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#Tropical Geometry

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M-Seminar, Kansas State University

Superabundance and Unobstructedness in Lagrangian Torus Fibrations - Lecture

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Explore the concept of Lagrangian realization in tropical geometry through this M-Seminar talk by Jeff Hicks from the University of Edinburgh. Delve into the relationship between tropical curves in the base of a Lagrangian torus fibration and their corre…
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Tropical Functions on Skeletons

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Explore tropical functions on skeletons in valued fields with Antoine Ducros' insightful mathematical conference talk from CIRM's Audiovisual Mathematics Library.
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1 Lesons
58 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Complex Dynamics in the Tropics - Structures on 2- and 3-Manifolds Coming from Dynamical Systems

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Explore complex dynamics in the tropics, focusing on structures in 2- and 3-manifolds derived from dynamical systems. Gain insights into multimodal maps, hyperbolic groups, and related mathematical concepts.
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8 Lesons
43 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Commutative Algebra and Algebraic Geometry - 15th ALGA Meeting

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Explore geometric methods and tropical geometry in algebraic curves, focusing on Abel maps and Jacobians. Compare algebraic and tropical approaches for deeper mathematical insights.
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12 Lesons
12 minutes
On-Demand
Free-Video
Institute for Advanced Study

Tropical Vector Bundles and Matroids

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Delve into advanced geometric concepts exploring toric vector bundles, matroids, and their tropical counterparts through classification, equivariant K-theory, and characteristic classes.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institute for Advanced Study

Cohomologically Tropical Varieties and Mixed Hodge Structures

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Delve into advanced geometric concepts exploring tropicalizations of torus subvarieties, focusing on Poincaré duality and mixed Hodge structures in relation to hyperplane arrangements.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Institute for Advanced Study

Tropicalizing Principal Minors of Positive Definite Matrices

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Delve into advanced mathematical concepts exploring tropicalization of principal minors, M-concave functions, and their relationship with tropical Grassmannian and Flag varieties.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Face Structures of Tropical Polyhedra

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Explore tropical polyhedra's face structures, focusing on monomial tropical polyhedra to overcome issues in classical definitions and investigate combinatorial properties.
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8 Lesons
29 minutes
On-Demand
Free-Video
IMSA

Enumerative Geometry and the Quantum Torus

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Explore enumerative geometry through tropical curves, pseudotropical curves, and their connection to Lie algebras and quantum torus. Discover innovative approaches to classical counting problems in algebraic geometry.
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10 Lesons
1 hour
On-Demand
Free-Video
IMSA

A Tropical Approach to Homological Mirror Symmetry of Quadrics

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Tropical geometry approach to homological mirror symmetry of quadrics, exploring new anti-canonical divisor and potential construction. Compares with previous work and discusses exceptional collections.
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11 Lesons
1 hour 7 minutes
On-Demand
Free-Video
IMSA

Birational Geometry of Moduli Spaces via the Essential Skeleton

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Explore the essential skeleton in birational geometry, linking it to tropical geometry and moduli spaces, with a focus on $\mathcal{M}_{0,n}$ and potential applications to hyperplane arrangements.
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10 Lesons
53 minutes
On-Demand
Free-Video
International Mathematical Union

The Positive Grassmannian, the Amplituhedron, and Cluster Algebras

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Explore the positive Grassmannian and amplituhedron, delving into their combinatorial structures and connections to physics, integrable systems, and scattering amplitudes using oriented matroids, tropical geometry, and cluster algebras.
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15 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Tropical Geometry of Phylogenetic Tree Spaces

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Explore tropical geometry's application to phylogenetic tree spaces, examining BHV space, tropical Grassmannians, and their implications for computational biology and statistics.
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14 Lesons
59 minutes
On-Demand
Free-Video
ICTP Mathematics

Kirchhoff’s Theorem and Semi-Canonical Representatives for the Tropical Prym Variety

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Explore Kirchhoff's theorem, metric graphs, and tropical Prym varieties. Delve into divisors, Jacobians, and double covers, gaining insights into advanced algebraic geometry concepts.
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13 Lesons
34 minutes
On-Demand
Free-Video
ICTP Mathematics

Tropical Prym Varieties

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Explore tropical geometry, divisors, chip firing, and Jacobians. Learn about double covers, induced maps, and generic curves in relation to Prym varieties.
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13 Lesons
29 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Tropical Limit of String Theory and Feynman Integrals

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Explore the intersection of string theory, Feynman integrals, and tropical geometry. Discover how tropical limits provide insights into complex physical phenomena and algebraic structures.
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28 Lesons
1 hour 19 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Geometry of Tropical Varieties with Applications - Lecture 3

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Explore advanced concepts in tropical geometry, including fans, fanfolds, and tropical modifications. Learn about operations, constructions, and theorems applicable to tropical varieties and their geometric properties.
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21 Lesons
1 hour 9 minutes
On-Demand
Free-Video
IMSA

A Splitting Formula for Punctured Gromov-Witten Invariants

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Explore punctured Gromov-Witten theory and its role in mirror symmetry. Learn about a new formula for reconstructing invariants, generalizing Jun Li's degeneration formula.
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1 Lesons
51 minutes
On-Demand
Free-Video
IMSA

Top Weight Cohomology of M_g

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Explore the top-graded weight filtration on open moduli spaces, with applications to exponential growth in H^{4g-6}(M_g, Q) dimensions, disproving previous conjectures.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
IMSA

Tropical Analog of the Hodge Conjecture for Smooth Algebraic Varieties Over Trivially Valued Fields

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Explore tropical geometry's approach to cycle class maps, focusing on a proof of the Hodge conjecture's tropical analog for smooth algebraic varieties over trivially valued fields.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
IMSA

Tropical Geometry & Artificial Life

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Explore self-organized criticality in artificial life models through tropical geometry, examining its applications and implications for understanding complex systems.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Tropical Coordinates on the Space of Persistence Barcodes

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Explore tropical coordinates in persistence barcodes, a key concept in applied algebraic topology, and their applications in data analysis and shape recognition.
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1 Lesons
54 minutes
On-Demand
Free-Video
ICTP Mathematics

Basic Notions Seminar on Tropical Geometry

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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.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Fields Institute

Moduli Spaces in Tropical Geometry

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Explore moduli spaces in tropical geometry, examining their structure and applications in algebraic geometry, with insights from Brown University expert Melody Chan.
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1 Lesons
57 minutes
On-Demand
Free-Video
Joint Mathematics Meetings

Tropical Geometry and Shallow Water Waves

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Explore the fascinating intersection of tropical geometry and shallow water waves in this engaging lecture by Harvard mathematician Lauren Kiyomi Williams.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Fields Institute

Tropical Intersections in Algebraic Geometry

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Explore tropical intersections in algebraic geometry, examining their applications and implications for mathematical research and problem-solving.
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1 Lesons
33 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Symmetries of Discrete and Ultradiscrete Integrable Systems - Lecture 3

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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.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Symmetries of Discrete and Ultradiscrete Integrable Systems - Lecture 1

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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.
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1 Lesons
1 hour
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Symmetries of Discrete and Ultradiscrete Integrable Systems - Lecture 2

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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.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Tropical Contributions to Enumerative Geometry of Target Dimension One - Lecture 3

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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.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Tropical Contributions to Enumerative Geometry of Target Dimension One - Lecture 2

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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.
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1 Lesons
54 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Tropical Contributions to Enumerative Geometry of Target Dimension One - Lecture 1

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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.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Tropicalization of the Universal Jacobian: Logarithmic and Non-Archimedean Views

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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.
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1 Lesons
43 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Complex Dynamics in the Tropics - Critical Locus for Complex Henon Maps

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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.
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1 Lesons
43 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Exponential Volumes in Geometry and Representation Theory

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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.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Institut Henri Poincaré

Tropical Fukaya Algebras

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Explore multiple cut operations on symplectic manifolds and their impact on curve count-based invariants, focusing on Fukaya algebras and tropical graph representations.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Cluster Duality and Non-Holomorphic Spectral Curves

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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.
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9 Lesons
49 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

The Nullstellensatz and Positivstellensatz for Sparse Tropical Polynomial Systems

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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.
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1 Lesons
46 minutes
On-Demand
Free-Video
Institute for Advanced Study

Tropical Quiver Representations and Their Geometric Applications

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Delve into advanced algebraic geometry concepts through tropical quiver representations, exploring Grassmannians, flag varieties, and their matroidal analogues as fundamental moduli spaces.
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1 Lesons
58 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Combinatorics and Geometry of the Amplituhedron

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Explore the amplituhedron's geometric properties, connections to various mathematical fields, and recent progress on key conjectures in this advanced mathematical lecture.
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1 Lesons
54 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Quivers, Flow Trees, and Log Curves

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Explore the connection between Donaldson-Thomas invariants, attractor flow trees, and log Gromov-Witten invariants in quiver theory and toric geometry.
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1 Lesons
1 hour 27 minutes
On-Demand
Free-Video
Institute for Advanced Study

The Moduli Space of Matroids - Lecture 1

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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.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Extensions of Discrete Toda Lattices and their Application to Box-Ball Systems

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Delve into discrete integrable systems, exploring Toda lattices, box-ball systems, and their mathematical applications through advanced theoretical physics and mathematical frameworks.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Quadratic Differentials and Degenerate Eigenvalues

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Explore the relationship between quadratic differentials and degenerate eigenvalues in discrete integrable systems through advanced mathematical concepts and theoretical physics applications.
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1 Lesons
26 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Integrable Difference Equations and Orthogonal Polynomials with respect to a Discrete Measure

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Explore advanced mathematical concepts in discrete integrable systems, focusing on difference equations, cluster algebras, and probabilistic models through expert-led mini-courses and workshops.
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1 Lesons
58 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Skew Column RSK Dynamics and the Box-Ball System

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Explore discrete integrable systems through RSK dynamics and Box-Ball systems, focusing on mathematical structures, quantum groups, and stochastic processes in theoretical physics.
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1 Lesons
58 minutes
On-Demand
Free-Video
Institute for Advanced Study

Twisted (Co)homology of Matroids and Hyperplane Arrangement Complements

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Delve into advanced mathematical concepts exploring twisted (co)homology, hyperplane arrangements, and matroidal pairings, with applications to scattering amplitudes in physics.
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1 Lesons
1 hour 51 minutes
On-Demand
Free-Video