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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've come to recognize lately how much mathematics bear similarity to the music industry. Much in the same way that young musicians are inspired by previously established artists, I have my own mathematical "influences". My advisor, Edray Goins, is certain my greatest among these, but the two of us are both heavily influenced by Barry Mazur.
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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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Anyone who's met Mazur quickly realizes that his enthusiasm for doing mathematics is downright infectious. (c.f. [http://video.google.com/videoplay?docid=8269328330690408516# this documentary] 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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= Projects =
  
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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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I'm hoping to use this space to describe some of my current projects. These include
  
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While I immediately identified with this passage when I read it in January, I've found it even more relevant in the past two months. In that time I've traveled from West Lafayette, to Switzerland, to Boston, back to West Lafayette, off to Berkeley and finally back to West Lafayette to wrap up what my friends have dubbed MathTour 2010. Surely this constitutes ''traveling some distance''.  
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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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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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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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I'm presently communicating to you, ''my fellow creatures'', what I have done and where I have been. Should be be stickler for details, I'm now officially using [http://www.webhamster.com/ dance]. :)
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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've spoken with several experts about my research, attended over 40 lectures, and I've returned to the hive with more than just a drop of honey. I have acquired a clearer picture of the mathematical landscape in which I work. I'm now ready to explore in greater breadth and depth than I previously believe possible. Surely this will be quite a challenge. Just as there is hard work behind me, there is hard work ahead of me, but as Mazur says, it is activity that I will do without contortion. It is indeed who I am.
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= Essay Contest Entry =
  
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And that, is why I "math".
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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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