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I was a Program in Computing Assistant Adjunct Professor in the Department of Mathematics at UCLA (2007-2011) and am a SAGEvangelist (2005-).
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Describe the pages in this category...   - http://www-scf.usc.edu/~burhanud
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To add a page to this category, add a link to this page on the last line of the page. You can add multiple categories to a page.   - http://www.math.ucla.edu/people/pages/burhanud.shtml
  
  - http://sage.math.washington.edu/home/burhanud
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'''List of pages in this category:''' === Papers ===
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[[FullSearch()]] http://sage.math.washington.edu/home/burhanud/papers
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CategoryCategory
1. Deciding whether the p-torsion group of the Q_p-rational points of an elliptic curve is non-trivial.
ANTS VI Poster Abstracts. SIGSAM Bulletin, Volume 38, Number 3 September 2004 Issue 149.
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www-scf.usc.edu/~burhanud Abstract: This note describes an algorithm to decide whether an elliptic curve over Q_p has a non-trivial p-torsion part (# E(Q_p)[p] is not equal to 1) under certain assumptions.

http://sage.math.washington.edu/home/burhanud/papers/burhanuddin.elliptic.curve.p-adic.torsion.pdf

2. Elliptic curve torsion points and division polynomials
Computational Aspects of Algebraic Curves, T. Shaska (Ed.), Lecture Notes Series on Computing, 13 (2005), 13--37, World Scientific.

Abstract: We present two algorithms - p-adic and l-adic - to determine E(Q)_{tors} the group of rational torsion points on an elliptic curve. Another algorithm we introduce is one which decides whether an elliptic curve over Q_p has a non-trivial p-torsion part and this comes into play in the p-adic torsion computation procedure. We also make some remarks about the discriminant of the m-division polynomial of an elliptic curve and the information it reveals about torsion points.

http://sage.math.washington.edu/home/burhanud/papers/burhanuddin.elliptic.curve.rational.torsion.pdf

3. Some computational problems motivated by the Birch and Swinnerton-Dyer conjecture, Ph.D. dissertation, University of Southern California, 2007.

Abstract:

http://sage.math.washington.edu/home/burhanud/papers/burhanuddin.dissertation.pdf

4. On projectively rational lifts of mod $7$ Galois representations, with Luis Dieulefait. JP Journal of Algebra, Number Theory and Applications, Volume 20, Issue 1, 109 -- 119, February 2011.

Abstract:

http://sage.math.washington.edu/home/burhanud/papers/burhanuddin.mod.7.galois.representations.pdf

5. Elliptic curves with large Shafarevich-Tate group

Abstract: We show that there exist infinitely many elliptic curves with Shafarevich-Tate group of order essentially as large as the the square root of the minimal discriminant assuming certain conjectures. This improves on a result of de Weger.

http://sage.math.washington.edu/home/burhanud/papers/burhanuddin.elliptic.curve.large.sha.pdf



=== Stuff I have worked/am working/plan to work on wrt to SAGE ===

* Doctoral dissertation [[http://www.sagemath.org/files/thesis/burhanuddin-thesis-2007.pdf]]

* On the reducibility of Hecke polynomials over ZZ [[http://sage.math.washington.edu/home/burhanud/heckered/heckered.pdf]]


* Mestre's method of graphs project which started at the [[http://modular.math.washington.edu/msri06|MSRI Computing with Modular Forms]] workshop.

  Check out:

    code http://sage.math.washington.edu/home/burhanud/SSMod/ssmod.py.txt

    slides http://sage.math.washington.edu/home/burhanud/msri_talk.pdf

    pictures http://sage.math.washington.edu/home/burhanud/msri06

* Implementing asymptotically fast elliptic curve rational torsion computation algorithms.

  kurrently kludgey kode http://sage.math.washington.edu/home/burhanud/tor/tor.py.txt

  algorithms http://modular.math.washington.edu/home/burhanud/volume.pdf


* My research is pretty SAGEy

  Research Statement http://sage.math.washington.edu/home/burhanud/app11/restat11/iftikhar.burhanuddin.restat11.pdf


=== Old Stuff ===

* [[Talks| Make wikipage about Talks related to SAGE (plan)]]

