The Southwest Center for Arithmetic Geometry
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Course and project description: pdf
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Course notes: pdf
- Video:
- Notes written during the
lecture: pdf
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Course and project
description: pdf
- Video:
- Notes written during the
lecture: pdf
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Course and project
description: pdf
- Video:
- Notes written during the
lecture: pdf
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Course and project
description: pdf
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Course notes: pdf
- Video:
- Notes written during the lecture: pdf
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Course and project
description: pdf
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Loeser's course notes (revised 9/03): pdf
- Video:
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Course and project
description: pdf
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Course notes: pdf
- Video:
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Course and project
description: pdf
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Notes for the first two and a half lectures by
Pillay: pdf
- Video of Pillay's lectures:
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Notes for the following three lectures by
Scanlon: pdf
- Video of Scanlon's lectures:
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Slides Scanlon projected during his
lectures: pdf
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Course and project
description: pdf
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Course notes: pdf
- Video:
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Course and project
description: html
- Notes:
- The students' project write
up: dvi, ps, pdf.
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The project participants were Jim Brown, Kirsten Eisentrager,
Krzysztof Klosin, Jorge Pineiro, Mak Trifkovic, and Oliver Watson.
Jim, Kirsten, Krzysztof, Jorge, and Oliver did the write up.
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Course description: dvi, ps, pdf
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Project description: dvi, ps, pdf
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Preliminary notes by Kiran Kedlaya on Deligne's lectures,
in pdf. A final
version may eventually appear
on Kedlaya's site.
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Course and project
description: dvi, ps, pdf
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Course and project
description: html
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Project references:
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An extract from Voisin's book on Hodge theory (in
French): ps
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A paper by
Kimura: ps
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Descriptions: html
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Deborah Hughes Hallet's lecture on “Mathematics
for the Reluctant”:
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Shuzo Takahashi's lecture on “Spreadsheet
Software as a Teaching Tool for Introductory Mathematics
Courses”:
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Powerpoint slides
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Zip archive with 7
spreadsheets and a Powerpoint file from the business Math
course.
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Bill Velez's lecture on “The Calculator Based
Laboratory”:
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The Texas
Instruments web page on the Calculator Based
Laboratory
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Doug Ulmer's lecture on “A simple simulation to
value stock options”:
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Powerpoint slides
on a model to value options
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Zip archive of 3 Excel
spreadsheets with simulations illustrating the model. (There
are links to these spreadsheets in the slide show. These
links will most likely not work on your computer, but you can
manually open the spreadsheets.)
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One-page note on risk-neutral valuation (also linked to in the
slides): pdf
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- Lecture notes:
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Project on computing the U operator on overconvergent 2-adic
modular forms of level 1 and even
weight: dvi, ps, pdf
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Buzzard's students' write-up of their
lecture: dvi, ps, pdf
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Project description: html
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Preliminary lecture
notes: dvi, ps, pdf
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More detailed notes by Mazur's
students: dvi, ps, pdf
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Project
description: dvi, ps, pdf
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“Notes on Kato-Siegel functions,” used in Mazur's
students'
lectures: dvi, ps, pdf
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A paper by Tom Weston on “The modular curves
X0(11) and
X1(11)”: ps, pdf
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Another paper by Tom Weston, on “The Euler system of Heegner
points”: dvi, ps, pdf
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A repository at Harvard
of documents related to Mazur's lectures and
project
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Course outline and project
description: dvi, ps, pdf
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Course description and
projects: html
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References: dvi, ps, pdf
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Course description: html
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“Notes on fermionic Fock space for number
theorists” (snapshot at the time of the Winter School): dvi, ps,
pdf. Later versions may
appear on Greg's web site.
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“A determinantal procedure for calculating Jacobians of genus
1 curves.” project description: dvi, ps,
pdf
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Fragment of Maple code for calculating the tau functions appearing
in the lectures: txt
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Polished course write-up, “L-functions and monodromy: four
lectures on Weil
II.”: pdf
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“Mysterious formulae involving the numbers of points in some
families of elliptic curves.” project
description: html
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Course description: html
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Schoof's Abuja notes are a good
reference: dvi, ps, pdf.
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Kristin Lauter and Michael Zieve have a three-part project
entitled “Using class field theory to construct curves with
many points.” (Kristin will supervise Parts 1 and 2 and
Michael will supervise Part 3.)
