The Southwest Center for Arithmetic Geometry


Course description: html

“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.

“A determinantal procedure for calculating Jacobians of genus
1 curves.” project description: dvi, ps,
pdf

Fragment of Maple code for calculating the tau functions appearing
in the lectures: txt



Course and project description: pdf

Course notes: pdf
 Video:
 Notes written during the
lecture: pdf






AWS 2012
Irene Bouw and Stefan Wewers: Group actions on curves and the lifting problem


 Lecture notes:

Project on computing the U operator on overconvergent 2adic
modular forms of level 1 and even
weight: dvi, ps, pdf

Buzzard's students' writeup of their
lecture: dvi, ps, pdf



Course and project
description: pdf
 Video:
 Notes written during the
lecture: pdf





Project description: html




“The localglobal principle” project
description: dvi, ps,
pdf

References for
talks: dvi, ps, pdf

Slides for Barbu's talk on the Brauer
group: dvi, ps, pdf




Abstract: html

Reading list: html

“Rigid local systems, Hilbert modular forms, and
Fermat’s last theorem,” CICMA preprint submitted for
publication:
dvi,
ps,
pdf

Web site





Course and project
description: html
 Notes:
 The students' project write
up: dvi, ps, pdf.

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.


Course description: dvi, ps, pdf

Project description: dvi, ps, pdf

Preliminary notes by Kiran Kedlaya on Deligne's lectures,
in pdf. A final
version may eventually appear
on Kedlaya's site.






Abstract: html

Frankenhuysen: “The abc conjecture implies Roth's theorem and Mordell's conjecture”: dvi, ps, pdf







Polished course writeup, “Lfunctions and monodromy: four
lectures on Weil
II.”: pdf

“Mysterious formulae involving the numbers of points in some
families of elliptic curves.” project
description: html



Course description: html

Schoof's Abuja notes are a good
reference: dvi, ps, pdf.

Kristin Lauter and Michael Zieve have a threepart 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.)

Description: dvi, ps, pdf

Reference [6] in their
bibliography: ps, pdf

Reference
[7]: ps, pdf


Course and project
description: pdf

Loeser's course notes (revised 9/03): pdf
 Video:



Course and project
description: pdf

Course notes: pdf
 Video:





Abstract: html

Reading list: html

“Three lectures about the arithmetic of elliptic curves”:
dvi,
ps,
pdf


“Visualizing elements in the ShafarevichTate group” project:

Bibliography: dvi, ps, pdf

Mazur's comments on “visualizing elements in the
ShafarevichTate
group,”: dvi, ps, pdf

“Visualizing elements in the ShafarevichTate group,” by
Cremona and Mazur (to appear in the Journal of Experimental
Math): dvi, ps, pdf

“Visualizing elements of order three in the ShafarevichTate
group,” (to appear in the Journal of Asian
Mathematics): dvi, ps, pdf

The Mazur student project led to a preprint by William Stein
entitled “Some Abelian Varieties with Visible
ShafarevichTate
Groups.”: dvi, ps, pdf. Stein's web site also has many interesting
tables, preprints, and program related to modular forms and
modular Jacobians.


Preliminary lecture
notes: dvi, ps, pdf

More detailed notes by Mazur's
students: dvi, ps, pdf

Project
description: dvi, ps, pdf

“Notes on KatoSiegel functions,” used in Mazur's
students'
lectures: dvi, ps, pdf

A paper by Tom Weston on “The modular curves
X_{0}(11) and
X_{1}(11)”: ps, pdf

Another paper by Tom Weston, on “The Euler system of Heegner
points”: dvi, ps, pdf

A repository at Harvard
of documents related to Mazur's lectures and
project


Pavlos Tzermias' lectures on “The ManinMumford Conjecture: A
Brief
Survey”: dvi, ps, pdf

Wetherell's project on “An application of the method of
Coleman and
Chabauty.”: description. It refers to Wetherell's
thesis: dvi, ps,
pdf

Cathy O'Neil's thesis (dvi, ps, pdf) on Jacobians of Curves of Genus One was the basis of Tomas Klenke's talk.

