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NPTEL

Coding Theory

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This course provides an introduction to traditional and modern coding theory. Topics covered include linear block codes, cyclic codes (BCH and RS codes), convolutional codes, turbo codes and low-density parity-check (LDPC) codes.
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38 Lesons
1 day 13 hours
On-Demand
Free-Video
Hausdorff Center for Mathematics

A Polynomial Bogolyubov-Type Result for the Special Linear Group

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Explore a mathematical lecture on a polynomial Bogolyubov-type result for the special linear group. Delve into the analogy between subset properties in finite dimensional vector spaces and the special linear group over a finite field. Learn about the ach…
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
University of Chicago Department of Mathematics

The Weil Conjectures and A1-homotopy Theory

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Dive into the Weil Conjectures and A1-homotopy theory, exploring connections between algebraic topology and finite field equations in this mathematical colloquium.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
University of Chicago Department of Mathematics

Representations of Reductive Groups Over Local and Global Fields

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Dive into Langlands' theory of reductive groups and their representations in number theory, exploring local and global fields and their connections to arithmetic and geometry.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Algebraic Attacks for the Rank Decoding Problem - Lecture 1

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Explorez les attaques algébriques pour le problème du décodage de rang dans cette conférence mathématique approfondie, mettant l'accent sur les concepts clés et les techniques avancées.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Sharp Fourier Restriction Theory Over Finite Fields

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Explore recent developments in sharp Fourier restriction theory over finite fields, examining the intersection of two key areas in mathematical research.
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1 Lesons
52 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

On the Fourier Weight of F2 Polynomials

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Explore Fourier weight of F2 polynomials, focusing on level k and degree d relationships. Gain insights into pseudorandom generators and recent mathematical proofs.
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1 Lesons
36 minutes
On-Demand
Free-Video
BunG Seminar

The Stacks of n-Truncated Barsotti-Tate Groups - Part 2

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Delve into advanced algebraic geometry concepts, focusing on n-truncated Barsotti-Tate groups and n-smooth group schemes over F_p-algebras, with emphasis on their structural properties and relationships.
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1 Lesons
1 hour 58 minutes
On-Demand
Free-Video
TheIACR

Cryptanalysis 2

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Explore cryptanalysis techniques, focusing on discrete logarithm problems in finite fields. Learn about L notation, historical developments, and computational complexity.
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14 Lesons
52 minutes
On-Demand
Free-Video
Insights into Mathematics

Differential Geometry With Finite Fields - Differential Geometry

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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.
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11 Lesons
50 minutes
On-Demand
Free-Video
Insights into Mathematics

Infinitesimal Calculus with Finite Fields - Famous Math Problems

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Explore infinitesimal calculus in finite fields through the semi-cubical parabola over F_7, challenging traditional real number analysis and emphasizing polynumbers and de Casteljau Bezier curves.
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9 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

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

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Exploring the construction of true complex numbers using field theory and linear algebra, challenging traditional approaches and introducing novel concepts for a modern understanding.
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8 Lesons
37 minutes
On-Demand
Free-Video
Insights into Mathematics

Isometry Groups of the Projective Line - Rational Geometry Math Foundations

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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.
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8 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

Ptolemy's Theorem and Generalizations - Rational Geometry Math Foundations

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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.
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9 Lesons
46 minutes
On-Demand
Free-Video
Ryan O'Donnell

Polynomials

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Explore polynomials, from formal definitions to applications in finite fields, interpolation, and error-correcting codes for noisy communication channels.
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17 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Insights into Mathematics

An Informal Introduction to Abstract Algebra

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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.
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12 Lesons
49 minutes
On-Demand
Free-Video
Simons Institute

Randomness in Number Theory

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Explore randomness in number theory, covering topics like finite fields, graphs, quantum gates, and the Riemann Hypothesis with Princeton's Peter Sarnak.
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11 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

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

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Explore advanced techniques for counting points on curves over finite fields and estimating exponential sums using auxiliary polynomials and character sums.
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10 Lesons
45 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

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

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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.
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12 Lesons
1 hour 1 minute
On-Demand
Free-Video
International Mathematical Union

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

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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.
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1 Lesons
56 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

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

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Explore advanced polynomial techniques for solving geometric problems, including Dvir's method, polynomial partitioning, and slice rank method in finite-field settings.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Simons Institute

