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I'm Jamie Weigandt, I am graduate student in the department of mathematics specializing in Algorithmic Number Theory, Arithmetic Algebraic Geometry, and Arithmetic Statistics.
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==Jamie Weigandt==
  
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= Note on this page  =
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[[Image:jamie.jpg|160px]]
  
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For the time being I will use LaTeX code freely when editing this page.  
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Jamie Weigandt is an alumnus of the Purdue mathematics department (2008) and starting his third year of graduate studies in the same department. He's beginning his second year in the National Science Foundation's Graduate Research Fellowship Program studying Algebra and Number Theory with Prof. Edray Goins. He's particularly interested computational and statistical questions concerning the arithmetic of elliptic curves.
  
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== Random Thoughts About Rhea as I use it  ==
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= Note on this page  =
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*Can we add LaTeX functionality with jsmath, at least for the pages relevant to mathematicians?
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*Can we add the option to "Open Poor editior in a new window"? The sidebar gets too big when I increase the font size to see in safari.
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= Musician of Number Theorist =
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This is game that my friend Beard and I invented. You go about describing someone, and then you ask if they are a musician or a number theorist.
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SPOILER: the one caveat of the game is that no matter how much the person sounds like a musician, they're always a number theorist. Clearly choosing Daniel Snaith or Noam Elkies is just cheating. :)
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= The Bigfoot Project  =
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As a motivating project for learning a lot of background material I am engaged in what I consider a mythical quest to find an elliptic curve over $\Bbb Q$ with torsion subgroup $Z_2 \times Z_8$ and Mordell-Weil rank at least 4. Such a curve is affectionally referred to by my friends and I as "The Bigfoot." This nomenclature is somewhat misleading, such a curve, should it exist is not by any stretch of the imagination expected to be unique. I hope to expound on the status of this project at a later date.
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For now I will be motivated in my development of this page by 3 facts:
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*My bank account is suffering from conference fatigue.
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*There is an essay contest for which I can win $100.
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*I'd like to stop eating at Taco Bell.
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That being said I'll get right to this following section:
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= Why do I "math"? =
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I spent a few days spinning my wheels thinking about why I do mathematics, getting bogged down in details quite a bit. Then suddenly I realized that a friend had asked me this question just a month ago, at which point I'd instantly given a concise three-word answer.  
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For the time being I will use LaTeX code freely when editing this page. When the jsmath plugin is installed it should TeX on the fly in your browser.
  
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I doubt this three word answer will be sufficient for anyone reading this who hasn't experienced a great passion for mathematics firsthand, so I will attempt henceforth to paint a picture of what went through my mind in the split-second before I gave my answer.
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= Projects =
  
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I've come to recognize mathematics as both a game and an art form, much like I fell profession musicians view their craft. Much the way that young musicians are inspired by previously established artists, I have my own mathematical "influences". First and foremost is my advisor Edray Goins. The two of us are both very influenced by Barry Mazur, whose enthusiasm for the beauty of mathematics is infections. (See [http://video.google.com/videoplay?docid=8269328330690408516# this video] about the proof of Fermat's Last Theorem.) In his popular book ''Imagining Numbers: Particularly the Square Root of Minus Fifteen'', Mazur compares mathematicians to bees.  
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I'm hoping to use this space to describe some of my current projects. These include
  
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''Our gathering of the honey of the imaginative world is not immediate; it takes work. But though it requires traveling some distance, merging with something not of our species, communicating by dance to our fellow creatures what we've done and where we've been, and, finally, bringing back that single glistening drop, it is an activity we do without contortion. It is who we bees are.''
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* A database of Elliptic Curves with Prescribed Torsion
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* Connections between the Mordell-Weil ranks and Szpiro Ratios of elliptic curves
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* Finding elliptic curves of conductor less than $10^6$ which do not appear in the Stein-Watkins database.
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* Transfers that Track Down Atypical ABC Triples. (I was feeling whimsical... deal with it!)
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* Work with Matt Davis and James Ryan concerning the Erdös-Woods problem.
  
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While I immediately identified with these bees months ago I've found it even more relevant in the past two months. I've spent the last two months traveling from West Lafayette, to Switzerland, to Boston, back to West Lafayette, to Berkeley and finally back to West Lafayette to wrap up what my friends have dubbed MathTour 2010. This certainly seems to constitute ''traveling some distance''.  
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There are also a number of current developments in the field that I will be trying to learn about. These include
  
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As for ''merging with something not of our species'', I've recently gotten involved with WIlliam Stein's project Sage, which has been compared by some to the ominous Borg from Star Trek. Reports of my assimilation are... likely accurate.  
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* The work of Mazur and Rubin reducing Hilbert's Tenth Problem for the rings of integers of number fields to the Shafarevich-Tate conjecture.
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* The work of Bhargava the average size of Selmer groups of elliptic curves.
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* Heath-Brown's result on the distribution of Selmer ranks of elliptic curves, and the subsequent generalization to "generic" curves with full two-torsion by Swinnerton-Dyer.
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* The two recent proofs of the ABC conjecture for the ring of entire functions. I will need to learn some Nevanlinna theory to understand this business.
  
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Through all of this, I have gathered several beautiful new ideas and techniques, which I've now brought back to my hive in West Lafayette. As Mazur says, it's taken work, but it's something I've done without contortion, because its who I am.
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= Essay Contest Entry =
  
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During the brief time I was in West Lafayette between my stays at Harvard and Berkeley, I discussed with whimsical nomadic lifestyle with a friend. She was somewhat overwhelmed that she'd soon be leaving West Lafayette and traveling around intensely for the foreseeable future. In mild frustration she asked me, "why do we do this?" It was to this question that I gave my aforementioned 3 word response, "because it's awesome!"
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If you're looking for my essay contest entry for "Why do I 'math'?", it can be found [[Why_do_I_math_-_Weigandt | here ]].

Latest revision as of 05:18, 13 August 2010

Jamie Weigandt

Jamie.jpg

Jamie Weigandt is an alumnus of the Purdue mathematics department (2008) and starting his third year of graduate studies in the same department. He's beginning his second year in the National Science Foundation's Graduate Research Fellowship Program studying Algebra and Number Theory with Prof. Edray Goins. He's particularly interested computational and statistical questions concerning the arithmetic of elliptic curves.

Note on this page

For the time being I will use LaTeX code freely when editing this page. When the jsmath plugin is installed it should TeX on the fly in your browser.

Projects

I'm hoping to use this space to describe some of my current projects. These include

  • A database of Elliptic Curves with Prescribed Torsion
  • Connections between the Mordell-Weil ranks and Szpiro Ratios of elliptic curves
  • Finding elliptic curves of conductor less than $10^6$ which do not appear in the Stein-Watkins database.
  • Transfers that Track Down Atypical ABC Triples. (I was feeling whimsical... deal with it!)
  • Work with Matt Davis and James Ryan concerning the Erdös-Woods problem.

There are also a number of current developments in the field that I will be trying to learn about. These include

  • The work of Mazur and Rubin reducing Hilbert's Tenth Problem for the rings of integers of number fields to the Shafarevich-Tate conjecture.
  • The work of Bhargava the average size of Selmer groups of elliptic curves.
  • Heath-Brown's result on the distribution of Selmer ranks of elliptic curves, and the subsequent generalization to "generic" curves with full two-torsion by Swinnerton-Dyer.
  • The two recent proofs of the ABC conjecture for the ring of entire functions. I will need to learn some Nevanlinna theory to understand this business.

Essay Contest Entry

If you're looking for my essay contest entry for "Why do I 'math'?", it can be found here .

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