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#Algebraic Number Theory

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Fields Institute

Certain Polytopes Associated to Algebraic Integer Conjugates

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Explore the fascinating world of algebraic number theory in this 40-minute Fields Number Theory Seminar presented by Samprit Ghosh from the University of Calgary. Delve into the intriguing relationship between certain polytopes and algebraic integer conj…
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1 Lesons
40 minutes
On-Demand
Free-Video
ICTP Mathematics

Standard and Less Standard Asymptotic Methods - Lecture 3

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Explore advanced asymptotic methods for evaluating infinite sums and recognizing sequence patterns, with practical examples and techniques for high-precision numerical computations.
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11 Lesons
1 hour 41 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Using Structured Variants in Lattice-Based Cryptography - Lecture 1

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Explorez les variantes structurées en cryptographie post-quantique basée sur les réseaux. Approfondissez les fondements mathématiques et les applications pratiques de cette approche innovante.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Using Structured Variants in Lattice-Based Cryptography - Lecture 2

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Explorez les variantes structurées en cryptographie sur réseaux. Approfondissez les concepts avancés et leurs applications dans ce domaine mathématique complexe.
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1 Lesons
1 hour 25 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Galois Representations and Statistics - Lecture 1

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Explore Galois representations and statistics in arithmetic through an advanced mathematical lecture by René Schoof.
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1 Lesons
1 hour
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Class Field Theory Standpoint and Its Three Fundamental Generalisations - Lecture 2

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Delve into advanced class field theory concepts, exploring Takagi's existence theory, Mochizuki's IUT theory, and modern perspectives on Langlands program and anabelian geometry.
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1 Lesons
2 hours 2 minutes
On-Demand
Free-Video
Insights into Mathematics

Algebraic Number Theory and Rings I - Math History - NJ Wildberger

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Explore algebraic number theory and rings, focusing on extension fields, Gaussian integers, and the development of abstract ring theory in 19th-century mathematics.
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7 Lesons
48 minutes
On-Demand
Free-Video
ICTP Mathematics

From Knots to Number Theory II

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Explore connections between quantum knot invariants and number theory, covering topics like hyperbolic topology, Kashaev invariant, and quantum modularity. No prior knowledge required.
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13 Lesons
1 hour 21 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Two Mathematicians, Their Work and Career Experiences - Radhika Ganapathy and Purvi Gupta

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Explore cyclotomic fields in number theory and convexity in complex analysis through lectures by two accomplished mathematicians, offering insights into their research and career experiences.
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1 Lesons
2 hours 53 minutes
On-Demand
Free-Video
ICTP Mathematics

From Knots to Number Theory I

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Explore connections between quantum knot invariants and number theory, covering hyperbolic topology, Kashaev invariant, and quantum modularity. No prior knowledge required.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
ICTP Mathematics

Bounds on the Number of Generators of Prime Ideals

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Explore prime ideals and their generators, focusing on mathematical bounds and theoretical implications in algebraic geometry and commutative algebra.
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1 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

Algebraic Number Theory and Rings - Math History II

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Explores 19th-century algebraic number theory, focusing on extension fields, abstract rings, and algebraic integers. Discusses Gaussian integers, unique factorization, and foundational challenges in the field.
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1 Lesons
27 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Genus of Division Algebras Over Discrete Valued Fields

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Exploration of division algebras over discrete valued fields, focusing on their genus. Covers advanced algebraic concepts and their applications in number theory and field theory.
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1 Lesons
21 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 2

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Explore advanced topics in linear groups and Diophantine approximation, focusing on bounded generation and its applications in number theory and geometric analysis.
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1 Lesons
53 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Hasse Principle for Reductive Groups over P-Adic Function Fields

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Explore the Hasse Principle for reductive groups over p-adic function fields in this advanced mathematics lecture by Raman Parimala, part of a program on Zariski dense subgroups and number theory.
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1 Lesons
58 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Central Extensions of Arithmetic Lattices by Matthew Stover

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Explore central extensions of arithmetic lattices, focusing on techniques from algebraic and analytic number theory. Gain insights into applications in geometry, topology, and mathematical physics.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Conjugacy Width in Higher Rank Arithmetic Groups of Orthogonal Type by Chen Meiri

