every Day! 🚀100% Profit ➡ https://t.me/CryptoTopX +🔥Hurry to Sign Up Crypto Exchange (💲Only 1000 users/day)+Bonus ➡ https://goo.gl/cy6fmV Also a simple example of how cryptography is applied in web browsers.... Application to cryptography (screencast 3. Interesting primitives/applications of cryptography | o s l bhavana | csauss17. Public key cryptography - computerphile. [hindi] what is cryptography ? His research interests include computational and algorithmic aspects of number theory and arithmetic algebraic geometry with applications in cryptography and coding theory.Understand the basics of cryptography and the concept of symmetric or private key and asymmetric or public key cryptography.Application to cryptography (screencast 3. Spies used to meet in the park to exchange code words now things have moved on - robert miles explains the principle of public/private key cryptography.. Classical cryptography - stacey jeffery - qcsys 2011. Interesting primitives/applications of cryptography | o s l bhavana | csauss17.
Views: 0 Crypto Trade
Explicit, Almost Optimal, Epsilon-Balanced Codes
 
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Amnon Ta-Shma, Tel Aviv University https://simons.berkeley.edu/talks/amnon-ta-shma-2017-03-07 Proving and Using Pseudorandomness
Views: 362 Simons Institute
1.1.2 Intro to Proofs: Part 1
 
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MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 32510 MIT OpenCourseWare
Cryptographic Asymmetry -- Some Math Options
 
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The mathematical challenge of asymmetry is met via a substitution 'table' over a very large alphabet, where a key is the power to raise a letter of this alphabet to compute another letter in it, and then finding a corresponding power (the decryption key) to raise the new letter back to the original.
Views: 3760 Gideon Samid
Confluences in Programming Languages Research
 
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David Walker
Views: 280 Ras Bodik
Theoretical Physicist Finds Computer Code in String Theory
 
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Working on a branch of physics called supersymmetry, Dr. James Gates Jr., discovered what he describes as the presence of what appear to resemble a form of computer code, called error correcting codes, embedded within, or resulting from, the equations of supersymmetry that describe fundamental particles. Gates asks, “How could we discover whether we live inside a Matrix? One answer might be ‘Try to detect the presence of codes in the laws that describe physics.'” And this is precisely what he has done. Specifically, within the equations of supersymmetry he has found, quite unexpectedly, what are called “doubly-even self-dual linear binary error-correcting block codes.” That’s a long-winded label for codes that are commonly used to remove errors in computer transmissions, for example to correct errors in a sequence of bits representing text that has been sent across a wire. Gates explains, “This unsuspected connection suggests that these codes may be ubiquitous in nature, and could even be embedded in the essence of reality. If this is the case, we might have something in common with the Matrix science-fiction films, which depict a world where everything human being’s experience is the product of a virtual-reality-generating computer network.”
Views: 959123 LR
Lattice (group)
 
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In mathematics, especially in geometry and group theory, a lattice in is a discrete subgroup of which spans the real vector space . Every lattice in can be generated from a basis for the vector space by forming all linear combinations with integer coefficients. A lattice may be viewed as a regular tiling of a space by a primitive cell. Lattices have many significant applications in pure mathematics, particularly in connection to Lie algebras, number theory and group theory. They also arise in applied mathematics in connection with coding theory, in cryptography because of conjectured computational hardness of several lattice problems, and are used in various ways in the physical sciences. For instance, in materials science and solid-state physics, a lattice is a synonym for the "frame work" of a crystalline structure, a 3-dimensional array of regularly spaced points coinciding with the atom or molecule positions in a crystal. More generally, lattice models are studied in physics, often by the techniques of computational physics. This video is targeted to blind users. Attribution: Article text available under CC-BY-SA Creative Commons image source in video
Views: 520 Audiopedia
Attacks on Ring-LWE
 
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Kristin Lauter, Microsoft Research Redmond The Mathematics of Modern Cryptography http://simons.berkeley.edu/talks/kristin-lauter-2015-07-07
Views: 660 Simons Institute
COLLOQUIUM: Foundations of Lattice-based Cryptography (November 2017)
 
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Speaker: Divesh Aggarwal, Centre for Quantum Technologies, NUS Abstract: Lattice-based cryptosystems are perhaps the most promising candidates for post-quantum cryptography as they have strong security proofs based on worst-case hardness of computational lattice problems and are efficient to implement due to their parallelizable structure. Attempts to solve lattice problems by quantum algorithms have been made since Shor’s discovery of the quantum factoring algorithm in the mid-1990s, but have so far met with little success if any at all. The main difficulty is that the periodicity finding technique, which is used in Shor’s factoring algorithm and related quantum algorithms, does not seem to be applicable to lattice problems. In this talk, I will survey some of the main developments in lattice cryptography over the last decade or so. The main focus will be on the Learning With Errors (LWE) and the Short Integer Solution (SIS) problems, their ring-based variants, their provable hardness under the intractability assumptions of lattice problems and their cryptographic applications.
Lattices with Symmetry
 
