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#Arithmetic Geometry

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Tom Rocks Maths

Mordell Conjecture and the 1986 Fields Medal - Interview with Gerd Faltings

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Explore Gerd Faltings' groundbreaking work on the Mordell Conjecture, his Fields Medal journey, and insights into Arithmetic Geometry through an engaging interview with Oxford mathematician Dr Tom Crawford.
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1 Lesons
18 minutes
On-Demand
Free-Video
Institute for Advanced Study

On the Converse to Eisenstein's Last Theorem

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Explore Eisenstein's theorem and its converse, examining algebraic functions, Taylor expansions, and ODEs. Delve into joint research on conditions for algebraicity and related conjectures.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Institute for Advanced Study

Galois, Grothendieck and Voevodsky - George Shabat

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Explore the mathematical legacies of Galois, Grothendieck, and Voevodsky, focusing on their contributions to group theory, algebraic geometry, and category theory, with insights into dessins d'enfants and Belyi pairs.
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20 Lesons
58 minutes
On-Demand
Free-Video
ICTP Mathematics

Ecuaciones Diofantinas con Pocas Soluciones - Lecture 4

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Explora teoremas y aplicaciones en ecuaciones diofantinas, incluyendo el teorema de Faltings para curvas y ejemplos prácticos, profundizando en la teoría de números.
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5 Lesons
50 minutes
On-Demand
Free-Video
ICTP Mathematics

AGRA IV - Diophantine Equations with Few Solutions - Lecture 5

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Exploración avanzada de ecuaciones diofantinas con énfasis en casos con soluciones limitadas, presentada por el experto Hector Pasten de la PUC, Chile.
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1 Lesons
42 minutes
On-Demand
Free-Video
ICTP Mathematics

Ecuaciones Diofantinas con Pocas Soluciones - Lecture 3

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Explora ecuaciones diofantinas con pocas soluciones, profundizando en conceptos avanzados de teoría de números y álgebra abstracta.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
ICTP Mathematics

Ecuaciones Diofantinas con Pocas Soluciones - Lecture 1

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Exploración de ecuaciones diofantinas con soluciones limitadas, enfocándose en técnicas avanzadas para analizar y resolver problemas en teoría de números.
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1 Lesons
50 minutes
On-Demand
Free-Video
ICTP Mathematics

Superficies Racionales sobre un Cuerpo - AGRA IV Minicourse 2, Lecture 1

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Exploración de superficies racionales sobre cuerpos: conceptos fundamentales y aplicaciones en geometría algebraica y teoría de números.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Hidden Symmetries of the Work of Jan Nekovář

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Explorez les principes unificateurs de la recherche de Jan Nekovar, des systèmes d'Euler aux variétés de Shimura quaternioniques, en passant par les résultats de parité pour les fonctions L.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Crystallinity Properties and Rigid Flat Connections Revisited

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Explorez les propriétés de cristallinité et les connexions plates rigides dans un cadre non propre, avec une nouvelle approche topologique et p-adique.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Formalizing Deligne's Theorem in Number Theory

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Explore Deligne's theorem in number theory, focusing on its formalization and implications for mathematical research and understanding.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Cycles de Torsion Non Détectés par l'Application de Jannsen

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Explorez les cycles de torsion non détectés par l'application de Jannsen dans cette conférence mathématique approfondie sur la géométrie arithmétique.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Torsion Points of Elliptic Curves via Berkovich Spaces over Z

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Explore torsion points of elliptic curves using Berkovich spaces over Z in this advanced mathematical lecture by Jérôme Poineau at CIRM's thematic meeting on global invariants of arithmetic varieties.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Fields Institute

Artin Reciprocity via Spheres

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Explore Artin reciprocity through spheres, covering functionality, logical construction, global fields, spectra, and K theory in this advanced mathematics lecture.
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11 Lesons
46 minutes
On-Demand
Free-Video
Fields Institute

