Number Theory over Function Fields - Lecture 3
Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
Number Theory over Function Fields - Lecture 2
Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
Number Theory over Function Fields - Lecture 1
Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
Local-Global Principles for Homogeneous Spaces Over Arithmetic Function Fields
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.
Tensor Rank and Bias of Multilinear Forms Over Finite Fields
Explorez les liens entre le rang tensoriel et le biais des formes multilinéaires sur les corps finis dans cette conférence mathématique approfondie.
Finite Point Configurations in Euclidean, Discrete, and Arithmetic Settings
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.
Point Counting over Finite Fields and the Cohomology of Moduli Spaces of Curves
Explore algebraic geometry through point counting over finite fields and cohomology of moduli spaces of curves, resolving longstanding questions and confirming Langlands program predictions.
Structure in the Search for Structure - Algebraic Number Theory and Motivic Cohomology
Explore algebraic number theory through analogies between numbers and shapes, including quadratic reciprocity and linking numbers, leading to insights on Tate's 1966 conjecture.
Towards a Mod p Langlands Correspondence for GL2
Explore the mod $p$ Langlands correspondence for $\mathrm{GL}_2(K)$, examining conjectures and recent progress in this open area of mathematical research.
Progression-Free Sets in Arithmetic Sequences
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.
Frobenius写像の周辺 - 第2回
Delve into advanced mathematical concepts of Frobenius mappings, finite fields, and Witt vectors through an accessible exploration of number theory fundamentals and polynomial rings.
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.
Homomorphic Encryption and Encrypted Search - Asiacrypt 2021
Explore advanced cryptographic techniques including balanced non-adjacent forms, encrypted data search, homomorphic encryption for finite fields, and improved bootstrapping for TFHE.
Parameterized Inapproximability of the Minimum Distance Problem over All Fields
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.
Fast List-Decoding of Univariate Multiplicity and Folded Reed-Solomon Codes
Explore advanced techniques for efficient list-decoding of Reed-Solomon codes, focusing on univariate multiplicity and folded variants in error-correcting code theory.
Codes with the Multiplication Property - Advances in Error-Correcting Codes Theory
Explore error-correcting codes with multiplication properties, focusing on recent advancements and theoretical implications in coding theory.
Dual of Evaluation Codes in Error-Correcting Theory
Explore the mathematical concept of dual codes in error correction, focusing on evaluation codes and their properties in coding theory.
Higher Order MDS Codes - Advances in Error-Correcting Code Theory
Explore advanced concepts in error-correcting codes, focusing on Higher Order MDS Codes and their applications in data integrity and communication systems.
Algebra in Algorithmic Coding Theory
Explore algebraic techniques in algorithmic coding theory, focusing on error-correcting codes and their applications in computer science and information theory.
Automated Detection of Under-Constrained Circuits in Zero-Knowledge Proofs
Discover a novel technique for detecting vulnerabilities in zero-knowledge proof circuits, combining SMT solving with uniqueness inference to enhance security in blockchain applications.
The Stacks of n-Truncated Barsotti-Tate Groups - Part 3
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.