Southwestern Center
Lecture Notes by Author

  • Anderson, AWS 2000 course description: html.
  • Anderson, “Notes on fermionic Fock space for number theorists” (snapshot at the time of the Winter School): dvi, ps, pdf
  • Anderson, AWS 2000 project description: dvi, ps, pdf
  • Anderson, fragment of Maple code for calculating the tau functions appearing in his AWS 2000 lectures: text
  • Anderson, web site
  • Anderson, “Interpolation of numbers of Catalan type in a local field of positive characteristic”: pdf
  • Anderson, “A two-variable refinement of the Stark conjecture in the function field case”: pdf
  • Barbu, slides for AWS 1999 talk: dvi, ps, pdf
  • Batyrev, AWS 2004 course description: pdf
  • Batyrev, AWS 2004 course notes: pdf
  • Bernstein, AWS 2006 course description: pdf
  • Bernstein, AWS 2006 course notes: pdf
  • Bernstein, AWS 2006 project report: pdf
  • Bernstein, AWS 2006 slides from lectures:
    • Lecture 1, pdf
    • Lecture 2, pdf
    • Lecture 3, pdf
    • Lecture 4, pdf
  • Borisov, AWS 1998 abstract of contributed talk: html
  • Buium, AWS 1998 course abstract: html
  • Buium, AWS 1998 reading list: html
  • Buium, AWS 1998 lecture notes: dvi, ps, pdf
  • Buzzard, AWS 2001 Lecture 1: dvi, ps, pdf
  • Buzzard, AWS 2001 Lecture 2: dvi, ps, pdf
  • Buzzard, AWS 2001 Lecture 3: dvi, ps, pdf
  • Buzzard, AWS 2001 Lecture 4: dvi, ps, pdf
  • Buzzard, AWS 2001 project description: dvi, ps, pdf
  • Buzzard, AWS 2001 students' write-up of their lecture: dvi, ps, pdf
  • Candelas, AWS 2004 course description: pdf
  • Carlson, notes by Sharifi, “An introduction to Hodge theory and its applications”: dvi, ps, pdf
  • Clozel, AWS 2001 project description: html
  • Cohen, AWS 2006 course description: pdf
  • Cohen, AWS 2006 course notes: pdf
  • Cohen, AWS 2006, extract from a forthcoming book relevant to the course: pdf
  • Cohen, AWS 2006, references for the book: pdf
  • Cohen, AWS 2006 lecture slides: pdf
  • Colliot-Thélène, AWS 1999 project description: dvi, ps, pdf
  • Colliot-Thélène, “Algebraic families of nonzero elements of Shafarevich-Tate groups” (with Poonen): pdf
  • Colliot-Thélène, AWS 1999 references: dvi, ps, pdf
  • Cremona, AWS 1999 project description: html
  • Cremona, AWS 1999 reading list:html
  • Cremona, web site
  • Cremona, (with Mazur), “Visualizing elements in the Shafarevich-Tate group,” (to appear in the Journal of Experimental Math): dvi, ps, pdf)
  • Darmon, AWS 1998 course abstract: html
  • Darmon, AWS 1998 reading list: html
  • Darmon, AWS 1998, “Rigid local systems, Hilbert modular forms, and Fermat’s last theorem”: dvi, ps, pdf
  • Darmon, web site
  • deJong, AWS 2002 course and project description: html
  • deJong, AWS 2002 course notes:
    • Lecture 1 in pdf
    • Lecture 2 in pdf
    • Lecture 3 in pdf
    • Lecture 4 in pdf
  • deJong students, write up of deJong's project: dvi, ps, pdf. The participants on the project were Jim Brown, Kirsten Eisentrager, Krzysztof Klosin, Jorge Pineiro, Mak Trifkovic, and Oliver Watson. The write up was done by Jim, Kirsten, Krzysztof, Jorge, and Oliver.
