PhD, IMPA, Rio de Janeiro,RJ-Brasil, 1989

Office: L874

Position: Associate Professor

Phone: (21) 3527-1741

E-mail: craizer

*Differential Geometry*

Marcos Craizer obtained his Ph.D. at IMPA in 1989 and is a professor at the Math Department of PUC-Rio since 1988. His research area lies between Affine Differential Geometry and Singularity Theory. He is also interested in Discrete Geometry, considering its applications to Computer Vision.

**RECENT PUBLICATIONS**

**Improper affine spheres**. There is a strong connection between Area Distance and non-convex Improper Affine Spheres that was explored in [1] and [2]. In [5], one can find a classification of stable singularities of convex Improper Affine Spheres.**Volume distance to hypersurfaces**. Although the Area Distance in the plane is an Improper Affine Sphere, this property does not hold in higher dimensions. Nevertheless, the volume distance have some nice affine differential properties [4].**Affine evolutes and symmetry sets**. In [7], several properties of the Area Evolute and Center Symmetry Set are described. A discrete version of these results can be found in [6]. In [3], one can find a discrete version of the Affine Evolute, Affine Distance Symmetry Set. In the same paper there are discrete versions of the the Six Vertex Theorem and an affine isoperimetric inequality.

- Marcos Craizer, Moacyr Alvim, Ralph Teixeira: Area Distances of Convex Plane Curves and Improper Aﬃne Spheres, SIAM Journal on Mathematical Imaging, 1(3), p.209-227, 2008.
- Marcos Craizer, Ralph Teixeira, Moacyr Alvim: Affine properties of convex equal-area polygons, Discrete and Computational Geometry, 48(3), 580-595, 2012.
- Marcos Craizer, Equiaffine Characterization of Lagrangian Surfaces in R^4, International Journal of Mathematics, 26(9), 1550074, 2015.
- Marcos Craizer, Wojtek Domitrz, Pedro Rios: Even Dimensional Improper Affine Spheres, Journal of Mathematical Analysis and Applications, 421, 1803-1826, 2015.
- Marcos Craizer, Ralph Teixeira, Vitor Balestro: Discrete cycloids from convex symmetric polygons, Discrete and Computational Geometry, 60, 859-884, 2018.
- Marcos Craizer, Marcelo Saia, Luis Sánchez: Affine focal set of codimension 2 submanifolds contained in hypersurfaces, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 148A, 995-1016, 2018.
- Marcos Craizer, Sinesio Pesco: Affine geometry of equal-volume polygons in 3-space, Computer Aided Geometric Design 57, 44-56, 2017.
- Marcos Craizer, Sinesio Pesco: Centroaffine duality for spatial polygons, aceito para publicação no Discrete and Computational Geometry, 2019
- Marcos Craizer, Ronaldo Garcia: Quadratic points of surfaces in projective 3-space, aceito para publicação no Quarterly Journal of Mathematics, 2019.
- Marcos Craizer, Ronaldo Garcia: Centroaffine duality and Loewner’s type conjectures, pré-publicação, 2019.

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