Real Invariants in Arithmetic Geometry and Theta Series

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Explore arithmetic geometry, theta series, and real invariants in this advanced mathematical lecture, focusing on Euclidean lattices, algebraic geometry, and chromological invariants.
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14 Lesons
46 minutes
On-Demand
Free-Video
Simons Institute

Effective Arithmetic Geometry

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Explore advanced concepts in arithmetic geometry, focusing on effective methods and their applications in number theory and algebraic geometry.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Complex Dynamics and Arithmetic Geometry by Laura DeMarco

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Exploring connections between dynamical systems and arithmetic geometry, focusing on periodic points, torsion points, and algebraic curves in genus 2. Insights from polynomial dynamics and Julia sets illustrate key concepts.
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14 Lesons
1 hour 1 minute
On-Demand
Free-Video
ICTP Mathematics

Combinatoria de Superficies Quadriculadas e Geometria de Espacos de Modulos - Lecture 5

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Combinatoria de superficies quadriculadas e geometria de espacos de modulos: explorando conexões entre topologia, geometria e teoria dos números em espaços de módulos.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
ICTP Mathematics

Superficies Racionales sobre un Cuerpo - AGRA IV Minicourse 2 - Lecture 5

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Explora superficies racionales sobre cuerpos en esta conferencia avanzada de matemáticas, examinando conceptos clave y resultados recientes en geometría algebraica aritmética.
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1 Lesons
53 minutes
On-Demand
Free-Video
ICTP Mathematics

Combinatoria de Superficies Quadriculadas e Geometria de Espacos de Modulos - Lecture 4

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Exploración avanzada de combinatoria en superficies cuadriculadas y geometría de espacios de módulos, con énfasis en aplicaciones a la teoría de grupos y análisis.
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1 Lesons
57 minutes
On-Demand
Free-Video
ICTP Mathematics

Superficies Racionales sobre un Cuerpo - AGRA IV Minicourse 2 - Lecture 4

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Explora superficies racionales sobre cuerpos en esta conferencia avanzada de matemáticas, abordando conceptos de geometría algebraica y teoría de números.
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1 Lesons
56 minutes
On-Demand
Free-Video
ICTP Mathematics

Superficies Racionales sobre un Cuerpo - AGRA IV Minicourse 2 Lecture 3

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Explora superficies racionales sobre cuerpos, profundizando en conceptos avanzados de geometría algebraica y teoría de números con expertos internacionales.
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1 Lesons
55 minutes
On-Demand
Free-Video
ICTP Mathematics

AGRA IV - Combinatorics of Square-Tiled Surfaces and Geometry of Moduli Spaces - Lecture 2

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Exploración avanzada de combinatoria en superficies cuadriculadas y geometría de espacios de módulos, con énfasis en aplicaciones matemáticas y análisis profundo.
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1 Lesons
57 minutes
On-Demand
Free-Video
ICTP Mathematics

AGRA IV - Diophantine Equations with Few Solutions - Lecture 2

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Exploración avanzada de ecuaciones diofantinas con soluciones limitadas, enfocándose en técnicas analíticas y algebraicas para abordar problemas complejos en teoría de números.
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1 Lesons
58 minutes
On-Demand
Free-Video
ICTP Mathematics

Superficies Racionales sobre un Cuerpo - AGRA IV Minicourse 2, Lecture 2

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Explora superficies racionales sobre cuerpos, profundizando en conceptos avanzados de geometría algebraica y teoría de números con expertos internacionales.
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1 Lesons
55 minutes
On-Demand
Free-Video
ICTP Mathematics

Combinatoria de Superficies Quadriculadas e Geometria de Espacos de Modulos - Lecture 1

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Exploración de combinatoria en superficies cuadriculadas y geometría de espacios de módulos, abordando conceptos avanzados en matemáticas y análisis geométrico.
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1 Lesons
54 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Computational Aspects of Nonabelian Chabauty - Lecture 1

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Explore computational techniques for Nonabelian Chabauty methods in arithmetic geometry, focusing on rational points on modular curves and advanced number theory concepts.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 3