  • Deligne, AWS 2002 course description: dvi, ps, pdf
  • Deligne, AWS 2002 project description: dvi, ps, pdf
  • Deninger, May 2005 Distinguished Lecture Series on “Arithmetic geometry and analysis on foliated spaces”: pdf
  • Frankenhuysen, AWS 1998 abstract of contributed talk: html
  • Frankenhuysen, “The abc conjecture implies Roth's theorem and Mordell's conjecture”: dvi, ps, pdf
  • Goncharov, “Multiple zeta-values, Galois groups, and geometry of modular varieties”: link to ArXive
  • Goncharov, “Multiple polylogarithms and mixed Tate motives”: link to ArXive
  • Goncharov, “The dihedral Lie algebras and Galois symmetries of [a fundamental group]”: link to ArXive
  • Hain, AWS 2005 course description: text
  • Hain, AWS 2005 course notes: pdf
  • Hughes Hallet, “Mathematics for the Reluctant”: ppt
  • Hughes Hallet, AWS 2002 PD component spreadsheet on medical testing and Bayes' theorem: xls
  • Katz, “L-functions and monodromy: four lectures on Weil II.”: pdf
  • Katz, AWS 2000 project description: html
  • Kedlaya, Preliminary notes on Deligne's AWS 2002 lectures: pdf
  • Kessel, AWS 1998 course abstract: html
  • Kessel, “Teaching Mathematical Problem Solving”: ps, pdf
  • Kessel, AWS 1998 references: ps, pdf
  • Kim, with Ribet, “Torsion points on modular curves and Galois theory”: dvi, ps, pdf
  • Kimura, “Chow groups can be finite dimensional, in some sense”: ps
  • Lakatos, notes of a lecture series by Pillay, “Model theory and diophantine geometry”. These notes contain a few inaccuracies and should be considered as a preliminary draft: ps, pdf
  • Lauter, with Schoof and Zieve, AWS 2000 course description: html
  • Lauter, with Zieve, AWS 2000 project description: dvi, ps, pdf
  • Lauter, “Deligne-Lusztig curves as ray class fields”: ps pdf
  • Lauter, “A formula for constructing curves over finite fields with many rational points”: ps pdf
  • Levy, AWS 2001 course description: html
  • Loeser, AWS 2003 course and project description: pdf
  • Loeser, AWS 2003 course notes (revised 9/03): pdf
  • Luca, AWS 1998 abstract of contributed talk: html
  • Macintyre, AWS 2003 course and project description: pdf
  • Macintyre, AWS 2003 course notes: pdf
  • Marshall, AWS 1999 talk slides: dvi, ps, pdf
  • Masser, AWS 1998 reading list: html
  • Matsumoto, AWS 2005 course description: pdf
  • Matsumoto, AWS 2005 course notes: pdf
  • Mazur, AWS 1998 course abstract: html
  • Mazur, AWS 1998 reading list: html
  • Mazur, “Three lectures about the arithmetic of elliptic curves”: dvi, ps, pdf
  • Mazur, AWS 1999 bibliography: dvi, ps, pdf
  • Mazur, comments on “visualizing elements in the Shafarevich-Tate group,”: dvi, ps, pdf
  • Mazur, (with Cremona), “Visualizing elements in the Shafarevich-Tate group,” (to appear in the Journal of Experimental Math): dvi, ps, pdf
  • Mazur, “Visualizing elements of order three in the Shafarevich-Tate group,” (to appear in the Journal of Asian Mathematics): dvi, ps, pdf
  • Mazur, AWS 2001 preliminary lecture notes: dvi, ps, pdf
  • Mazur, AWS 2001, More detailed notes by Mazur's students: dvi, ps, pdf
  • Mazur, AWS 2001 project description: dvi, ps, pdf
  • Mazur's AWS 2001 students, “Notes on Kato-Siegel functions,”: dvi, ps, pdf
  • Mazur, A repository at Harvard of documents related to Mazur's lectures and project
  • McCallum's AWS 1999 student group, web site on Jacobians of genus 1 curves
  • Morrison, AWS 2004 course description: pdf
  • O'Neil, thesis: dvi, ps, pdf
  • Papikian, write up of Ulmer’s AWS 2000 project: ps, pdf
  • Pillay, notes by Lakatos, “Model theory and diophantine geometry”. These notes contain a few inaccuracies and should be considered as a preliminary draft: ps, pdf
  • Pillay and Scanlon, AWS 2003 course and project description: pdf
  • Pillay, Notes for AWS 2003 course: pdf
  • Poonen, “Algebraic families of nonzero elements of Shafarevich-Tate groups” (with Colliot-Thélène): pdf
  • Poonen, “Computational aspects of curves of genus at least 2”: ps, pdf
  • Poonen, AWS 1999 project description: html
  • Poonen, web site
  • Poonen, AWS 2003 course and project description: pdf
  • Poonen, AWS 2003 course notes: pdf and gzipped dvi
  • Pop, AWS 2003 course and project description: pdf
  • Pop, AWS 2003 course notes: pdf
  • Pop, AWS 2005 course description: pdf
  • Pop, AWS 2005 course notes: pdf