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



Course and project
description: pdf
 Video:
 Notes written during the
lecture: pdf






Course and project
description: pdf

Notes for the first two and a half lectures by
Pillay: pdf
 Video of Pillay's lectures:

Notes for the following three lectures by
Scanlon: pdf
 Video of Scanlon's lectures:

Slides Scanlon projected during his
lectures: pdf

AWS 2015
Alena Pirutka: Curves on varieties and topics on surfaces



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:

“Algebraic families of nonzero elements of
ShafarevichTate groups”, with
ColliotThélène: pdf

“Computational aspects of curves of genus at least
2”: ps, pdf

“The MordellWeil group of a genus 2
Jacobian”: project description




Course and project
description: pdf

Course notes: pdf
 Video:




Course outline and project
description: dvi, ps, pdf


Three papers related to Rubin's lectures:

“Elliptic curves with complex
multiplication”: dvi, ps, pdf

“Euler systems and modular elliptic
curves”: dvi, ps, pdf

“General Euler
systems”: dvi, ps, pdf

Karl's web site has other preprints that may be of interest.

“TateShafarevich groups of twists on an elliptic
curve”: project description



Course description and
projects: html

References: dvi, ps, pdf










Course description: html

Course
outline: dvi, ps, pdf

“Explicit calculations with elliptic
curves over function fields.” project description: dvi, ps,
pdf

A very nice writeup of the project by Mihran Papikian: ps, pdf

A related paper: “Elliptic curves with large rank over function fields.”: arXiv

AWS 2015 Ravi Vakil: Links between arithmetic and geometry: metaphor and motivation



Course and project
description: dvi, ps, pdf



Course and project
description: html

Project references:

An extract from Voisin's book on Hodge theory (in
French): ps

A paper by
Kimura: ps


Abstract: html

Reading list: html

“A more general abc conjecture”:
dvi,
ps,
pdf

“Chapter 0” of preliminary material on number theory and
algebraic geometry:
dvi,
ps,
pdf


 Course and project outline
 Draft lecture notes for lectures 1, 2, 3, 5
 Video:

Lecture 1: MP4, MPG, slides

Lecture 2: MP4, MPG, slides

Lecture 3: MP4, MPG, slides

Lecture 4: MP4, MPG, slides

Lecture 5: MP4, MPG, slides


Course and project
description: pdf

Course notes: pdf
 Video:
 Notes written during the lecture: pdf


Abstract: html

“A note on Wronskians and the abc theorem in function fields of prime characteristic”: dvi, ps, pdf

“ABC estimate, integral points, and geometry of Pn minus hyperplanes”: dvi, ps, pdf



Abstract: html

J. Yu: “On arithmetic of hyperelliptic curves”: dvi, ps, pdf



“Rational points on conics.”:
project description,
suggested readings

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.


Kessel spoke on “Removing the discontinuity between
highschool and college” and led a workshop on “Tools to
teach intuition”. There was also a panel discussion on lower
division courses.

Abstract: html

“Teaching Mathematical Problem Solving”:
ps,
pdf

References:
ps,
pdf



Descriptions: html

Deborah Hughes Hallet's lecture on “Mathematics
for the Reluctant”:

Shuzo Takahashi's lecture on “Spreadsheet
Software as a Teaching Tool for Introductory Mathematics
Courses”:

Powerpoint slides

Zip archive with 7
spreadsheets and a Powerpoint file from the business Math
course.

Bill Velez's lecture on “The Calculator Based
Laboratory”:

The Texas
Instruments web page on the Calculator Based
Laboratory

Doug Ulmer's lecture on “A simple simulation to
value stock options”:

Powerpoint slides
on a model to value options

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.)

Onepage note on riskneutral valuation (also linked to in the
slides): pdf