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Search results “Algebraic geometry in coding theory and cryptography”
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
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: 2120 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: 1547 Brown University
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: 267 Audiopedia
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: 13728 Simons Institute
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
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: 2737 Simons Institute
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
Tanja Lange - Code-Based Cryptography
 
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Title: Code-Based Cryptography Speaker: Tanja Lange (Technische Universiteit Eindhoven) 2016 Post-Quantum Cryptography Winter School https://pqcrypto2016.jp/winter/
Views: 1266 PQCrypto 2016
Coding Theory Lecture
 
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Teaser of my lecture on subspace codes and grassmannian codes held in Silpakorn University in Thailand last November 23.
Views: 34 Virgilio Sison
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
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
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: 3289 logicmonkeyuk
What is Modular Arithmetic - Introduction to Modular Arithmetic - Cryptography - Lesson 2
 
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Modular Arithmetic is a fundamental component of cryptography. In this video, I explain the basics of modular arithmetic with a few simple examples. Learn Math Tutorials Bookstore http://amzn.to/1HdY8vm Donate - http://bit.ly/19AHMvX
Views: 126348 Learn Math Tutorials
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: 2594 Peeter Joot
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: 7510 CodeChef
Algebra 2 - Inverse Matrices to Encrypt and Decrypt Messages
 
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25 80 12 3 5! With the appropriate matrix understanding, you'd know that I just said "Hello!" Yay Math in Studio presents how to use inverse matrices to encrypt and decrypt messages. This is a fascinating topic, and once you understand how it works, it's not so bad. In this video, we walk you through the process of setting up a message, encrypting it with what's called an "encoding matrix," then use the inverse of that matrix to decrypt. Then we round out the lesson with the same tasks on the TI-84 graphing calculator. Enjoy this peek into the world of code breaking, YAY MATH! Learning should be inspirational. Please visit yaymath.org for: all videos free quizzes free worksheets debut book on how to connect with and inspire students entire courses you can download
Views: 3139 yaymath
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.
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
Multi-Linear Secret Sharing Schemes
 
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Eleventh IACR Theory of Cryptography Conference TCC 2014 February 24-26, 2014 Amos Beimel and Aner M. Ben-Efraim and Carles Padró and Ilya Tomkin
Views: 1238 Calit2ube
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: 679 Simons Institute
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
Group theory -  Binary operation, Algebraic structure & Abelian Group in hindi
 
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This video is useful for students of BTech/BE/Engineering/ BSc/MSc Mathematics students. Also for students preparing IIT-JAM, GATE, CSIR-NET and other exams.
Quantum Computing for Computer Scientists
 
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This talk discards hand-wavy pop-science metaphors and answers a simple question: from a computer science perspective, how can a quantum computer outperform a classical computer? Attendees will learn the following: - Representing computation with basic linear algebra (matrices and vectors) - The computational workings of qbits, superposition, and quantum logic gates - Solving the Deutsch oracle problem: the simplest problem where a quantum computer outperforms classical methods - Bonus topics: quantum entanglement and teleportation The talk concludes with a live demonstration of quantum entanglement on a real-world quantum computer, and a demo of the Deutsch oracle problem implemented in Q# with the Microsoft Quantum Development Kit. This talk assumes no prerequisite knowledge, although comfort with basic linear algebra (matrices, vectors, matrix multiplication) will ease understanding. See more at https://www.microsoft.com/en-us/research/video/quantum-computing-computer-scientists/
Views: 70617 Microsoft Research
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
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
Tutorial on Using Sage for Algebraic Number Theory at University of Washington
 
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This is for http://wstein.org/edu/2012/ant/ Temporary offline version: http://wstein.org/tmp/tutorial.mp4
Views: 6187 William Stein
Affine Codes | Math | Chegg Tutors
 
