UPDATE (2 August): We have moved this talk to the room next door, Quadrangle Room S418. ----- This semester we will run a somewhat irregular SMRI seminar series, in which SMRI visiting researchers will speak about their own research or other topics of interest, complementing their contributions to the School’s existing seminar series. We will experiment with some venues in the Quadrangle as well as more customary locations. All are welcome, and please send feedback on the series to me at firstname.lastname@example.org . The first speaker in this SMRI seminar will be former School staff member Adam Parusinski, details below. Adam will also speak about a different topic in the Geometry & Topology seminar on 19 August. Anthony -------------------- Speaker: Adam Parusinski (University of Nice) Date: Friday 2 August 2019 Time: 11.05am - 12.55pm (with a break in the middle) Venue: Quadrangle Room S418, in the corner of the quadrangle closest to Carslaw (i.e. the one with the jacaranda tree), up a flight of stairs from ground level. Title: New methods of real algebraic geometry: continuous rational functions and arc-analytic geometry Abstract: We give a fairly elementary introduction to two recent techniques specific to real algebraic geometry. Continuous rational functions were introduced recently independently by W. Kucharz, J. Kollar, and G. Fichou, J. Huisman, F. Mangolte, and J.-P. Monnier. The arc-analytic functions form a wider class, in particular, every rational continuous function is arc-analytic. The arc-analytic functions and related arc-symmetric sets were introduced by K. Kurdyka. We discuss some recently obtained results on equisingularity, additive invariants and motivic integration, approximation of continuous maps, and classification of vector bundles.