Finite Fields Courses and Certifications

TheIACR

Cryptanalysis 2

Explore cryptanalysis techniques, focusing on discrete logarithm problems in finite fields. Learn about L notation, historical developments, and computational complexity.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Ryan O'Donnell

Polynomials

Explore polynomials, from formal definitions to applications in finite fields, interpolation, and error-correcting codes for noisy communication channels.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Valentin Blomer - The Polynomial Method for Point Counting and Exponential Sums, Lecture III

Explore advanced techniques for counting points on curves over finite fields and estimating exponential sums using auxiliary polynomials and character sums.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Marina Iliopoulou- Three Polynomial Methods for Point Counting, Lecture II

Explore three powerful polynomial methods for point counting: Dvir's Kakeya problem solution, Guth-Katz's polynomial partitioning, and the slice rank method for arithmetic progressions.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Society for Industrial and Applied Mathematics

Multivariate Cryptography and Polynomial System Solving Complexity

Explore multivariate cryptography, Gröbner bases, and polynomial system solving complexity. Gain insights into linear-algebra-based methods and their impact on cryptographic security.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Fields Institute

Topics in Applied Model Theory - Lecture 9

Explore finite fields, antibiotic geometry, and perfect fields in this advanced lecture on applied model theory by Zoé Chatzidakis.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video

International Mathematical Union

Marie-France Vignéras- Modular Representations of P-Adic Groups

Explore modular representations of p-adic groups in the Langlands program, examining their connections to number theory and geometry using various vector spaces and modules.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Insights into Mathematics

Barycentric Coordinates and Subtractive Arithmetic of Vectors - Algebraic Calculus and dCB Curves 9

Explore barycentric coordinates and vector arithmetic in affine geometry, enhancing understanding of de Casteljau Bezier polygons and curves. Gain insights into advanced mathematical concepts and their applications.

• YouTube
• 34 minutes
• On-Demand
• Free Video

TheIACR

Private Multiplication over Finite Fields

Explore secure multiparty computation techniques for private multiplication in finite fields, focusing on cryptographic protocols and their applications.

• YouTube
• 24 minutes
• On-Demand
• Conference Talk

TheIACR

Efficient Supersingularity Testing over F_p and CSIDH Key Validation - Part 1

Explore efficient supersingularity testing over F_p and CSIDH key validation techniques, including random point tests and product tree methods.

• YouTube
• 21 minutes
• On-Demand
• Free Video

Insights into Mathematics

An Informal Introduction to Abstract Algebra

Informal introduction to abstract algebra, covering fields, rings, and vector spaces. Explores key concepts and examples, from basic number systems to advanced constructions, providing essential background for algebraic topology.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Insights into Mathematics

How to Construct the True Complex Numbers I - Famous Math Problems

Exploring the construction of true complex numbers using field theory and linear algebra, challenging traditional approaches and introducing novel concepts for a modern understanding.

• YouTube
• 37 minutes
• On-Demand
• Free Video

Insights into Mathematics

Isometry Groups of the Projective Line - Rational Geometry Math Foundations

Exploring finite field geometry: isometries, rotations, and reflections on the projective line, revealing connections to relativistic geometry and offering a new perspective on Euclidean concepts.

• YouTube
• 35 minutes
• On-Demand
• Free Video

Insights into Mathematics

Ptolemy's Theorem and Generalizations - Rational Geometry Math Foundations

Explores Ptolemy's theorem in rational geometry, extending it to finite fields and relativistic planar geometry. Demonstrates how classical results can yield broader insights when formulated without infinite processes.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Insights into Mathematics

Differential Geometry With Finite Fields - Differential Geometry

Exploring differential geometry in finite fields, introducing arithmetic in prime fields, polynomial operations, and tangent conics to cubics. Highlights unique patterns and combinatorial structures in finite calculus.

• YouTube
• 50 minutes
• On-Demand
• Free Video