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Exploring advanced techniques in arithmetic geometry for analyzing rational points on modular curves, focusing on the Chabauty-Coleman-Kim method and its practical applications.
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1 Lesons
1 hour 51 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Classical and Quadratic Chabauty - Lecture 3

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Explore advanced techniques in arithmetic geometry: Classical and Quadratic Chabauty methods for studying rational points on modular curves, with applications to elliptic curves.
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1 Lesons
1 hour 51 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 2

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Explore advanced techniques in arithmetic geometry, focusing on the Chabauty-Coleman-Kim method for studying rational points on modular curves. Gain insights into theoretical foundations and practical applications.
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1 Lesons
1 hour 58 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 1

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Explore advanced techniques for studying rational points on modular curves, focusing on the Chabauty-Coleman-Kim method and its theoretical and practical applications in arithmetic geometry.
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1 Lesons
1 hour 54 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 4

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Explore advanced techniques in arithmetic geometry, focusing on the Chabauty-Coleman-Kim method for studying rational points on modular curves. Gain insights into theoretical foundations and practical applications.
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1 Lesons
1 hour 52 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Classical and Quadratic Chabauty - Lecture 3

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Explore advanced techniques in arithmetic geometry: Classical and Quadratic Chabauty methods for studying rational points on modular curves, with applications to elliptic curves.
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1 Lesons
1 hour 47 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Motivic Cohomology of Carlitz Twists and Its Relation to Zeta Values and Polylogarithms

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Explores t-motivic cohomology in function fields, focusing on Carlitz twists and their connections to zeta values and polylogarithms, drawing parallels with classical motivic theory.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Conjectural Asymptotics of Prime Orders of Points on Elliptic Curves Over Number

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Explores conjectural asymptotics of prime orders of points on elliptic curves over number fields, advancing understanding in arithmetic geometry and modular curve theory.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Automorphic Lefschetz Properties and L-Values

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Explore automorphic Lefschetz properties and L-values in arithmetic geometry with expert Arvind Nair. Gain insights into advanced concepts and their applications in number theory.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

On the Harris-Venkatesh Conjecture by Loic Merel

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Exploration of the Harris-Venkatesh conjecture in arithmetic geometry, focusing on rational points on modular curves and their implications for elliptic curves and modular forms.
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1 Lesons
3 hours 54 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

P-adic Adelic Metrics, P-adic Heights, and Rational Points on Curves by Padma Srinivasan

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Explore P-adic adelic metrics, P-adic heights, and their applications in studying rational points on curves with expert Padma Srinivasan in this advanced mathematics lecture.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Intersection Theory and the Mandelbrot Set

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Explores the Mandelbrot set's connections to arithmetic intersection theory, revealing new insights into this complex mathematical object. Joint work with Myrto Mavraki.
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1 Lesons
49 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Arakelov Self-Intersection Number on Modular Curves by Priyanka Mazumdar

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Exploration of Arakelov self-intersection numbers on modular curves, examining their geometric and arithmetic properties in the context of rational points and arithmetic geometry.
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1 Lesons
27 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

On the Local Constancy of Certain Mod P Galois Representations by Suneel Kumar

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Exploration of local constancy in mod p Galois representations, focusing on theoretical aspects and implications for arithmetic geometry and modular curves.
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1 Lesons
30 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Iwasawa Theory for the Fine Selmer Group of Elliptic Curves Over Anticyclotomic

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Explore Iwasawa theory for fine Selmer groups of elliptic curves over anticyclotomic extensions, delving into advanced arithmetic geometry concepts and their applications.
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1 Lesons
55 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

On Darmon's Program for the Generalized Fermat Equation of Signature - r, r, p - by Nicolas Billerey

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Exploration of Darmon's approach to solving generalized Fermat equations, focusing on signature (r,r,p). Discusses theoretical foundations and computational techniques in arithmetic geometry.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

On a Local-Global Principle for Quadratic Twists of Abelian Varieties by Francesc Fite