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This elementary encryption scheme goes back to ancient Roman times. In its simplest form, each letter is shifted forward by a fixed number of places. Imagine constructing an alphabet on a wheel, and rotating the wheel to generate the transformation. This can be achieved numerically by a linear modular transformation modulo 26: (Here P is plaintext, C the ciphertext.) C = P + k (mod 26) The encryption key is k, and clearly the decryption key is 26 - k (mod 26). ---------- Math tutoring on Chegg Tutors Learn about Math terms like Affine Codes on Chegg Tutors. Work with live, online Math tutors like Chris W. who can help you at any moment, whether at 2pm or 2am. Liked the video tutorial? Schedule lessons on-demand or schedule weekly tutoring in advance with tutors like Chris W. Visit https://www.chegg.com/tutors/Math-online-tutoring/?utm_source=youtube&utm_medium=video&utm_content=managed&utm_campaign=videotutorials ---------- About Chris W., Math tutor on Chegg Tutors: University of Pennsylvania, Class of 2007 Math, Computer Science major Subjects tutored: Trigonometry, Pre-Calculus, Linear Programming, GRE, Pre-Algebra, ACT (math), Web Design, SAT II Mathematics Level 2, Computer Science, PSAT (math), Discrete Math, Geometry (College Advanced), Information Technology, Set Theory, Applied Mathematics, Linear Algebra, Basic Math, Geometry, Computer Certification and Training, Software Engineering, LaTeX, SAT (math), Calculus, SAT II Mathematics Level 1, Number Theory, Algebra, Statistics, Numerical Analysis, and SSAT (math) TEACHING EXPERIENCE Over 7 years of experience teaching math at 3 universities and a community college. Courses ranged from Intermediate Algebra to Calculus II and class sizes varied from 2 to over 200 students. Tutoring since 2000 formally and informally, individually and in groups, for courses from Geometry to Differential Equations. Please note that I generally will not be available for audio and video in live lessons but my experience has been that audio and video aren't really needed. EXTRACURRICULAR INTERESTS Hiking, reading, video games, playing the guitar and piano. Want to book a private lesson with Chris W.? Message Chris W. at https://www.chegg.com/tutors/online-tutors/Chris-W-576966/?utm_source=youtube&utm_medium=video&utm_content=managed&utm_campaign=videotutorials ---------- Like what you see? Subscribe to Chegg's Youtube Channel: http://bit.ly/1PwMn3k ---------- Visit Chegg.com for purchasing or renting textbooks, getting homework help, finding an online tutor, applying for scholarships and internships, discovering colleges, and more! https://chegg.com ---------- Want more from Chegg? Follow Chegg on social media: http://instagram.com/chegg http://facebook.com/chegg http://twitter.com/chegg
Views: 756 Chegg
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: 34223 MIT OpenCourseWare
POLYNOMIAL DIVISION
 
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How to divide polynomials in GF(q). link to my channel- https://www.youtube.com/user/lalitkvashishtha link to data structure and algorithm playlist - https://www.youtube.com/watch?v=GbOW74e4xZE&list=PLLvKknWU7N4y_eGpQdg1Y-hORO7cxtoLU link to information theory and coding techniques playlist - https://www.youtube.com/watch?v=2qJ_mcjKYtk&list=PLLvKknWU7N4yDkIlN4YE-sXfFD4trDf6W link to compiler design playlist - https://www.youtube.com/watch?v=uAVkjTbB7Yc&list=PLLvKknWU7N4zpJWLqk7DXK26JwTB-gFmZ
Views: 572 Lalit Vashishtha
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.
Lecture on Chinese Remainder Theorem by Praveen Dhinwa | Indian Programming Camp 2016
 
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The lecture was conducted on the Day 2 of the training camp. More details about the series of lectures and assignments given on Day 2 can be found here: https://blog.codechef.com/2016/07/17/snackdown-training-camp-2016-day-2/
Views: 7049 CodeChef
A Theoretical Approach to Semantic Coding and Hashing
 
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Sanjeev Arora, Princeton University https://simons.berkeley.edu/talks/sanjeev-arora-2016-11-15 Learning, Algorithm Design and Beyond Worst-Case Analysis
Views: 606 Simons Institute
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: 103 AzitaGhassemi Media
Polynomial arithmetic
 
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Adding, subtracting, multiplying
Views: 3169 Jeessy Medina
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: 536 Audiopedia
Cryptology - Part 1: Matrices
 
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Would it be cool to work for the NSA? :-) Encode and Decode secret messages using matrices. www.learncryptology.appspot.com www.matrix-algebra.appspot.com www.chukwuemekasamuel.com www.samuelchukwuemeka.com
Views: 2380 Samuel Chukwuemeka
Nexus trimester - Alex Sprintson (Texas A&M)
 
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Secure and Reliable Codes for Cooperative Data Exchange Alex Sprintson (Texas A&M) February 09, 2016 Abstract: In many practical settings, a group of clients needs to exchange data over a shared broadcast channel. The goal of cooperative data exchange problem is to find a schedule and an encoding scheme that minimize the total number of transmissions. We focus a wide range of practical settings in which the communication is performed in the presence of unreliable clients as well as in the presence of active and passive adversaries. In such settings, the problem of finding an efficient code is computationally intractable (NP-hard). Accordingly, we present approximation schemes with provable performance guarantees. We also focus on the design of coding schemes that achieve weak security, i.e., prevent the adversary from being able to obtain information about any individual file in the system. The weak security is a low-overhead light-weight approach for protecting users’ data. In contrast to traditional information-theoretic and cryptographic tools, it does not require an exchange of secure keys and does not reduce the capacity of the network. We conjecture that it is possible to linearly transform a Vandermonde matrix to obtain a weakly secure code over a small field. This conjecture admits a number of reformulations that lead to interesting conjectures in algebraic geometry, abstract algebra and number theory.
Lecture 3:  Grobner bases - Multi-variable Polynomial Division
 
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In this video series we will shed light on the many applications of Grobner bases.
Views: 985 maya ahmed
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

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