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William Stein's Number Theory Research Blog

William Stein's Number Theory Research Blog. Monday, January 31, 2011. Higher rank curves with nontrivial Sha. I wonder if all of the problems are open. Here we consider pairs (E,p) where E is an elliptic curve over Q and p is a prime. Prove there are infinitely many pairs (E,p) such that: (a) E(Q) has rank = 2, and (b) Sha(E/Q)(p) is finite. Prove there are infinitely many pairs (E,p) such that: (a) E(Q) has rank = 2, and (b) Sha(E/Q)(p) is nonzero. Same questions but over a number field K. The computat...

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William Stein's Number Theory Research Blog | 389a.blogspot.com Reviews

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William Stein's Number Theory Research Blog. Monday, January 31, 2011. Higher rank curves with nontrivial Sha. I wonder if all of the problems are open. Here we consider pairs (E,p) where E is an elliptic curve over Q and p is a prime. Prove there are infinitely many pairs (E,p) such that: (a) E(Q) has rank = 2, and (b) Sha(E/Q)(p) is finite. Prove there are infinitely many pairs (E,p) such that: (a) E(Q) has rank = 2, and (b) Sha(E/Q)(p) is nonzero. Same questions but over a number field K. The computat...

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William Stein's Number Theory Research Blog | 389a.blogspot.com Reviews

https://389a.blogspot.com

William Stein's Number Theory Research Blog. Monday, January 31, 2011. Higher rank curves with nontrivial Sha. I wonder if all of the problems are open. Here we consider pairs (E,p) where E is an elliptic curve over Q and p is a prime. Prove there are infinitely many pairs (E,p) such that: (a) E(Q) has rank = 2, and (b) Sha(E/Q)(p) is finite. Prove there are infinitely many pairs (E,p) such that: (a) E(Q) has rank = 2, and (b) Sha(E/Q)(p) is nonzero. Same questions but over a number field K. The computat...

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389a.blogspot.com

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William Stein's Number Theory Research Blog: Tamagawa numbers and components groups at additive primes

http://389a.blogspot.com/2010/02/tamagawa-numbers-and-components-groups.html

William Stein's Number Theory Research Blog. Thursday, February 11, 2010. Tamagawa numbers and components groups at additive primes. I had an idea while driving back from snowboarding today that could lead to a nice paper if worked out. The problem is to find an algorithm to compute Tamagawa numbers of optimal newform modular abelian varieties $A$ at primes $p$ of additive reduction, say quotients of $J 0(N)$ with $p 2 mid N$. Cases this may already be enough to nail down the component group. I am a prof...

2

William Stein's Number Theory Research Blog: August 2010

http://389a.blogspot.com/2010_08_01_archive.html

William Stein's Number Theory Research Blog. Tuesday, August 24, 2010. Computational Projects: Part 1. I made a diagram that illustrates most of the algorithms I wish Sage. Had to support my current mathematical research program. I am focusing most of my Sage development effort on ensuring that these get implemented as soon as possible. I will not depend. Already, which makes it much easier for me to implement them in Sage. Research Versus the Goals of the Sage Project. For basic arithmetic, which at lea...

3

William Stein's Number Theory Research Blog: February 2010

http://389a.blogspot.com/2010_02_01_archive.html

William Stein's Number Theory Research Blog. Thursday, February 11, 2010. Tamagawa numbers and components groups at additive primes. I had an idea while driving back from snowboarding today that could lead to a nice paper if worked out. The problem is to find an algorithm to compute Tamagawa numbers of optimal newform modular abelian varieties $A$ at primes $p$ of additive reduction, say quotients of $J 0(N)$ with $p 2 mid N$. Cases this may already be enough to nail down the component group. I am a prof...

4

William Stein's Number Theory Research Blog: Kolyvagin's Conjecture: a status report

http://389a.blogspot.com/2010/08/kolyvagins-conjecture-status-report.html

William Stein's Number Theory Research Blog. Friday, August 20, 2010. Kolyvagin's Conjecture: a status report. During the Summer of 2009, I read some papers of Cornut, Vatsal, and Jetchev-Kane that were motivated by Mazur's conjecture about Heegner points. Meanwhile, I was thinking about Kolyvagin's conjecture on nontriviality of his Euler system of Heegner points. This is a conjecture about any elliptic curve E. The conjecture is simply that one of Kolyvagin's cohomology classes in H 1 (K. Last summer, ...

5

William Stein's Number Theory Research Blog: Computational Projects: Part 1

http://389a.blogspot.com/2010/08/computational-projects-part-1.html

William Stein's Number Theory Research Blog. Tuesday, August 24, 2010. Computational Projects: Part 1. I made a diagram that illustrates most of the algorithms I wish Sage. Had to support my current mathematical research program. I am focusing most of my Sage development effort on ensuring that these get implemented as soon as possible. I will not depend. Already, which makes it much easier for me to implement them in Sage. Research Versus the Goals of the Sage Project. For basic arithmetic, which at lea...

