Tropical Algebraic Geometry  A tropical count of binodal cubic surfaces
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Title 
Tropical Algebraic Geometry  A tropical count of binodal cubic surfaces

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CC Attribution 3.0 Germany:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
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Release Date 
2020

Language 
English

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2020

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Abstract 
In this talk I will give a short introduction to tropical algebraic geometry based on a tropical count of binodal cubic surfaces (joint work with Madeline Brandt). There are 280 binodal cubic surfaces through 17 points in general position. They can be counted using tropical geometry. After a brief introduction into tropical geometry we see how the dual subdivision of the Newton polytope allows us to count surfaces through points in Mikhalkin position via floor plans. We will see that we can recover 214 binodal surfaces with separated nodes in their tropicalizations and we will also have a short look at the complexes hiding the remaining 66 surfaces.

Keywords  Tropical Geometry Enumerative Geometry binodal cubic surfaces 
00:00
Surface
Geometry
Algebraic number
Mathematical optimization
00:36
Surface
Rational number
Conic section
Number theory
Weight
Mathematical singularity
Maxima and minima
Curve
Dreiecksnetz
Geometry
Duality (mathematics)
Polytop
Object (grammar)
Cubic graph
Glattheit <Mathematik>
Vertex (graph theory)
Configuration space
Binodal
Linear map
Unimodulare Matrix
Polynomial
Geometry
Tropische Geometrie
Correspondence (mathematics)
Valuation (algebra)
Algebraic number
Point (geometry)
Complex (psychology)
Enumerated type
Plane (geometry)
Theorem
Acoustic shadow
Condition number
Block (periodic table)
Combinatorics
14:03
Surface
Duality (mathematics)
Polytop
Weight
Point (geometry)
Complex (psychology)
Cubic graph
Vertex (graph theory)
Configuration space
Enumerated type
Dreiecksnetz
Binodal
14:31
Surface
Cubic graph
Enumerated type
Binodal
14:57
Surface
Coefficient
Kettenkomplex
Mathematical singularity
Point (geometry)
Cubic graph
Hausdorff dimension
Theorem
Enumerated type
Binodal
17:58
Surface
Kettenkomplex
Cubic graph
Vertex (graph theory)
Enumerated type
Binodal
18:43
Surface
Geometry
Linear algebra
Tropische Geometrie
Kettenkomplex
Algebraic number
Point (geometry)
Theory
Curve
Enumerated type
Flächensingularität
Planar graph
Geometry
Hausdorff space
Canadian Mathematical Society
Cubic graph
Partial derivative
Vertex (graph theory)
Multiplication
Binodal
Hyperplane