Tropical Coordinates on the Space of Persistence Barcodes
Explore tropical coordinates in persistence barcodes, a key concept in applied algebraic topology, and their applications in data analysis and shape recognition.
Basic Notions Seminar on Tropical Geometry
Introduction to tropical geometry, focusing on plane tropical curves as piecewise linear graphs and their applications in enumerative geometry. Explores the combinatorial aspects that reflect properties of algebraic varieties.
Moduli Spaces in Tropical Geometry
Explore moduli spaces in tropical geometry, examining their structure and applications in algebraic geometry, with insights from Brown University expert Melody Chan.
Tropical Geometry and Shallow Water Waves
Explore the fascinating intersection of tropical geometry and shallow water waves in this engaging lecture by Harvard mathematician Lauren Kiyomi Williams.
Tropical Intersections in Algebraic Geometry
Explore tropical intersections in algebraic geometry, examining their applications and implications for mathematical research and problem-solving.
Symmetries of Discrete and Ultradiscrete Integrable Systems - Lecture 3
Explore symmetries in discrete and ultradiscrete integrable systems, focusing on KdV equation, Toda lattice, and box-ball system. Discover connections to tropical geometry and crystal base theory.
Symmetries of Discrete and Ultradiscrete Integrable Systems - Lecture 1
Explore symmetries in discrete and ultradiscrete integrable systems, focusing on KdV equation, Toda lattice, and box-ball system. Discover connections to tropical geometry and crystal base theory.
Symmetries of Discrete and Ultradiscrete Integrable Systems - Lecture 2
Explore symmetries in discrete and ultradiscrete integrable systems, focusing on KdV equation, Toda lattice, and box-ball system. Discover connections to tropical geometry and crystal base theory.
Tropical Contributions to Enumerative Geometry of Target Dimension One - Lecture 3
Explore tropical geometry's impact on enumerative problems in moduli spaces of curves. Delve into tropical Hurwitz numbers, k-DR cycles, and leaky Hurwitz numbers, with insights on incorporating descendants.
Tropical Contributions to Enumerative Geometry of Target Dimension One - Lecture 2
Explore tropical geometry's impact on enumerative problems in moduli spaces of curves. Delve into tropical Hurwitz numbers, k-DR cycles, and leaky Hurwitz numbers. Examine ongoing research on descendants in tropical algorithms.
Tropical Contributions to Enumerative Geometry of Target Dimension One - Lecture 1
Explore tropical geometry's impact on enumerative problems in moduli spaces of curves. Delve into tropical Hurwitz numbers, branch polynomials, and k-DR cycles, uncovering new perspectives in algebraic combinatorics.
Tropicalization of the Universal Jacobian: Logarithmic and Non-Archimedean Views
Explore tropicalization of universal Jacobians, examining logarithmic and non-archimedean perspectives. Gain insights into moduli spaces, cone stacks, and new stability conditions for compactified Jacobians.
Complex Dynamics in the Tropics - Critical Locus for Complex Henon Maps
Explore complex dynamics in the tropics, focusing on critical locus for complex Henon maps. Gain insights from T. Firsova's presentation at IMPA's international congress celebrating Carsten Lunde Petersen.
Exponential Volumes in Geometry and Representation Theory
Explore exponential volumes in geometry and representation theory, focusing on moduli spaces, hyperbolic structures, and Lie groups. Discover connections to Mirzakhani's recursions and Whittaker functions.
Tropical Fukaya Algebras
Explore multiple cut operations on symplectic manifolds and their impact on curve count-based invariants, focusing on Fukaya algebras and tropical graph representations.
Cluster Duality and Non-Holomorphic Spectral Curves
Explore cluster duality, geometric interpretations of tropical points, and their connections to local systems on curves through graphs, Lagrangian coverings, and affine group-valued local systems.
The Nullstellensatz and Positivstellensatz for Sparse Tropical Polynomial Systems
Explorez les avancées en algèbre tropicale, notamment le Nullstellensatz et le Positivstellensatz pour les systèmes polynomiaux tropicaux clairsemés, avec des applications aux jeux à paiement moyen paramétrique.
Tropical Quiver Representations and Their Geometric Applications
Delve into advanced algebraic geometry concepts through tropical quiver representations, exploring Grassmannians, flag varieties, and their matroidal analogues as fundamental moduli spaces.
Combinatorics and Geometry of the Amplituhedron
Explore the amplituhedron's geometric properties, connections to various mathematical fields, and recent progress on key conjectures in this advanced mathematical lecture.
Quivers, Flow Trees, and Log Curves
Explore the connection between Donaldson-Thomas invariants, attractor flow trees, and log Gromov-Witten invariants in quiver theory and toric geometry.
The Moduli Space of Matroids - Lecture 1
Delve into advanced mathematical concepts exploring matroid theory, F1-geometry, and tropical schemes, focusing on Baker-Bowler's theory and its applications to Grassmannians and representation theory.