A Polynomial Bogolyubov Type Result for the Special Linear Group

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Explores a polynomial density result for the special linear group over finite fields, using hyper-contractive estimates derived from 2-to-2 games research.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Insights into Mathematics

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

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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.
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1 Lesons
34 minutes
On-Demand
Free-Video
Fields Institute

Moments of Artin-Schreier L-functions

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Explore the mathematical intricacies of Artin-Schreier L-functions and their moments in this advanced Fields Institute lecture by Matilde Lalín from Université de Montréal.
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1 Lesons
38 minutes
On-Demand
Free-Video
Fields Institute

Equidistribution of Polynomial Sequences in Function Fields

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Explore equidistribution of polynomial sequences in function fields, examining mathematical concepts and their applications in number theory and algebraic geometry.
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1 Lesons
28 minutes
On-Demand
Free-Video
Fields Institute

Artin's Primitive Root Conjecture

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Explore Artin's primitive root conjecture with Kumar Murty, delving into its mathematical significance and implications for number theory and algebraic structures.
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1 Lesons
44 minutes
On-Demand
Free-Video
Fields Institute

Towards the Classification of MVSPs over Finite Fields

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Explore the classification of MVSPs over finite fields in this mathematical talk by Lucas Reis, delving into advanced algebraic concepts and their applications.
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1 Lesons
23 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Vector Delannoy Categories and Further Developments

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Exploration of quantum analogues of Delannoy categories, focusing on constructions, properties, and connections to related mathematical concepts in symmetric tensor categories.
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1 Lesons
54 minutes
On-Demand
Free-Video
Wolfram

Finite Fields and Their Applications

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Explore new Mathematica 13.3 features for finite field computations, including arithmetic, mappings, and polynomials. Learn about upcoming linear algebra and equation solving capabilities.
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1 Lesons
27 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Algebraic Automatic Continued Fraction in Characteristic 2

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Explore algebraic automatic continued fractions in characteristic 2, delving into advanced mathematical concepts and their applications.
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1 Lesons
41 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Existence Theorem for Finite Fields

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Explore the existence theorem for finite fields, proving their existence for every prime power order.
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1 Lesons
15 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Subfields of a Finite Field

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Explore the concept of subfields within finite fields, understanding their properties and significance in abstract algebra and number theory.
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1 Lesons
12 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Lower Bound on the Maximal Number of Rational Points on Curves over Finite Fields

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Explore lower bounds on maximal rational points for curves over finite fields. Delve into strategies, Kzarnak Theory, and proofs in algebraic geometry.
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13 Lesons
1 hour
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Asymptotic Distribution of Frobenius Roots for Curves and Abelian Varieties

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Explore asymptotic distribution of Frobenius roots for curves and abelian varieties in this advanced mathematical lecture by Michael Tsfasman.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

An Overview of Algebraic Geometry Codes from Surfaces

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Explore algebraic geometry codes from surfaces, covering effective divisors, evaluation maps, minimum distance, and toric varieties. Gain insights into parameters, restrictions, and decoding techniques.
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24 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Algebraic Curves with Many Rational Points over Finite Fields

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Explore algebraic curves with many rational points over finite fields, focusing on maximum curves, automorphisms, and their applications in coding theory.
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15 Lesons
49 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Lang-Weil Type Bounds in Finite Difference Fields

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Explore Lang-Weil type bounds in finite difference fields with Martin Hils, delving into advanced mathematical concepts and their applications.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Frobenius Distributions - Lecture 1

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Explore Frobenius distributions in arithmetic statistics through an advanced mathematical lecture by Kiran Kedlaya at CIRM's Spring School.
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1 Lesons
50 minutes
On-Demand
Free-Video
Big Ideas In Dynamics

Factoring Gleason Polynomials Modulo 2 - Pre-Talk

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Explore factoring Gleason polynomials modulo 2 with postdoc Malavika Mukundan, delving into advanced mathematical concepts in dynamics.
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1 Lesons
35 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Number Theory over Function Fields - Lecture 6

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Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
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1 Lesons
1 hour 59 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Number Theory over Function Fields - Lecture 5

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Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
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1 Lesons
2 hours 6 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Number Theory over Function Fields - Lecture 4

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Explore recent progress in number theory using polynomial analogues over finite fields, connecting geometric perspectives to topology, probability, and automorphic forms.
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1 Lesons
1 hour 59 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Number Theory over Function Fields - Lecture 3

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Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
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1 Lesons
2 hours
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Number Theory over Function Fields - Lecture 2