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Explore conjugacy width in higher rank arithmetic groups of orthogonal type, examining its properties and implications for group theory and related mathematical fields.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

On the Hasse Principle for Reductive Algebraic Groups Over Finitely Generated

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Explore the Hasse Principle for reductive algebraic groups over finitely generated fields, delving into advanced number theory and algebraic geometry concepts.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Fields Institute

Some Research Problems in Number Theory

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Explore intriguing research problems in number theory with Ram Murty, delving into advanced mathematical concepts and unsolved questions in this fascinating field.
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1 Lesons
43 minutes
On-Demand
Free-Video
Fields Institute

The ABC Conjecture in Number Theory

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Explore the ABC conjecture with insights from Prof. M. Ram Murty, presented by Hector Pasten Vasquez. Gain a deeper understanding of this fundamental mathematical concept.
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1 Lesons
31 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

Number Systems - Foundations and Applications in Mathematics

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Explore the foundations of mathematics through an in-depth examination of number systems, presented by Kevin Hare from the University of Waterloo.
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1 Lesons
49 minutes
On-Demand
Free-Video
Fields Institute

Exponential Relations Among Algebraic Integer Conjugates

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Explore exponential relations between algebraic integer conjugates, delving into advanced number theory concepts and their implications in mathematical research.
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1 Lesons
17 minutes
On-Demand
Free-Video
Fields Institute

Hasse Principle for Function Fields

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Explore the Hasse principle's application to function fields, delving into its mathematical implications and theoretical foundations.
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1 Lesons
37 minutes
On-Demand
Free-Video
Fields Institute

Iwasawa Theory in a Family of Z_p-Extensions

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Explore advanced number theory concepts, focusing on Iwasawa theory in Z_p-extensions families. Gain insights from expert Sujatha Ramdorai on this specialized mathematical topic.
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1 Lesons
44 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Finite Flat Group Schemes over Z

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Explore finite flat group schemes over Z with René Schoof in this advanced arithmetic geometry lecture from the CIRM Symposium.
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1 Lesons
53 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Counting S4 and S5 Extensions Satisfying the Hasse Norm Principle

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Explore counting techniques for S4 and S5 extensions satisfying the Hasse norm principle in this advanced mathematical lecture by Rachel Newton.
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1 Lesons
56 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

An Invitation to Globally Valued Fields

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Explore globally valued fields in mathematics through an in-depth lecture by Ehud Hrushovski, delving into advanced concepts and their applications.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Existential Closedness of Qalg as a Globally Valued Field

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Explore existential closedness of Qalg as a globally valued field in advanced mathematical theory. Delve into complex concepts with expert Michal Szachniewicz.
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1 Lesons
42 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

The Average Size of 3-Torsion in Class Groups of 2-Extensions

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Explore 3-torsion in class groups of 2-extensions with Melanie Matchett Wood. Delve into advanced number theory concepts and their statistical implications in this mathematical lecture.
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1 Lesons
53 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Arithmetic Statistics: Concepts and Applications

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Explore arithmetic statistics through an in-depth lecture, covering key concepts and recent developments in this mathematical field.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Subrings of Number Fields

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Explore subrings of number fields with Hendrik Lenstra in this advanced mathematical lecture on arithmetic statistics.
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1 Lesons
53 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Class Field Theory - Lecture 1

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Explore fundamental concepts of class field theory in this advanced mathematics lecture, delving into algebraic number theory and Galois theory.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Institute for Advanced Study

Determinants of Cohomology for Number Fields

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Explore determinants of cohomology in number fields, delving into advanced mathematical concepts and their applications in algebraic number theory.
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1 Lesons
18 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Local Fields in Lean

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Explore local fields using the Lean theorem prover, focusing on mathematical foundations and practical applications in number theory and algebraic geometry.
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1 Lesons
56 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Sato-Tate Conjecture for Bianchi Modular Forms

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Explore potential automorphy results for Ramanujan and Sato-Tate conjectures in GL(2) over imaginary quadratic fields, extending previous work and introducing new mathematical concepts.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
BIMSA

The Langlands Project - Connecting Automorphic Forms and Number Theory

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Explore the Langlands project's deep connection between automorphic forms and arithmetic, tracing its roots and current challenges in mathematics.
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1 Lesons
56 minutes
On-Demand
Free-Video
BIMSA

