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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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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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*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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= The Bigfoot Project =
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= Projects =
  
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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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I'm hoping to use this space to describe some of my current projects. These include
  
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For now I will be motivated in my development of this page by 3 facts:
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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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*My bank account is suffering from conference fatigue.
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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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*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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* 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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= Why do I "math"? =
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= Essay Contest Entry =
  
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== Note about the Development of this Essay ==
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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 ]].
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As this is a wiki page, I will take the liberty to develop my essay freely on this page. That being said, there will initially be a lot of material that is unclear. I won't make sense to anyone but myself, or perhaps not even myself. Hopefully, since a record of these edits will remain, it will provide insight anyone trying to write a similar essay. This seems quite similar to one of those "Statement of Purpose" type questions that anyone wanting to go to grad school will have to write about.
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== A Remark About the Question ==
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It has occurred to me, thinking about this question, that the question is very general and open to interpretation. It also presents us with the verbification (is that the correct term?) of math. Often a general question like this can get one stuck, it's not entirely clear in what style the answer should be given.
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It just hit me that the generality of the question is a good thing. I don't have to answer all possible forms of the question I can think of, rather I can start writing as ideas come to me. This will eventually formulate an answer. At that point I will be able to craft a story by starting with the interpretation of the question that I have already answered.  
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For me, questions are a fundamentally important part of the mathematical experience. As are the stories we tell when we get answers. Of course, in between questions and answers we must experience a great deal of confusion, and hopefully some moment of epiphany or revelation. This provides a rough idea of what the main steps in the mathematical experience are.
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* Questions
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* Revelation
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* Exposition
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It seems that any essay about why I do mathematics should discuss my personal views on these stages of mathematical development...
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==Questions==
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==Revelation==
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==Exposition==
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==Quotes to maybe include==
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"... number theory has an annoying habit: the field produces, without effort, innumerable problems which have a sweet, innocent air about them, tempting flowers; and yet ... the quests for the solutions to these problems have been known to lead to the creation (from nothing) of theories which spread their light on all mathematics, have been known to goad mathematicians on to achieve major unifications of their science, have been known to entail painful exertion in other branches of mathematics to make those branches serviceable. Number theory swarms with bugs, waiting to bit the tempted flower-lovers who, once bitten, are inspired to excesses of effort!"
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-Barry Mazur, "Number Theory as Gadfly"
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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 .

Retrieved from "https://www.projectrhea.org/rhea/index.php?title=User:Jweigand&oldid=39732"
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