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Explore a local-global principle for quadratic twists of abelian varieties in this advanced mathematics lecture, delving into arithmetic geometry and number theory concepts.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Explicit Motivic Chabauty-Kim Method by David Corwin

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Explore the Explicit Motivic Chabauty-Kim Method for studying rational points on modular curves, combining advanced arithmetic geometry with computational techniques.
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1 Lesons
56 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Computing Local Galois Representations Modulo 2 by Shalini Bhattacharya

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Explore techniques for computing local Galois representations modulo 2, focusing on arithmetic geometry and modular curves. Gain insights into advanced mathematical concepts and their applications.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Eisenstein Cycles and Manin-Drinfeld Properties

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Explore Eisenstein cycles and Manin-Drinfeld properties in modular curves, focusing on rational points and their significance in arithmetic geometry. Gain insights from expert Debargha Banerjee.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

On the Solutions of Certain Diophantine Equations Over Totally Real Fields

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Explore solutions to specific Diophantine equations over totally real fields, delving into advanced number theory and algebraic geometry concepts.
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1 Lesons
30 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Bipartite Euler Systems for Certain Galois Representations by Pronay Karmakar

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Exploration of bipartite Euler systems for specific Galois representations, discussing advanced concepts in arithmetic geometry and number theory.
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1 Lesons
23 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Principle of Quadratic Chabauty and Nonsplit Cartan Modular Curves

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Explore advanced techniques for studying rational points on modular curves, focusing on quadratic Chabauty methods and nonsplit Cartan modular curves in arithmetic geometry.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Rational Points on Modular Curves - Lecture 3

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Explore advanced techniques for studying rational points on modular curves, focusing on geometry, Q-rational points, Chabauty methods, and computational aspects in arithmetic geometry.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Rational Points on Modular Curves - Lecture 2

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Explore advanced techniques for studying rational points on modular curves, focusing on geometry, Q-rational points, Chabauty methods, and computational aspects in arithmetic geometry.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Classical and Quadratic Chabauty - Lecture 2

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Explore advanced techniques in arithmetic geometry: Classical and Quadratic Chabauty methods for studying rational points on modular curves, with applications to elliptic curves.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Linear Representations of the Grothendieck-Teichmuller Group

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Explore linear representations of the Grothendieck-Teichmuller group in this advanced mathematics lecture, delving into complex algebraic and geometric concepts.
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1 Lesons
46 minutes
On-Demand
Free-Video
IMSA

Eigenvarieties and Arithmetic - Connection to L-Functions

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Explore eigenvarieties, p-adic automorphic forms, and their connection to L-functions. Discover the local geometry of eigenvarieties and its significance in arithmetic.
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1 Lesons
57 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 3

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Explores advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Builds on previous lectures to deepen understanding of these fundamental objects.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Rational Points on Modular Curves by Jan Vonk

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Explore advanced techniques for studying rational points on modular curves, focusing on theoretical and computational aspects in arithmetic geometry.
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1 Lesons
1 hour 34 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Ribet's Lemma in Residually Indistinguishable Case by Mahesh Kakde

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Exploration of Ribet's Lemma in the context of residually indistinguishable cases, delving into advanced concepts in arithmetic geometry and modular curves theory.
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1 Lesons
59 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Iwasawa Theory for Rankin-Selberg L-Function at an Eisenstein Prime

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Explores Iwasawa theory for Rankin-Selberg L-functions at Eisenstein primes, delving into advanced arithmetic geometry concepts and their applications in number theory.
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1 Lesons
31 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 1

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Explore modular forms, elliptic curves, and modular curves in this advanced lecture. Gain insights into arithmetic geometry and the study of rational points on varieties.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 2

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Explore advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Gain insights into rational points and their significance in number theory.
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1 Lesons
1 hour 40 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 4

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Explore advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Gain insights from expert Eknath Ghate in this in-depth lecture.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Singular Moduli for Real Quadratic Fields - An Update by Jan Vonk

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Explore singular moduli for real quadratic fields with Jan Vonk. Learn about recent developments, theoretical insights, and computational aspects in this advanced arithmetic geometry lecture.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Equidistribution of Matrix Valued Gauss Sums by C. S. Rajan

