Latest revision as of 05:18, 13 August 2010

Jamie Weigandt

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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-I'm Jamie Weigandt, I am graduate student in the department of mathematics specializing in Algorithmic Number Theory, Arithmetic Algebraic Geometry, and Arithmetic Statistics.
+==Jamie Weigandt==
-= Note on this page  =
+[[Image:jamie.jpg|160px]]
-For the time being I will use LaTeX code freely when editing this page.
+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.
-== Random Thoughts About Rhea as I use it  ==
+= Note on this page  =
-*Can we add LaTeX functionality with jsmath, at least for the pages relevant to mathematicians?
-*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.
-= The Bigfoot Project  =
-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.
-For now I will be motivated in my development of this page by 3 facts:
-*My bank account is suffering from conference fatigue.
-*There is an essay contest for which I can win $100.
-*I'd like to stop eating at Taco Bell.
-That being said I'll get right to this following section:
-= Why do I "math"?  =
-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.
-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.
-I've always considered myself somewhat of a nerd. In fact, I'm proud to have caused one professor in my department to utter the phrase, "this is why you can't eat dinner with nerds!" So last September, when I attended my first conference on computational number theory, I was quick to describe the gathering as a hive of nerds of the highest caliber. Paul Gunnells proceeded to correct me. "We're not just nerds," he said, "we're the rock stars of science!" At first this sounded somewhat absurd, but after experiencing another year as a mathematician, and hearing my closest friends make the same comparisons, I've come to believe that the two lifestyles, while seeming the most disparate one could possibly imagine, are quite similar.
-Much like music, mathematics is an inherently creative activity. I've come to realize that mathematics is an exhilarating game, and I'm very privileged to be able to play professionally. Much the way that young musicians are inspired by artists who come before them, there are many mathematicians that I've come to see as "influences". Barry Mazur comes to mind as someone whose enthusiasm for 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 Fifthteen'', Mazur compares mathematicians to bees,
-''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.''
-Notice that this could easily describe rock stars with little or not modification. I've spent the last two months traveling around to various conferences, in what my friends have referred to as MathTour 2010. It started with a redeye flight into Zurich, Switzerland which got me to the ETH just in time to follow Sir Peter Swinnerton-Dyer to the first lecture in a weeklong workshop entitled Rational Points: Theory and Experiment.
-'''Joke''':
-Person A: How do you find Rational Points?
-Person B: Just follow Swinnerton-Dyer.
-Person A: Which paper?
-Also like a young musician, I've spent the last two months traveling around, carrying a piece of electronic equipment worth more than anything else I own, sleeping on peoples couches and living out of a suitcase.
-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!"
-==OLD DRAFT==
-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.
-== We're the Rock Stars of Science! ==
-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!"
-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 mathematicians from rock stars, that somehow mathematicians are slingshotted around some kind of gravitation field directly into the lifestyle of a rock stars. He and I call this the "Brian May Effect" in honor of the legendary guitarist Brian May or Queen, who is also and astrophysicist.
-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":
-''"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."''
-Notice that this description, quote could just as easily be about rock stars.
+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 List==
+* 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.
-The following topics are in no particular order... yet!
+= Essay Contest Entry =
-*Relating to other mathematicians
+If you're looking for my essay contest entry for "Why do I 'math'?", it can be found [[Why_do_I_math_-_Weigandt | here ]].
-*Being an expert
-*Engaging in a personal quest for truth
-*Moments when you realize that you've "done it already!"
-*The simplicity of Mathematics compared with the rest of our lives
-*The permanence of mathematics
-*Telling Stories about mathematics

Difference between revisions of "User:Jweigand" - Rhea

Latest revision as of 05:18, 13 August 2010

Contents

Jamie Weigandt

Note on this page

Projects

Essay Contest Entry

Alumni Liaison