* Editing the SAGE programming guide in time for the release of sage-2.0

  http://modular.math.washington.edu/sage/doc/html/prog/index.html

* Editing the SAGE reference manual (and build process?) in time for the release of sage-2.0 (plan)

  http://sage.math.washington.edu/sage/doc/html/ref/index.html


* Wrapping Denis Simon's 2-descent (plan)

* Dekinking some SAGE tab completion kinks (plan)

* SAGE + Parallel, The Problem Book (plan)
  
  http://sage.math.washington.edu/msri07

* [[http://modular.math.washington.edu/sage/apps/|Example Scripts]]

CategoryHomepage

I was a Program in Computing Assistant Adjunct Professor in the Department of Mathematics at UCLA (2007-2011) and am a SAGEvangelist (2005-).

Papers

http://sage.math.washington.edu/home/burhanud/papers

1. Deciding whether the p-torsion group of the Q_p-rational points of an elliptic curve is non-trivial. ANTS VI Poster Abstracts. SIGSAM Bulletin, Volume 38, Number 3 September 2004 Issue 149.

Abstract: This note describes an algorithm to decide whether an elliptic curve over Q_p has a non-trivial p-torsion part (# E(Q_p)[p] is not equal to 1) under certain assumptions.

http://sage.math.washington.edu/home/burhanud/papers/burhanuddin.elliptic.curve.p-adic.torsion.pdf

2. Elliptic curve torsion points and division polynomials Computational Aspects of Algebraic Curves, T. Shaska (Ed.), Lecture Notes Series on Computing, 13 (2005), 13--37, World Scientific.

Abstract: We present two algorithms - p-adic and l-adic - to determine E(Q)_{tors} the group of rational torsion points on an elliptic curve. Another algorithm we introduce is one which decides whether an elliptic curve over Q_p has a non-trivial p-torsion part and this comes into play in the p-adic torsion computation procedure. We also make some remarks about the discriminant of the m-division polynomial of an elliptic curve and the information it reveals about torsion points.

http://sage.math.washington.edu/home/burhanud/papers/burhanuddin.elliptic.curve.rational.torsion.pdf

3. Some computational problems motivated by the Birch and Swinnerton-Dyer conjecture, Ph.D. dissertation, University of Southern California, 2007.

Abstract:

http://sage.math.washington.edu/home/burhanud/papers/burhanuddin.dissertation.pdf

4. On projectively rational lifts of mod 7 Galois representations, with Luis Dieulefait. JP Journal of Algebra, Number Theory and Applications, Volume 20, Issue 1, 109 -- 119, February 2011.

Abstract:

http://sage.math.washington.edu/home/burhanud/papers/burhanuddin.mod.7.galois.representations.pdf

5. Elliptic curves with large Shafarevich-Tate group

Abstract: We show that there exist infinitely many elliptic curves with Shafarevich-Tate group of order essentially as large as the the square root of the minimal discriminant assuming certain conjectures. This improves on a result of de Weger.

http://sage.math.washington.edu/home/burhanud/papers/burhanuddin.elliptic.curve.large.sha.pdf

Stuff I have worked/am working/plan to work on wrt to SAGE

* Doctoral dissertation http://www.sagemath.org/files/thesis/burhanuddin-thesis-2007.pdf

* On the reducibility of Hecke polynomials over ZZ http://sage.math.washington.edu/home/burhanud/heckered/heckered.pdf

* Mestre's method of graphs project which started at the MSRI Computing with Modular Forms workshop.

* Implementing asymptotically fast elliptic curve rational torsion computation algorithms.

* My research is pretty SAGEy

Old Stuff

* Make wikipage about Talks related to SAGE (plan)

* Editing the SAGE programming guide in time for the release of sage-2.0

* Editing the SAGE reference manual (and build process?) in time for the release of sage-2.0 (plan)

* Wrapping Denis Simon's 2-descent (plan)

* Dekinking some SAGE tab completion kinks (plan)

* SAGE + Parallel, The Problem Book (plan)

* Example Scripts

CategoryHomepage

IftikharBurhanuddin (last edited 2022-04-11 03:51:51 by mkoeppe)