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homotopical.wordpress.com

2012 June « Motivic stuff

https://homotopical.wordpress.com/2012/06

Cohomology, homotopy theory, and arithmetic geometry. AMS Grad student blog. Archive for June, 2012. A long list of postdoc opportunities. Posted by Andreas Holmstrom on June 7, 2012. Having been through the process of finding and applying for postdoc positions in Europe over the last couple of years, here is now the big list that I wished someone had given me. A few years ago. Posted in Job opportunities. Posted by Andreas Holmstrom on June 6, 2012. Were delivered in February 2012 at IHES.

homotopical.wordpress.com

Resources « Motivic stuff

https://homotopical.wordpress.com/links

Cohomology, homotopy theory, and arithmetic geometry. AMS Grad student blog. A maths journal resource page. A short list of random links – this list will be much longer and more organised at some point. Motivic homotopy theory resources. Lecture notes of Jardine. GRASP: Geometric Langlands and more. The Black Forest volume. On the Beilinson conjectures. Ravenel’s page on the Arf-Kervaire invariant problem. Mathematical resources of Jinhyun Park. Leave a Reply Cancel reply. Enter your comment here.

wstein.org

students

http://wstein.org/wiki/students.html

See my research blog. Current Students (who I mentor). All students listed below are at University of Washington, unless otherwise noted. Alyson Deines (Ph.D. student):. Kolyvagin's conjecture over totally real fields. Joanna Gaski (Masters thesis student). Recent Students (who I played a nontrivial role mentoring). Robert Bradshaw (Ph.D. student, expected Ph.D. 2010):. Rigorous computation with complex-analytic L-functions (building on work of Dokchitser). P-adic heights and Monsky-Washnitzer cohomology.

automorphicforum.wordpress.com

Lectures on the Langlands conjectures | Automorphic Forum

https://automorphicforum.wordpress.com/2012/02/07/lectures-on-the-langlands-conjectures

Automorphic forms, number theory, representation theory, algebraic geometry, and other mathematics. Lectures on the Langlands conjectures. February 7, 2012 in number theory. One of the motivations of studying the Langlands Conjectures is the question. What are the finite extensions of the rational numbers? The local Langlands Conjectures give a dictionary between the Galois Theory of local fields and the representation theory of locally compact reductive groups. A Mind for Madness. Enter your comment here.

automorphicforum.wordpress.com

Local factors of automorphic representations associated to paramodular forms in the span of Gritsenko lifts | Automorphic Forum

https://automorphicforum.wordpress.com/2012/12/01/local-factors-of-automorphic-representations-associated-to-paramodular-forms-in-the-span-of-gritsenko-lifts

Automorphic forms, number theory, representation theory, algebraic geometry, and other mathematics. Local factors of automorphic representations associated to paramodular forms in the span of Gritsenko lifts. December 1, 2012 in automorphic forms. There are two well-known. Functions attached to Siegel modular forms of degree two. These are the Spin and the standard. Function. They have been studied by Andrianov, Böcherer, Shimura, and others. Other. Of cuspidal Jacobi newforms to. Were computed by Schmid...

homotopical.wordpress.com

2011 February « Motivic stuff

https://homotopical.wordpress.com/2011/02

Cohomology, homotopy theory, and arithmetic geometry. AMS Grad student blog. Archive for February, 2011. Motives conference in Mainz, July 4-8. Posted by Andreas Holmstrom on February 16, 2011. Conference on Motives, see webpage here. Invited speakers include Consani, Rost, Morel and Nori. Conference on Birch and Swinnerton-Dyer conjecture. Posted by Andreas Holmstrom on February 7, 2011. In Cambridge, May 4-6, 2011. Conference website. Derived categories workshop at Newton Institute in April. Chern: Dif...

homotopical.wordpress.com

2011 April « Motivic stuff

https://homotopical.wordpress.com/2011/04

Cohomology, homotopy theory, and arithmetic geometry. AMS Grad student blog. Archive for April, 2011. Summer school: Roadmap to cohomology theories. Posted by Andreas Holmstrom on April 24, 2011. Summer school in Brixen. Motivic conferences in 2011. Posted by Andreas Holmstrom on April 4, 2011. In addition to the already mentioned conference in Mainz. Here are some other events of possible interest:. Multiple zeta values, Modular forms, and Elliptic motives. Bristol, 3-6 May). Paris, 9-17 June). Oberwolf...

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William Stein's Number Theory Research Blog

William Stein's Number Theory Research Blog. Monday, January 31, 2011. Higher rank curves with nontrivial Sha. I wonder if all of the problems are open. Here we consider pairs (E,p) where E is an elliptic curve over Q and p is a prime. Prove there are infinitely many pairs (E,p) such that: (a) E(Q) has rank = 2, and (b) Sha(E/Q)(p) is finite. Prove there are infinitely many pairs (E,p) such that: (a) E(Q) has rank = 2, and (b) Sha(E/Q)(p) is nonzero. Same questions but over a number field K. The computat...

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