We say that a real closed field is an IPA-real closed field if it admits an integer part (IP) which is a model of Peano Arithmetic (PA). In [2] we prove that the value group of an IPA-real closed field must satisfy very restrictive conditions (i.e. must be an exponential group in the residue field, in the sense of [4]). Combined with the main result of [1] on recursively saturated real closed fields, we obtain a valuation theoretic characterization of countable IPA-real closed fields. Expanding on [3], we conclude the talk by considering recursively saturated o-minimal expansions of real closed fields and their IPs.

References:
[1] D'Aquino, P. - Kuhlmann, S. - Lange, K. : A valuation theoretic characterization ofrecursively saturated real closed fields ,
Journal of Symbolic Logic, Volume 80, Issue 01, 194-206 (2015)
[2] Carl, M. - D'Aquino, P. - Kuhlmann, S. : Value groups of real closed fields and
fragments of Peano Arithmetic, arXiv: 1205.2254, submitted
[3] D'Aquino, P. - Kuhlmann, S : Saturated o-minimal expansions of real closed fields, to appear in Algebra and Logic (2016)
[4] Kuhlmann, S. :Ordered Exponential Fields, The Fields Institute Monograph Series, vol 12. Amer. Math. Soc. (2000)
 

Quadrature is the term for the numerical evaluation of integrals.  It's a beautiful subject because it's so accessible, yet full of conceptual surprises and challenges.  This talk will review ten of these, with plenty of history and numerical demonstrations.  Some are old if not well known, some are new, and two are subjects of my current research.

Graded affine Hecke algebras were introduced by Lusztig for studying the representation theory of p-adic groups. In particular, some problems about extensions of representations of p-adic groups can be transferred to problems in the graded Hecke algebra setting. The study of extensions gives insight to the structure of various reducible modules. In this talk, I shall discuss some methods of computing Ext-groups for graded Hecke algebras.
The talk is based on arXiv:1410.1495, arXiv:1510.05410 and forthcoming work.