James Borger
Special topics class: Witt vectors, lambdarings, and arithmetic jet spaces, University of Copenhagen, 2016. Papers: 9. Witt vectors, semirings, and total positivity, to appear in Absolute Arithmetic and F1Geometry. EMS Publishing House, 2016 (expected). 8. Boolean Witt vectors and an integral EdreiThoma theorem (with Darij Grinberg), Selecta Mathematica 22(2) (2016), pp 595629 7. Differential calculus on arithmetic jet spaces (with Alexandru Buium), Selecta Mathematica 17 (2011), no. 2, pp 301335. 6. The basic geometry of Witt vectors, II: Spaces, Mathematische Annalen 351 (2011), no. 4, pp 877933. 5. The basic geometry of Witt vectors, I: The affine case, Algebra & Number Theory 5 (2011), no. 2, pp 231285. 4. Galois theory and integral models of Lambdarings (with Bart de Smit), Bulletin of the London Mathematical Society 40 (2008), no. 3, pp 439446. 3. Plethystic algebra (with Ben Wieland), Advances in Mathematics 194/2 (2005), pp 246283 2. Conductors and the moduli of residual perfection, Mathematische Annalen 329 No. 1 (2004), pp 130 1. A monogenic HasseArf theorem, Journal de Théorie des Nombres de Bordeaux 16 (2004), pp 7981 Preprints: 5. On Frobenius and Fibers of Arithmetic Jet Spaces (with Arnab Saha) 4. Differential characters of Drinfeld modules and de Rham cohomology (with Arnab Saha) 3. Canonical lifts of families of elliptic curves (with Lance Gurney) 2. Lambda actions of rings of integers (with Bart de Smit) 1. Lambdarings and the field with one element Conferences: Geometry and Lie Theory: A Conference Marking Gus Lehrer's 60th Birthday, ANU and Sydney U, July 2007 Fourth Pacific Rim Conference on Mathematics, special session on algebraic geometry, City University of Hong Kong, December 2007 Frobenius Lifts, 2009 October 59, Leiden, The Netherlands. Mathematics and Physics on the Borderline between Algebraic and Differential Geometry, ANU, July 2010. Witt vectors, foliations, and absolute de Rham cohomology, 2010 November 2226, Nagoya, Japan. Witt vectors in arithmetic, geometry, and topology, University of New Mexico, Albuquerque, USA 1418 May 2012 Arithmetic and Algebraic Differentiation: Witt vectors, number theory and differential algebra In honor of Alexandru Buium , UC Berkeley, USA 610 May 2015 Geometry at the ANU , ANU, Canberra, Australia 2226 August 2016 Regional and national conferences: Australian Mathematical Society, 50th Annual Meeting, number theory special session, September 2006 The MorganPhoa Mathematics Workshop, ANU, November 2006 The Third MorganPhoa Mathematics Workshop, ANU, January 2010 ANU/Macquarie Category Theory Workshop, ANU, January 2013 Algebraic geometry and related fields, ANU, May 2013 Slides: (I usually give board talks.) Generalized symmetries in categories of algebras (following TallWraith, BergmanHausknecht,...) Videos: The motivic logarithm and its realisations, Differential Geometry Seminar, U Adelaide, August 2012 Lambdaalgebraic geometry 1: The categorical package, Frobenius Lifts, Leiden, 2009 Lambdaalgebraic geometry 2: The geometry of W and Lambda, Frobenius Lifts, Leiden, 2009 Lambdaalgebraic geometry 3: Absolute algebraic geometry I , Frobenius Lifts, Leiden, 2009 Lambdaalgebraic geometry 4: Absolute algebraic geometry II , Frobenius Lifts, Leiden, 2009 For students: Are you considering asking me to supervise you for something? If so, click here. Some less serious things.