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Explore equidistribution of matrix-valued Gauss sums in this advanced mathematics lecture, delving into arithmetic geometry and modular curves.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Towards Strong Uniformity for Isogenies of Prime Degree by Barinder Singh Banwait

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Explores strong uniformity for prime degree isogenies in arithmetic geometry, focusing on modular curves and rational points. Advances theoretical understanding and computational methods in this specialized field.
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1 Lesons
57 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Quadratic Twist of Epsilon Factor of Symmetric Cube Transfers of Modular Form by Sudipa Mondal

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Explores quadratic twists of epsilon factors for symmetric cube transfers of modular forms, delving into advanced concepts in arithmetic geometry and number theory.
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1 Lesons
26 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

On the Pseudonullity of Fine Selmer Groups Over Function Fields by Sohan Ghosh

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Explores pseudonullity of fine Selmer groups over function fields, advancing understanding in arithmetic geometry and modular curves. Contributes to research on rational points and algebraic structures.
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1 Lesons
22 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Uniform Versions of Shafarevich Conjecture by Plawan Das

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Exploring uniform versions of Shafarevich Conjecture in arithmetic geometry, focusing on rational points on modular curves and their implications for elliptic curves and modular forms.
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1 Lesons
54 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Rational Points on Modular Curves - Lecture 1

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Explore advanced concepts in arithmetic geometry, focusing on rational points on modular curves. Gain insights into theoretical and computational aspects of this fascinating field of mathematics.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Classical and Quadratic Chabauty - Lecture 1

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Explore advanced techniques for studying rational points on modular curves, focusing on classical and quadratic Chabauty methods in arithmetic geometry.
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1 Lesons
1 hour 23 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
Hausdorff Center for Mathematics

Beilinson's Conjecture for the Dwork Family

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Explores Beilinson's conjecture for the Dwork family, focusing on constructing classes in higher Chow groups and computing their regulators in relation to motivic L-functions and automorphic forms.
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1 Lesons
54 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Bruhat-Tits Theory - Lecture 1

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Comprehensive introduction to Bruhat-Tits theory, exploring its foundations and applications in algebraic groups and number theory. Ideal for advanced mathematics students and researchers.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 1

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Explore Zariski-dense subgroups, number theory, and geometric applications in this lecture on bounded generation of linear groups and Diophantine approximation.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Arithmetic Field Theory for Elliptic Curves by Minhyong Kim

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Explore advanced arithmetic field theory for elliptic curves, focusing on rational points on modular curves, Chabauty methods, and computational aspects in arithmetic geometry.
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1 Lesons
1 hour 47 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Counting Rational Points on Modular Curves of Genus 0 Over Number Fields by Peter Bruin

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Explore techniques for counting rational points on modular curves of genus 0 over number fields, advancing understanding in arithmetic geometry and algebraic number theory.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Diophantine Stability for Elliptic Curves on Average by Anwesh Ray

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Explore Diophantine stability for elliptic curves, focusing on average-case analysis. Gain insights into arithmetic geometry and modular curves through advanced theoretical and computational approaches.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

A Simple Dichotomy in Serre's Uniformity Question by Davide Lombardo

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Explore Serre's Uniformity Question in arithmetic geometry, focusing on rational points on modular curves and their implications for elliptic curves and number theory.
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1 Lesons
2 hours 4 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

A Chabauty-Coleman-Caro-Pasten Bound in Higher Dimensions by Netan Dogra

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Explore advanced techniques in arithmetic geometry, focusing on rational points on modular curves and higher-dimensional varieties using Chabauty-Coleman-Caro-Pasten methods.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The ABC Mysteries - Exploring the Controversy of Mochizuki's Proof

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Explore the ABC conjecture controversy, its mathematical implications, and the societal impact on mathematical practice with Professor Minhyong Kim, a renowned expert in arithmetic geometry.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
Fields Institute