  • Ramakrishnan, AWS 2001 course outline and project description: dvi, ps, pdf
  • Ribet, with Kim, “Torsion points on modular curves and Galois theory”: dvi, ps, pdf
  • Rohrlich, “False division towers of elliptic curves”: link to the Journal of Algebra
  • Rohrlich, “A deformation of the Tate module”: link to the Journal of Algebra
  • Rubin, “Elliptic curves with complex multiplication”: dvi, ps, pdf
  • Rubin, “Euler systems and modular elliptic curves”: dvi, ps, pdf
  • Rubin, “General Euler systems” (large: 840K dvi file, 9MB pdf file!): dvi, ps, pdf
  • Rubin, AWS 1999 project description: html
  • Rubin, web site
  • Sarnak, AWS 2001 course and project description: html
  • Sarnak, AWS 2001 references: dvi, ps, pdf
  • Scanlon and Pillay, AWS 2003 course and project description: pdf
  • Scanlon, AWS 2003 course notes: pdf
  • Scanlon, AWS 2003 Slides: pdf
  • Schneps, AWS 2005 course description: pdf
  • Schneps, AWS 2005 course notes: pdf
  • Schoof, with Lauter and Zieve, AWS 2000 course description: html
  • Schoof, “Algebraic curves and coding theory”: dvi, ps, pdf
  • Sharifi, notes of a lecture series by Carlson, “An introduction to Hodge theory and its applications”: dvi, ps, pdf
  • Stein, “Some Abelian Varieties with Visible Shafarevich-Tate Groups”: dvi, ps, pdf
  • Stein, web site
  • Stillman, AWS 2006 course description: pdf
  • Stillman, AWS 2006 course notes: pdf
  • Stillman, AWS 2006 slides from lectures:
    • Lecture 1, pdf
    • Lecture 2, pdf
    • Lecture 3, pdf
    • Lecture 4, pdf
  • Stillman, AWS 2006 Macaulay code: tar
  • Sturmfels, AWS 2006 course description: pdf
  • Sturmfels, AWS 2006 lecture notes: pdf by Silvia Adduci
  • Sturmfels, AWS 2006 slides from lectures:
    • Lecture 1, pdf
    • Lecture 2, pdf
    • Lecture 3, pdf
    • Lecture 4, pdf
  • Swinnerton-Dyer, “Diophantine Equations: Progress and Problems”: pdf
  • Swinnerton-Dyer, “A new method for certain Diophantine equations”: pdf
  • Szpiro, AWS 1998 reading list:html
  • Takahashi, “Spreadsheet Software as a Teaching Tool for Introductory Mathematics Courses”: ppt
  • Takahashi, Zip archive of 7 spreadsheets and a Powerpoint file to accompany his lecture: zip (2.6MB!)
  • Tsuji, “Explicit reciprocity law for Lubin-Tate groups”: dvi, ps, pdf
  • Tsuji, “Crystalline sheaves, syntomic cohomology, and p-adic polylogarithms”: dvi, ps, pdf
  • Tzermias, “The Manin-Mumford Conjecture: A Brief Survey”: dvi, ps, pdf
  • Ulmer, AWS 2000 course description: html
  • Ulmer, AWS 2000 course outline: dvi, ps, pdf
  • Ulmer, AWS 2000 project description: dvi, ps, pdf
  • Ulmer, AWS 2000 project, write-up by Papikian: ps, pdf
  • Ulmer, “Elliptic curves over function fields with large rank”: arXiv link
  • Ulmer, “A simple simulation to value stock options”: ppt
  • Ulmer, Zip archive of 3 spreadsheets on option valuation models: zip
  • Ulmer, “A note on ‘risk-neutral valuation’”: pdf
  • Villegas, AWS 2002 course and project description: dvi, ps, pdf
  • Voisin, AWS 2002 course and project description: html
  • Voisin, Extract from a book on Hodge theory: ps
  • Vojta, AWS 1998 course abstract: html
  • Vojta, AWS 1998 reading list: html
  • Vojta, “A more general abc conjecture”: dvi, ps, pdf
  • Vojta: “Chapter 0” of preliminary material on number theory and algebraic geometry: dvi, ps, pdf
  • Voloch, AWS 1998 course abstract: html
  • Voloch, AWS 1998 reading list: html
  • Voloch, AWS 1998 lecture notes: dvi, ps, pdf
  • Wan, AWS 2004 course description: pdf
  • Wan, AWS 2004 course notes: pdf
  • Wang, “A note on Wronskians and the abc theorem in function fields of prime characteristic”: dvi, ps, pdf
  • Wang, “ABC estimate, integral points, and geometry of Pn minus hyperplanes”: dvi, ps, pdf
  • Wang, AWS 1998 abstract of contributed talk: html
  • Weston, “The modular curves X0(11) and X1(11)”: ps, pdf
  • Weston, “The Euler system of Heegner points”: dvi, ps, pdf
  • Wetherell, AWS 1999 project description: html
  • Wetherell, thesis: dvi, ps, pdf
  • J. Yu, AWS 1998 abstract of contributed talk: html
  • J. Yu, “On arithmetic of hyperelliptic curves”: dvi, ps, pdf
  • K. Yu, AWS 1998 abstract of contributed talk: html
  • Zieve, with Lauter and Schoof, AWS 2000 course description: html
  • Zieve, with Lauter, AWS 2000 project description: dvi, ps, pdf