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Alice Silverberg, UC Irvine The Mathematics of Modern Cryptography http://simons.berkeley.edu/talks/alice-silverberg-2015-07-09
Views: 246 Simons Institute
Marc Hindry: Brauer-Siegel theorem and analogues for varieties over global fields
 
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Abstract: The classical Brauer-Siegel theorem can be seen as one of the first instances of description of asymptotical arithmetic: it states that, for a family of number fields Ki, under mild conditions (e.g. bounded degree), the product of the regulator by the class number behaves asymptotically like the square root of the discriminant. This can be reformulated as saying that the Brauer-Siegel ratio log(hR)/ logD‾‾√ has limit 1. Even if some of the fundamental problems like the existence or non-existence of Siegel zeroes remains unsolved, several generalisations and analog have been developed: Tsfasman-Vladuts, Kunyavskii-Tsfasman, Lebacque-Zykin, Hindry-Pacheco and lately Griffon. These analogues deal with number fields for which the limit is different from 1 or with elliptic curves and abelian varieties either for a fixed variety and varying field or over a fixed field with a family of varieties. Recording during the thematic meeting : "Arithmetic, Geometry, Cryptography and Coding Theory" the June 20, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent 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, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area
Valentin Suder - Sparse Permutations with Low Differential Uniformity
 
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Sparse Permutations with Low Differential Uniformity
Views: 75 Institut Fourier
lattices
 
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Views: 364 Jeff Suzuki
Andrew Sutherland: Computing the image of Galois representations attached to elliptic curves
 
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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, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area Let E be an elliptic curve over a number field K. For each integer n[greater than]1 the action of the absolute Galois group GK:=Gal(K/K) on the n-torsion subgroup E[n] induces a Galois representation ρE,n:GK→ Aut(E[n])⋍GL2(ℤ/nℤ). The representations ρE,n form a compatible system, and after taking inverse limits one obtains an adelic representation ρE:GK→GL2(ℤ̂ ). If E/K does not have CM, then Serre's open image theorem implies that the image of ρE has finite index in GL2(ℤ̂ ); in particular, ρE,ℓ is surjective for all but finitely many primes ℓ. I will present an algorithm that, given an elliptic curve E/K without CM, determines the image of ρE,ℓ in GL2(ℤ/ℓℤ) up to local conjugacy for every prime ℓ for which ρE,ℓ is non-surjective. Assuming the generalized Riemann hypothesis, the algorithm runs in time that is polynomial in the bit-size of the coefficients of an integral Weierstrass model for E. I will then describe a probabilistic algorithm that uses this information to compute the index of ρE in GL2(ℤ̂ ). Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' the May 18, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
Marco Streng: Generators for the group of modular units for Γ1(N) over the rationals
 
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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, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area The modular curve Y1(N) parametrises pairs (E,P), where E is an elliptic curve and P is a point of order N on E, up to isomorphism. A unit on the affine curve Y1(N) is a holomorphic function that is nowhere zero and I will mention some applications of the group of units in the talk. The main result is a way of generating generators (sic) of this group using a recurrence relation. The generators are essentially the defining equations of Y1(N) for n[is less than](N+3)/2. This result proves a conjecture of Maarten Derickx and Mark van Hoeij. Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' the May 18, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
Modular Arithmetic in Musical Scales
 
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My final project is an examination of the modular arithmetic in the circle of fifths, with some review from the lesson. A certain background in basic number theory is assumed.
Views: 87 Sarah Hudadoff
Combinatorics and Complexity of Kronecker Coefficients
 
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Greta Panova, University of Pennsylvania Geometric Complexity Theory http://simons.berkeley.edu/talks/greta-panova-2014-09-19
Views: 310 Simons Institute
Some of My Favorite Open Problems on Expanders and Extractors
 
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Avi Wigderson, Institute for Advanced Study https://simons.berkeley.edu/talks/avi-wigderson-01-31-2017 Expanders and Extractors
Views: 819 Simons Institute
Chasing Lower Bounds
 
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Avi Widgerson, Institute for Advanced Study, Princeton Connections Between Algorithm Design and Complexity Theory https://simons.berkeley.edu/talks/avi-wigderson-2015-09-29
Views: 341 Simons Institute