Homological Aspects of Branching Laws in p-adic Groups

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Explore homological aspects of branching laws for p-adic group representations, focusing on restriction to subgroups and projective representations in Bernstein blocks.
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1 Lesons
59 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Dense Embeddings of Hyperbolic Manifold Groups

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Explore dense embeddings of hyperbolic manifold groups, focusing on amalgamated products and linear Lie groups. Learn strategies to control properties of output embeddings.
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1 Lesons
41 minutes
On-Demand
Free-Video
BIMSA

Homological Aspects of Branching Laws in p-adic Groups

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Explore homological aspects of branching laws for p-adic group representations, focusing on restriction to subgroups and projective representations in Bernstein blocks.
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1 Lesons
59 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

Average Heights of Abelian Varieties with Complex Multiplication

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Explore the arithmetic properties of abelian varieties with complex multiplication, focusing on Colmez's conjecture and its implications for periods and L-functions.
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1 Lesons
50 minutes
On-Demand
Free-Video
BIMSA

The Combinatorics of Finite Simple Groups - ICBS 2024

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Explore the interplay between finite simple groups, combinatorics, and group theory, examining recent developments and introducing algebraic tools for geometric structures.
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1 Lesons
43 minutes
On-Demand
Free-Video
BIMSA

Multivariable (φ, Γ)-Modules and Local-Global Compatibility

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Explore multivariable $(\varphi, \Gamma)$-modules, extending Colmez's construction to $\mathrm{GL}_2(K)$ representations and comparing with Galois representations in mod $p$ cohomology of Shimura curves.
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1 Lesons
54 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

K2 of Elliptic Curves over Non-Abelian Cubic and Quartic Fields

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Explore K_2 of elliptic curves over non-Abelian fields, including constructions, integral elements, and numerical verification of Beilinson's conjecture. Joint work with Brunault, Hang, and Rodriguez Villegas.
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1 Lesons
59 minutes
On-Demand
Free-Video
TheIACR

Mildly Short Vectors in Ideals of Cyclotomic Fields Without Quantum Computers - MathCrypt 2022

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Explore norm relations in cyclotomic fields and their applications to cryptography, focusing on finding short vectors in ideals without quantum computers.
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9 Lesons
25 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Low Lying Zeros in Families Related to Complex Multiplication Elliptic Curves

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Delve into advanced number theory concepts focusing on low-lying zeros and their relationship to CM elliptic curves, exploring mathematical patterns and theoretical frameworks in this specialized mathematical domain.
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1 Lesons
51 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

On Lehmer's Problem and Hyperbolic Geometry

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Delve into the fascinating connection between Lehmer's problem and hyperbolic geometry through an advanced mathematical exploration of number theory concepts and geometric principles.
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1 Lesons
54 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Factorizations, Elasticities and Zero-Sum Sequences

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Delve into advanced number theory concepts focusing on factorizations, elasticities, and zero-sum sequences through a mathematical exploration of their properties and relationships.
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1 Lesons
51 minutes
On-Demand
Free-Video
Fields Institute

The Period-Index Problem for Higher Degree Galois Cohomology Groups Over Hensel Semi-Global Fields

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Delve into advanced Galois cohomology theory, exploring period-index relationships over Hensel semi-global fields and their implications for higher degree groups.
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1 Lesons
51 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

L-functions of Elliptic Curves Over Real Quadratic Fields as Special Values of Automorphic Green's Functions

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Delve into advanced number theory concepts exploring L-functions of elliptic curves over real quadratic fields and their relationship to automorphic Green's functions through expert mathematical analysis.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
BIMSA

Heuristics for the Arithmetic of Elliptic Curves and Abelian Varieties

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Explore probabilistic models for elliptic curve arithmetic, examining theoretical evidence and predictions for higher-dimensional abelian varieties.
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1 Lesons
1 hour
On-Demand
Free-Video
International Centre for Theoretical Sciences

Relation Between Low-lying Zeros and Central Values

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Explore the intricate relationship between low-lying zeros and central values in number theory through advanced mathematical analysis and circle method applications.
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1 Lesons
57 minutes
On-Demand
Free-Video