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Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
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1 Lesons
2 hours
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Number Theory over Function Fields - Lecture 1

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Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
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1 Lesons
2 hours 4 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Local-Global Principles for Homogeneous Spaces Over Arithmetic Function Fields

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Explore local-global principles for homogeneous spaces over arithmetic function fields, focusing on function fields of curves over complete discretely valued fields and related patching methods.
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1 Lesons
58 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Tensor Rank and Bias of Multilinear Forms Over Finite Fields

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Explorez les liens entre le rang tensoriel et le biais des formes multilinéaires sur les corps finis dans cette conférence mathématique approfondie.
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1 Lesons
54 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Finite Point Configurations in Euclidean, Discrete, and Arithmetic Settings

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Explore finite point configurations across Euclidean, discrete, and arithmetic spaces. Discover size requirements for subsets containing congruent copies of given configurations, with connections to learning theory.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Point Counting over Finite Fields and the Cohomology of Moduli Spaces of Curves

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Explore algebraic geometry through point counting over finite fields and cohomology of moduli spaces of curves, resolving longstanding questions and confirming Langlands program predictions.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
BIMSA

Structure in the Search for Structure - Algebraic Number Theory and Motivic Cohomology

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Explore algebraic number theory through analogies between numbers and shapes, including quadratic reciprocity and linking numbers, leading to insights on Tate's 1966 conjecture.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
BIMSA

Towards a Mod p Langlands Correspondence for GL2

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Explore the mod $p$ Langlands correspondence for $\mathrm{GL}_2(K)$, examining conjectures and recent progress in this open area of mathematical research.
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1 Lesons
1 hour
On-Demand
Free-Video
BIMSA

Progression-Free Sets in Arithmetic Sequences

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Explore lower and upper bounds for progression-free sets in $\mathbb{Z}_m^n$, examining the polynomial method's application to $r_k(\mathbb{Z}_m^n)$ and related problems.
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1 Lesons
48 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Frobenius写像の周辺 - 第2回

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Delve into advanced mathematical concepts of Frobenius mappings, finite fields, and Witt vectors through an accessible exploration of number theory fundamentals and polynomial rings.
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6 Lesons
1 hour 10 minutes
On-Demand
Free-Video
TheIACR

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

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Explore efficient supersingularity testing over F_p and CSIDH key validation techniques, including random point tests and product tree methods.
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7 Lesons
21 minutes
On-Demand
Free-Video
TheIACR

Homomorphic Encryption and Encrypted Search - Asiacrypt 2021

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Explore advanced cryptographic techniques including balanced non-adjacent forms, encrypted data search, homomorphic encryption for finite fields, and improved bootstrapping for TFHE.
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1 Lesons
48 minutes
On-Demand
Free-Video
Simons Institute

Parameterized Inapproximability of the Minimum Distance Problem over All Fields

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Explores inapproximability of Minimum Distance Problem for linear codes over finite fields, proving W[1]-hardness. Extends results to Shortest Vector Problem on integer lattices.
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1 Lesons
48 minutes
On-Demand
Free-Video
Simons Institute

Fast List-Decoding of Univariate Multiplicity and Folded Reed-Solomon Codes

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Explore advanced techniques for efficient list-decoding of Reed-Solomon codes, focusing on univariate multiplicity and folded variants in error-correcting code theory.
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1 Lesons
52 minutes
On-Demand
Free-Video
Simons Institute

Codes with the Multiplication Property - Advances in Error-Correcting Codes Theory

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Explore error-correcting codes with multiplication properties, focusing on recent advancements and theoretical implications in coding theory.
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1 Lesons
46 minutes
On-Demand
Free-Video
Simons Institute

Dual of Evaluation Codes in Error-Correcting Theory

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Explore the mathematical concept of dual codes in error correction, focusing on evaluation codes and their properties in coding theory.
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1 Lesons
41 minutes
On-Demand
Free-Video
Simons Institute

Higher Order MDS Codes - Advances in Error-Correcting Code Theory

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Explore advanced concepts in error-correcting codes, focusing on Higher Order MDS Codes and their applications in data integrity and communication systems.
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1 Lesons
49 minutes
On-Demand
Free-Video
Fields Institute

Algebra in Algorithmic Coding Theory

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Explore algebraic techniques in algorithmic coding theory, focusing on error-correcting codes and their applications in computer science and information theory.
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1 Lesons
39 minutes
On-Demand
Free-Video
ACM SIGPLAN

