Diophantine geometry | Zeta and L-functions | Millennium Prize Problems | Number theory | Conjectures
In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after mathematicians Bryan John Birch and Peter Swinnerton-Dyer, who developed the conjecture during the first half of the 1960s with the help of machine computation. As of 2022, only special cases of the conjecture have been proven. The modern formulation of the conjecture relates arithmetic data associated with an elliptic curve E over a number field K to the behaviour of the Hasse–Weil L-function L(E, s) of E at s = 1. More specifically, it is conjectured that the rank of the abelian group E(K) of points of E is the order of the zero of L(E, s) at s = 1, and the first non-zero coefficient in the Taylor expansion of L(E, s) at s = 1 is given by more refined arithmetic data attached to E over K. The conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay Mathematics Institute, which has offered a $1,000,000 prize for the first correct proof. (Wikipedia).
On the Fourier coefficients of a Cohen-Eisenstein series by Srilakshmi Krishnamoorthy
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
Rigidity of p-adic local systems and Abapplications to Shimura varieties by Ruochuan Liu
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
Root numbers and parity of local Iwasawa invariants by Suman Ahmed
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
The Most Difficult Math Problem You've Never Heard Of - Birch and Swinnerton-Dyer Conjecture
The Birch and Swinnerton-Dyer Conjecture is a millennium prize problem, one of the famed seven placed by the Clay Mathematical Institute in the year 2000. As the only number-theoretic problem in the list apart from the Riemann Hypothesis, the BSD Conjecture has been haunting mathematicians
From playlist Math
Stark-Heegner points and generalised Kato classes by Henri Darmon
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
On the 2-part of the Birch–Swinnerton-Dyer conjecture for elliptic curves by Zhibin Liang
12 December 2016 to 22 December 2016 VENUE Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution. An
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
A twisting result in non-commutative Iwasawa theory by Somnath Jha
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
Solving Diophantine equations using elliptic curves + Introduction to SAGE by Chandrakant Aribam
12 December 2016 to 22 December 2016 VENUE Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution. An
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
Solving Diophantine equations using elliptic curves + Introduction to SAGE by Chandrakant Aribam
12 December 2016 to 22 December 2016 VENUE Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution. An
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
Solving Diophantine equations using elliptic curves + Introduction to SAGE by Chandrakant Aribam
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
On exceptional zero conjecture (Mazur-Tate-Teitelbaum) by Srilakshmi Krishnamoorthy
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
On Class Number of Number Fields by Debopam Chakraborty
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
Introduction to the Birch-Swinnerton-Dyer conjecture - Talk by Prof. Dr. Guido Kings (Regensburg)
Aufzeichnung des Vortrags "Introduction to the Birch-Swinnerton-Dyer conjecture" von Prof. Dr. Guido Kings (Uni Regensburg). Teil der bundesweiten Reihe "Die 7 größten Abenteuer der Mathematik" zu den Millennium-Problemen. Teil des Colloquium Wilhelm Killing der WWU Münster. Abstract: A k
From playlist Mathematics Münster News
Torsion points of the Jacobian of modular curves X0(p2 ) and non- by Debargha Banerjee
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
p-adic uniformization of locally symmetric spaces by Aditya Karnataki
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
Coates-Wiles Theorem by Anupam Saikia
12 December 2016 to 22 December 2016 VENUE Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution. An
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
Comparing the corank of fine Selmer group and Selmer group of elliptic curves by Sudhanshu Shekhar
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture