PROGRAM

Seminar Kombinatorika, Geometrija, Topologija, Algebra (KGTA)

PLAN RADA ZA OKTOBAR 2026:

Petak, 02.10.2026. u 14:15, Kneza Mihaila 36, sala 301f i Online
Min Yan, Hong Kong university for Science and technology (HKUST)
TILINGS OF SURFACES
There are three types of surfaces, according to the curvature: (1) spherical, (2) planar, and (3) hyperbolic. I will survey tilings of surfaces, mostly about monohedral tilings, i.e., tilings by congruent polygons.

1. We present new results for spherical tilings, with the emphasys on the
   1. classification of tilings of the sphere by regular polygons,
   2. the edge-to-edge tilings of the sphere by arbitrary congruent polygons,
   3. the most general non-edge-to-edge tilings by congruent triangles.
2. New advances in the classification of planar tilings and the classification of convex polygons that can tile the plane, the so called Einstein polygons. Suprisingly, the hexagonal tilings, despite being universally considered as settled long ago, actually needed a recent completion.
3. Major results are obtained for hyperbolic tilings by $n$-gons with $n>6$. The focus is on extremal tilings, with (respectively) the minimal, respectively the maximal number of tiles. The later study is intimately related to hexagonal tilings of the plane.

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