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Description: dvi, ps, pdf
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Reference [6] in their
bibliography: ps, pdf
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Reference
[7]: ps, pdf
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Course description: html
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Course
outline: dvi, ps, pdf
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“Explicit calculations with elliptic
curves over function fields.” project description: dvi, ps,
pdf
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A very nice write-up of the project by Mihran Papikian: ps, pdf
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A related paper: “Elliptic curves with large rank over function fields.”: arXiv
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“The local-global principle” project
description: dvi, ps,
pdf
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References for
talks: dvi, ps, pdf
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Slides for Barbu's talk on the Brauer
group: dvi, ps, pdf
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“Visualizing elements in the Shafarevich-Tate group” project:
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Bibliography: dvi, ps, pdf
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Mazur's comments on “visualizing elements in the
Shafarevich-Tate
group,”: dvi, ps, pdf
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“Visualizing elements in the Shafarevich-Tate group,” by
Cremona and Mazur (to appear in the Journal of Experimental
Math): dvi, ps, pdf
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“Visualizing elements of order three in the Shafarevich-Tate
group,” (to appear in the Journal of Asian
Mathematics): dvi, ps, pdf
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The Mazur student project led to a preprint by William Stein
entitled “Some Abelian Varieties with Visible
Shafarevich-Tate
Groups.”: dvi, ps, pdf. Stein's web site also has many interesting
tables, preprints, and program related to modular forms and
modular Jacobians.
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Pavlos Tzermias' lectures on “The Manin-Mumford Conjecture: A
Brief
Survey”: dvi, ps, pdf
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Wetherell's project on “An application of the method of
Coleman and
Chabauty.”: description. It refers to Wetherell's
thesis: dvi, ps,
pdf
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Cathy O'Neil's thesis (dvi, ps, pdf) on Jacobians of Curves of Genus One was the basis of Tomas Klenke's talk.
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Several U of A graduates students worked with Bill McCallum on
constructing the Jacobian of a genus 1
curve. Their web site has the details. Slides for
David Marshall's talk on this
topic: dvi, ps,
pdf
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Poonen's lectures at the Winter School were on background
material, but two (or more) of the papers
on his web site are relelvant to the topic:
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“Algebraic families of nonzero elements of
Shafarevich-Tate groups”, with
Colliot-Thélène: pdf
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“Computational aspects of curves of genus at least
2”: ps, pdf
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“The Mordell-Weil group of a genus 2
Jacobian”: project description
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Three papers related to Rubin's lectures:
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“Elliptic curves with complex
multiplication”: dvi, ps, pdf
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“Euler systems and modular elliptic
curves”: dvi, ps, pdf
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“General Euler
systems”: dvi, ps, pdf
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Karl's web site has other preprints that may be of interest.
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“Tate-Shafarevich groups of twists on an elliptic
curve”: project description
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“Rational points on conics.”:
project description,
suggested readings
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Cremona's web site has a number of preprints
and and slides related to his talk at the Winter School, and to
his student project. It also contains a lots of information about
symbolic computation packages, other software, and mathematics.
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Abstract: html
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Reading list: html
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“Rigid local systems, Hilbert modular forms, and
Fermat’s last theorem,” CICMA preprint submitted for
publication:
dvi,
ps,
pdf
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Web site
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Abstract: html
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Frankenhuysen: “The abc conjecture implies Roth's theorem and Mordell's conjecture”: dvi, ps, pdf
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Abstract: html
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Reading list: html
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“Three lectures about the arithmetic of elliptic curves”:
dvi,
ps,
pdf
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Abstract: html
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Reading list: html
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“A more general abc conjecture”:
dvi,
ps,
pdf
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“Chapter 0” of preliminary material on number theory and
algebraic geometry:
dvi,
ps,
pdf
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Abstract: html
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“A note on Wronskians and the abc theorem in function fields of prime characteristic”: dvi, ps, pdf
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“ABC estimate, integral points, and geometry of Pn minus hyperplanes”: dvi, ps, pdf
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Abstract: html
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J. Yu: “On arithmetic of hyperelliptic curves”: dvi, ps, pdf
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Kessel spoke on “Removing the discontinuity between
high-school and college” and led a workshop on “Tools to
teach intuition”. There was also a panel discussion on lower
division courses.
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Abstract: html
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“Teaching Mathematical Problem Solving”:
ps,
pdf
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References:
ps,
pdf