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Room P3.10, Mathematics Building
Herwig Hauser, University of Vienna.
The Geometry of Rings — Affine Schemes.
Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
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Room P3.10, Mathematics Building
Herwig Hauser, University of Vienna.
The Geometry of Rings — Affine Schemes.
Room P3.10, Mathematics Building
Herwig Hauser, University of Vienna.
Morphisms between Schemes and Basic Constructions - Universal Properties.
Room P3.10, Mathematics Building
Herwig Hauser, University of Vienna.
The Geometry of Schemes - Irreducible Components, Intersections, Smoothness, Singularities, Dimension.
Room P3.10, Mathematics Building
Herwig Hauser, University of Vienna.
Gluing - Projective and General Schemes - Sheaves.
Room P3.10, Mathematics Building
Francisco Nascimento, Instituto Superior Técnico.
Kinematic formulas in convex geometry.
We present a systematic study of kinematic formulas in convex geometry. We first give a classical presentation of kinematic formulas for integration with respect to the rotation group $SO(n)$, where Steiner's Formula, the intrinsic volumes and Hadwiger's Characterization Theorem play a crucial role. Then we will show a new extension to integration along the general linear group $GL(n)$. Using the bijection of matrix polar decomposition and a Gaussian measure to integrate along positive definite matrices, a new formula is obtained, for which the classical $SO(n)$ formula is a particular case. We also reference the unitary group $U(n)$ case and its corresponding extension to the symplectic group $Sp(2n,\mathbb{R})$.