James Borger


I work in number theory, algebraic geometry, and related fields. In particular, I'm interested in Lambda-algebraic geometry and (even more particularly) the de Rham cohomology of Witt spaces and the relation to the classical motivic realizations.

Special topics class:
Witt vectors, lambda-rings, and arithmetic jet spaces, University of Copenhagen, 2016.

Papers:
9. Witt vectors, semirings, and total positivity, to appear in Absolute Arithmetic and F1-Geometry. EMS Publishing House, 2016 (expected).
8. Boolean Witt vectors and an integral Edrei-Thoma theorem (with D. Grinberg), Selecta Mathematica 22(2) (2016), pp 595-629
7. Differential calculus on arithmetic jet spaces (with A. Buium), Selecta Mathematica 17 (2011), no. 2, pp 301-335.
6. The basic geometry of Witt vectors, II: Spaces, Mathematische Annalen 351 (2011), no. 4, pp 877-933.
5. The basic geometry of Witt vectors, I: The affine case, Algebra & Number Theory 5 (2011), no. 2, pp 231-285.
4. Galois theory and integral models of Lambda-rings (with B. de Smit), Bulletin of the London Mathematical Society 40 (2008), no. 3, pp 439-446.
3. Plethystic algebra (with B. Wieland), Advances in Mathematics 194/2 (2005), pp 246-283
2. Conductors and the moduli of residual perfection, Mathematische Annalen 329 No. 1 (2004), pp 1-30
1. A monogenic Hasse-Arf theorem, Journal de Théorie des Nombres de Bordeaux 16 (2004), pp 79-81

Preprints:
3. Canonical lifts of families of elliptic curves (with L. Gurney)
2. Lambda actions of rings of integers (with B. de Smit)
1. Lambda-rings 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 5-9, 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 22-26, Nagoya, Japan.
Witt vectors in arithmetic, geometry, and topology, University of New Mexico, Albuquerque, USA 14--18 May 2012
Arithmetic and Algebraic Differentiation: Witt vectors, number theory and differential algebra In honor of Alexandru Buium , UC Berkeley, USA 6--10 May 2015
Geometry at the ANU , ANU, Canberra, Australia 22--26 August 2016

Regional and national conferences:
Australian Mathematical Society, 50th Annual Meeting, number theory special session, September 2006
The Morgan--Phoa Mathematics Workshop, ANU, November 2006
The Third Morgan--Phoa 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 Tall-Wraith, Bergman-Hausknecht,...)

Videos:
The motivic logarithm and its realisations, Differential Geometry Seminar, U Adelaide, August 2012
Lambda-algebraic geometry 1: The categorical package, Frobenius Lifts, Leiden, 2009
Lambda-algebraic geometry 2: The geometry of W and Lambda, Frobenius Lifts, Leiden, 2009
Lambda-algebraic geometry 3: Absolute algebraic geometry I , Frobenius Lifts, Leiden, 2009
Lambda-algebraic 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.



Links
Mathematical Sciences Institute, ANU

Email Address
James.Borger at anu dot edu dot au

Postal Address
Centre for Mathematics and its Applications, Mathematical Sciences Institute
Australian National University, Canberra, ACT 0200, Australia.

Phone
(61-2) 6125 3750

FAX
(61-2) 6125 4984