Advanced Linear Algebra
Comprehensive exploration of advanced linear algebra concepts, including least squares approximation, error-correcting codes, functional calculus, affine transformations, and stochastic maps, with practical applications.
Locally Testable Codes with Constant Rate, Distance, and Locality, Part I - Irit Dinur
Explore locally testable codes with constant rate, distance, and locality. Learn about a new construction based on left-right Cayley complexes, addressing an open question in coding theory.
High Dimensional Expansion and Error Correcting Codes - Irit Dinur
Explore high-dimensional expansion, error-correcting codes, and their connections. Delve into expansion constructions, property testing, and revolution complexes with expert Irit Dinur.
Pseudorandom Error-Correcting Codes with Applications to Watermarking Generative AI
Explore the innovative framework of pseudorandom error-correcting codes and their application in watermarking AI-generated content, focusing on cryptographic implementations and robustness guarantees.
Algebraic Attacks for the Rank Decoding Problem - Lecture 2
Explorez les attaques algébriques pour le problème du décodage de rang dans cette conférence mathématique approfondie, axée sur les avancées récentes et les techniques avancées.
Cover Your Bases: Minimizing Sequencing Coverage in DNA Storage Systems
Explores minimizing DNA sequencing coverage in storage systems, focusing on error-correcting codes and retrieval algorithms to reduce costs and latency while optimizing information retrieval efficiency.
Great Ideas in Theoretical Computer Science - Polynomials
Explore theoretical computer science through polynomials, covering fields, division, evaluation, interpolation, and error-correcting codes. Gain insights into fundamental concepts and their applications.
Building Manifolds from Error Correcting Codes - IPAM at UCLA
Explore the intersection of error correcting codes and manifold construction, delving into quantum error correction, topology, and complex mathematical concepts.
High Dimensional Expanders - Introduction and Motivation
Explore high-dimensional expanders, their applications in error-correcting codes, and the motivations behind this emerging field of mathematics and computer science.
Linear Programming and Semidefinite Programming in Coding Theory - An Incomplete Overview
Explore linear programming in coding theory, including MRRW and Levenshtein bounds, spherical codes, and connections to combinatorial objects. Discover recent advances in equiangular lines and energy bounds.
The Hermitian Trace Code - Advances in Error-Correcting Codes
Explores character sum bias over high genus curves, strengthening Stepanov-Bombieri approach. Analyzes multiplicity in function fields using new 'universal derivative-fix' lemma.
Expanders in Higher Dimensions: From Local to Global Properties and Applications
Explore high-dimensional expanders, their local-to-global properties, and applications in coding theory, networking, and computational complexity.
Sparsification: Graphs, CSPs and Codes - Sublinear Graph Simplification
Explore graph sparsification, CSP compression, and code sparsification techniques. Learn about cutting-edge research in sublinear graph simplification and its applications to various domains.
Low Degree Testing over the Reals
Explore low degree testing over real numbers, focusing on theoretical concepts and applications in local algorithms.
Statistical Physics and Statistical Inference - Lecture 2
Explore statistical physics and inference, covering Bayesian methods, error correction, spin glasses, and advanced algorithms like belief propagation. Gain insights into phase transitions and applications in machine learning.
Efficient, Stable Presentations From Error-Correcting Codes
Explore error-correcting codes and their applications in efficient, stable presentations with Columbia University's Henry Yuen in this insightful talk from the Fields Institute workshop.
PCPs and Global Hyper-contractivity - Lecture 1
Explore advanced concepts in theoretical computer science, focusing on Probabilistically Checkable Proofs and global hyper-contractivity with expert Dor Minzer.
PCPs and Global Hyper-contractivity - Lecture 2
Explore advanced concepts in PCPs and global hyper-contractivity with Dor Minzer, delving into complex mathematical theories and their applications in analysis and theoretical computer science.
PCPs and Global Hyper-contractivity - Lecture 1
Explore advanced concepts in theoretical computer science, focusing on Probabilistically Checkable Proofs and global hyper-contractivity with expert Dor Minzer.
Mathematics of Computation Through the Lens of Linear Equations and Lattices
Explore mathematical foundations of computation through linear equations and lattices, covering error correction, vector problems, and lattice theory with implications for future computing.
Oscillator-to-Oscillator Codes Do Not Have a Threshold
Explores limitations of oscillator-to-oscillator codes in quantum information, proving they lack a threshold property for error correction when using constant squeezing and maximum likelihood decoding.