Automated Detection of Under-Constrained Circuits in Zero-Knowledge Proofs

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Discover a novel technique for detecting vulnerabilities in zero-knowledge proof circuits, combining SMT solving with uniqueness inference to enhance security in blockchain applications.
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1 Lesons
19 minutes
On-Demand
Free-Video
BunG Seminar

The Stacks of n-Truncated Barsotti-Tate Groups - Part 3

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Delve into advanced algebraic geometry concepts focusing on n-smooth group schemes over F_p-schemes and their relationship with BT_n groups, exploring commutative structures and theoretical foundations.
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1 Lesons
2 hours 22 minutes
On-Demand
Free-Video
TheIACR

Private Multiplication over Finite Fields

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Explore secure multiparty computation techniques for private multiplication in finite fields, focusing on cryptographic protocols and their applications.
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1 Lesons
24 minutes
On-Demand
Free-Video
QuICS

Fast Enumeration Algorithm for Multivariate Polynomials Over General Finite Fields - Session II

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Explore fast enumeration algorithms for multivariate polynomials over finite fields, enhancing post-quantum cryptography understanding and applications.
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1 Lesons
22 minutes
On-Demand
Free-Video
Bill Buchanan OBE

Cryptography Fundamentals - Finite Fields and Galois Fields - Podcast 4

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Explore finite fields (Galois fields) in cryptography, covering key concepts and applications in secure communication and data protection.
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1 Lesons
20 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Quasirandomness of Definable Subsets of Definable Groups in Finite Fields

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Delve into advanced mathematical concepts exploring quasirandomness in definable subsets of finite field groups through expert analysis and theoretical frameworks.
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1 Lesons
54 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Towards a Formulation of the Birch and Swinnerton-Dyer Conjecture for Abelian Schemes Over Varieties Over Finite Fields

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Delve into advanced number theory concepts exploring the Birch and Swinnerton-Dyer conjecture's formulation for abelian schemes over finite field varieties, presented by mathematician Amilcar Pacheco.
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1 Lesons
51 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Projective Reed Muller Codes Revisited

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Explore projective Reed Muller codes with Sudhir Ghorpade, revisiting key concepts and recent developments in algebraic coding theory.
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1 Lesons
35 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

APN and AB Power Functions in Cryptography

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Explore APN and AB power functions in algebraic cryptography, focusing on their properties and applications in secure communication systems.
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1 Lesons
47 minutes
On-Demand
Free-Video
Institute for Advanced Study

An Improved Line-Point Low-Degree Test for Polynomials Over Finite Fields - Lecture

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Explore an improved line-point low-degree test for polynomials over finite fields, addressing a long-standing open question in low-degree testing with novel analysis techniques.
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1 Lesons
59 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Applied l-adic Cohomology I - Lecture 3

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Delve into advanced number theory concepts, exploring l-adic cohomology and trace functions through examples from modern analytic theory, with insights from Gauss, Weil, and Grothendieck's foundational work.
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1 Lesons
1 hour 51 minutes
On-Demand
Free-Video
Institute for Advanced Study

Counting Representations of Fuchsian Groups Over Finite Fields

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Delve into advanced mathematical concepts exploring representation theory of Fuchsian groups, character bounds, and their applications in high-dimensional classical groups and Zariski-dense subgroups.
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1 Lesons
1 hour
On-Demand
Free-Video
International Centre for Theoretical Sciences

Applied l-adic Cohomology - Lecture 1

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Delve into advanced number theory concepts, exploring l-adic cohomology and trace functions through Gauss's congruence theory and its modern applications in analytic number theory.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Applied l-adic Cohomology - Lecture 2

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Delve into advanced number theory concepts, exploring trace functions, l-adic cohomology, and their applications in modern analytic theory through examples from Weil, Grothendieck, and Deligne's work.
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1 Lesons
1 hour 57 minutes
On-Demand
Free-Video
Google TechTalks

Limitations of Stochastic Selection with Pairwise Independent Priors

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Explore stochastic selection problems with pairwise-independent priors and matroid constraints, examining limitations and optimal bounds for contention resolution and prophet inequalities.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Applied l-adic Cohomology I - Lecture 4

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Delve into advanced analytic number theory concepts, exploring trace functions, l-adic cohomology, and their applications in modern mathematics through expert insights from Philippe Michel.
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1 Lesons
2 hours 14 minutes
On-Demand
Free-Video