Explicit Birational Geometry

Time:Tuesdays & Thurdays 9:50-11:25 am May 7 - July 11, 2024

Venue:Lecture Hall B725 Shuangqing Complex Building A Zoom Meeting ID: 271 534 5558 Passcode: YMSC

Speaker:Florin Ambro Institute of Mathematics of the Romanian Academy

Register Now


Toric varieties are geometric objects defined combinatorially, much like CW complexes in topology. They can be used to study geometrically combinatorial objects like semigroups, cones, polytopes or simplicial complexes. In Algebraic Geometry, toric varieties are a rich source of explicit examples, a good testing ground for gaining intuition for open problems.

The first part of this course is a general introduction to toric varieties. We assume basic knowledge of Algebraic Geometry.

The second part tours several topics of birational geometry, in the special case of toric varieties. The goal is to construct many explicit examples: of singularities, polarized varieties, and varieties of K-pure type (Fano, Calabi-Yau, canonically polarized). We assume basic knowledge of Birational Geometry.

We also present the combinatorial counterpart of part two, essentially criteria to construct central lattice points in convex sets.

About the Speaker

Florin Ambro is a Senior Researcher II at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy. His primary research interests are Algebraic Geometry, Classification theory, and Singularities.

Personal Website:

DATEMay 5, 2024
Related News
    • 0

      Introduction to Exceptional Geometry

      Record: YesLevel: GraduateLanguage: EnglishPrerequisiteLinear algebra, basics of Riemmanian geometryAbstractThe classification of Riemannian manifolds with special holonomy contains two “exceptional” cases: G2 and Spin(7). Manifolds with holonomy contained in G2 or Spin(7) are called G2-manifolds or Spin(7)-manifolds, respectively. In this course, I will introduce various topics of G2 and Spi...

    • 1

      Derived Algebraic/Differential Geometry

      Record: YesLevel: GraduateLanguage: EnglishPrerequisiteCommutative Algebra (Atiyah McDonald or Rottman), Algebraic Geometry (Hartshorne or Grothendieck’s EGA/SGA)AbstractDerived Algebraic Geometry is a machinery regarded as an extension of algebraic geometry, whose goal is to study exotic geometric settings and situations that might occur in algebraic geometry where algebraic geometry might no...