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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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= 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 the last couple days thinking about this question and trying to give a suitable answer. More and more however, I found myself getting bogged down in details, and my exposition was raising more questions than it was answering. Then suddenly I recalled a conversation I had with a friend in late June. We were discussing how our lives could sometimes be dominated by our travel schedules. Then, in a moment of frustration, she asked me the very question at hand. "Why do we do this?" In the context of this conversation, with her as my audience, I was able to give a concise and confident three-word answer to this question. "Because it's awesome!"
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Unfortunately I cannot fully describe the context of that conversation, or even the tone of my response, in plain text. I recently attended [http://www.msri.org/communications/vmath/VMathVideos/VideoInfo/4777/show_video this lecture] by Lloyd Kilford. During his talk, Lloyd alluded to a novel he was reading wherein the hero of the story is being prepared to consult a great and powerful oracle. The hero's priest advises him to, "pray that his answer, which will be true, will be meaningfully true to you." At this point, my response is probably not meaningfully true to you, unless you are already someone who is passionate about mathematics. To alleviate this, I'm expound upon my response by describing what I think are some of the most awesome things about doing mathematics.
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== We're the Rock Stars of Science! ==
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In September of 2009, I attended a workshop on Galois theory and explicit methods at the University of Warwick in the UK. It was great experience for me, because the room was full of computational number theorists. At some point I recall describing the conference as a hive of nerds of the highest caliber.  Paul Gunnells quickly corrected me saying, "We're not just nerds. We're the rock stars of science!"
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I know it seems strange to describe mathematicians as rock stars. A friend of mine has postulated that social norms try so hard to separate scientists and rocks stars, that they somehow miss their mark, and mathematicians are slingshotted around some kind of gravitation field directly into the lifestyle of a rock star. He and I call this the "Brian May Effect" in honor of the legendary guitarist Brian May or Queen, who is also and astrophysicist.
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Mathematics is a artful game, much like music, that people play because they enjoy it. Some people are passionate, talented, and fortunate enough that they can actually get paid to play. Those of us starting out are inspired and influenced by established figures in the industry, around whom we tend to build legend and folklore. I'm certainly influenced by my advisor, Edray Goins, and the two of us are both influenced by Barry Mazur. Mazur is the source of some of my favorite quotes about mathematics. I'm particularly fond of his description of mathematicians as "bees of the imaginative world":
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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."'' - [http://math.harvard.edu/~mazur Barry Mazur], Imagining Numbers
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Notice that this description, quote could just as easily be about rock stars.
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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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= Projects =
  
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I'm hoping to use this space to describe some of my current projects. These include
  
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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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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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==The List==
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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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The following topics are in no particular order... yet!
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= Essay Contest Entry =
  
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*Relating to other mathematicians
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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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*Being an expert
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*Engaging in a personal quest for truth
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*Being akin to rockstars
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*Moments when you realize that you've "done it already!"
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*The simplicity of Mathematics compared with the rest of our lives
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*The permanence of mathematics
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*Telling Stories about mathematics
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Latest revision as of 04:18, 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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