AbstractIn this talk, I will consider isomorphisms of Bergman fans of matroids. Motivated by algebraic geometry, these isomorphisms can be considered as matroid analogs of birational maps. I will introduce Cremona automorphisms of the coarsest fan structure. These produce a class of automorphisms which do not come from automorphisms of the underlying matroid. I will then explain that the automo...
Abstract：Alongside with conic bundles, del Pezzo surfaces are possible outcomes of the Minimal Model Program ran on a geometrically rational surface. Thus, many questions about birational geometry and birational automorphisms of geometrically rational surfaces reduce to similar questions for del Pezzo surfaces. I will survey some known results concerning birational models and birational automo...
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