Integral Canonical Models of Exceptional Shimura Varieties

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Explore advanced mathematical concepts in exceptional Shimura varieties and their integral canonical models, presented by Jacob Tsimerman from the University of Toronto.
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1 Lesons
33 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
Galileo Galilei Institute

Motivic Galois Theory of Algebraic Mellin Transforms

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Explore the intricate connections between algebraic geometry and number theory through the lens of motivic Galois theory and Mellin transforms.
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1 Lesons
41 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

The Geometry and Arithmetic of Banana Nano-Manifolds

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Explore the geometry and arithmetic of banana nano-manifolds, focusing on new rigid Calabi-Yau threefolds and their Donaldson-Thomas partition functions, Gromov-Witten potentials, and modular properties.
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1 Lesons
1 hour 19 minutes
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Free-Video
M-Seminar, Kansas State University

Empty Real Plane Sextic Curves

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Explore K3-surfaces, complex sextic curves, and real plane sextics through arithmetic and homological types. Gain insights into equivariant equisingular deformation classification.
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1 Lesons
1 hour 22 minutes
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Centre International de Rencontres Mathématiques

Motives and Automorphic Representations

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Explore motives and automorphic representations in advanced mathematics with James Arthur's insightful conference talk at CIRM.
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1 Lesons
1 hour 4 minutes
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Isaac Newton Institute for Mathematical Sciences

Hasse Principle for Simply Connected Groups - Kirk Lecture

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Explore the Hasse principle for simply connected groups, its significance in number fields, and recent progress in function fields of curves over p-adic fields.
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1 Lesons
1 hour 3 minutes
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Institut des Hautes Etudes Scientifiques (IHES)

Moduli Spaces of Points on the Projective Line and Other Varieties with Many Symmetries

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Explore equivariant birational geometry through recent results and constructions presented by Yuri Tschinkel from SCGP & NYU.
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1 Lesons
59 minutes
On-Demand
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Institute for Advanced Study

Arithmetic Quantum Unique Ergodicity for Hyperbolic Manifolds

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Explore quantum unique ergodicity in hyperbolic manifolds, focusing on arithmetic aspects and their implications in mathematical physics and number theory.
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1 Lesons
21 minutes
On-Demand
Free-Video
Institute for Advanced Study

Non Abelian Hodge Theory in Positive Characteristic

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Explore non-abelian Hodge theory in positive characteristic with Siqing Zhang, delving into advanced mathematical concepts and their applications.
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1 Lesons
19 minutes
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Centre International de Rencontres Mathématiques

Smooth Plane Models for Modular Curves of Shimura Type

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Explore smooth plane models for modular curves of Shimura type, delving into advanced mathematical concepts and their applications in number theory.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Graded Lie Algebras and Families of Algebraic Curves

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Explore graded Lie algebras and their connection to algebraic curve families. Gain insights into natural questions, philosophy, and Thorne's construction in this mathematical symposium talk.
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10 Lesons
51 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
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Centre International de Rencontres Mathématiques

Computing Euler Factors of Curves

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Explore computational methods for determining Euler factors of curves in arithmetic geometry, focusing on advanced mathematical techniques and applications.
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1 Lesons
59 minutes
On-Demand
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Centre International de Rencontres Mathématiques

Computing Ceresa Classes of Curves

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Explore computational methods for Ceresa classes of curves in algebraic geometry, focusing on arithmetic and geometric aspects.
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1 Lesons
1 hour
On-Demand
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Centre International de Rencontres Mathématiques

Probabilistic Approaches to Rational Points on Algebraic Surfaces

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Explore probabilistic methods for studying rational points on algebraic surfaces, delving into advanced mathematical concepts and recent research developments.
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1 Lesons
1 hour 1 minute
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
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Centre International de Rencontres Mathématiques

Beyond the Fontaine-Wintenberger Theorem

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Explore advanced mathematical concepts beyond the Fontaine-Wintenberger theorem in this in-depth conference talk by Konstantinos Kartas.
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1 Lesons
1 hour 1 minute
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