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#Rational Points

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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
International Mathematical Union

Olivier Wittenberg- Some Aspects of Rational Points and Rational Curves

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Explore rational points and curves in algebraic geometry, examining their properties and connections to other mathematical concepts.
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1 Lesons
45 minutes
On-Demand
Free-Video
International Mathematical Union

The Number of Rational Points on a Curve of Genus at Least Two

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Explore the intriguing mathematical concept of rational points on higher genus curves, delving into advanced number theory and algebraic geometry.
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1 Lesons
45 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Roger Heath Brown - The Determinant Method, Lecture III

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Explore variants of the determinant method and its application to consecutive "powerful" numbers in algebraic number theory.
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1 Lesons
53 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
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
ICTP Mathematics

The Variance of a General Class of Multiplicative Functions in Short Intervals

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Explore the variance of multiplicative functions in short intervals, applying Fourier analysis and rational point counting to derive asymptotic estimates for k-free numbers and other functions.
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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
Hausdorff Center for Mathematics

Sections of Fano Fibrations Over Curves

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Explores Manin's conjecture on rational points in Fano varieties, focusing on exceptional sets and their impact on moduli spaces of sections in Fano fibrations, particularly del Pezzo fibrations.
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1 Lesons
58 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 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

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

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
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
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
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
Free-Video
Centre International de Rencontres Mathématiques

Minimal Torsion Curves in Geometric Isogeny Classes

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Explore minimal torsion curves in geometric isogeny classes, delving into advanced number theory concepts and computational techniques.
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1 Lesons
56 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

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

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
BIMSA

Sparsity of Rational Points on Curves - What is Known and What is Expected

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Explore the known results and open questions surrounding the sparsity of rational points on curves, gaining insights into this mathematical concept.
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1 Lesons
49 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Classical Circle Method - Lecture 3

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Delve into advanced number theory concepts through the Classical Circle Method, exploring its applications in analytic theory and rational point counting on varieties.
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1 Lesons
1 hour 20 minutes
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
International Centre for Theoretical Sciences

Systems of Many Forms with Differing Degrees

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Explore advanced circle method applications in number theory, focusing on rational point counting, prime numbers, and recent developments in L-functions and Langlands program theory.
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1 Lesons
56 minutes
On-Demand
Free-Video