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#Algebraic Curves

Showing: 51 courses
ICTP Mathematics

Ecuaciones Diofantinas con Pocas Soluciones - Lecture 4

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Explora teoremas y aplicaciones en ecuaciones diofantinas, incluyendo el teorema de Faltings para curvas y ejemplos prácticos, profundizando en la teoría de números.
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5 Lesons
50 minutes
On-Demand
Free-Video
BunG Seminar

Introduction to Stacks and Principal G-Bundles in Algebraic Geometry - Talk 1

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Dive into algebraic stacks theory and principal G-bundles on algebraic curves, exploring their moduli stack properties and connections to geometric representation theory.
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1 Lesons
1 hour 46 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Moduli Spaces of Bundles on Curves with Abelian Motives

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Explore the mathematical theory behind abelian motives in bundle moduli spaces, examining motivic formulas and their relationship to cohomological phenomena on curves.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Insights into Mathematics

Curves, Functions and Surfaces - Math Terminology - NJ Wildberger

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Explore key mathematical concepts including curves, functions, and surfaces. Learn about conic sections, exponential and trigonometric functions, and their applications in calculus and three-dimensional geometry.
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8 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

The Differential Calculus for Curves - Differential Geometry

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Exploring advanced differential calculus for algebraic curves, including tangent lines, conics, and point classification. Extends to 3D surfaces, offering a comprehensive view of curve analysis.
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10 Lesons
48 minutes
On-Demand
Free-Video
Insights into Mathematics

The Curvature of a Parabola, Without Calculus - Rational Geometry Math Foundations

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Algebraic approach to calculate parabola curvature without calculus, using circle circumquadrance and triangle properties. Demonstrates wider applicability to various algebraic curves.
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5 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Parametrized Curves and Algebraic Curves - Differential Geometry

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Explore parametrization of curves, from ancient Greek conics to 17th-century algebraic curves. Discover fascinating mechanisms generating curves, including four-bar and Watt's linkages.
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7 Lesons
41 minutes
On-Demand
Free-Video
Insights into Mathematics

An Introduction to Algebraic Curves - Arithmetic and Geometry Math Foundations

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Explore the history and concepts of algebraic curves, from ancient Greek spirals to modern polynomial approaches, setting the stage for generalizing algebraic calculus beyond functions.
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10 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

Newton's Method and Algebraic Curves - Real Numbers and Limits Math Foundations

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Explore Newton's method for algebraic curves, examining Fermat curves and Bernoulli's Lemniscate. Learn about Taylor expansions, tangent planes, and iterative techniques for approximating curve intersections.
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8 Lesons
30 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Complex Dynamics and Arithmetic Geometry by Laura DeMarco

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Exploring connections between dynamical systems and arithmetic geometry, focusing on periodic points, torsion points, and algebraic curves in genus 2. Insights from polynomial dynamics and Julia sets illustrate key concepts.
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14 Lesons
1 hour 1 minute
On-Demand
Free-Video
IMSA

Donaldson-Thomas and Gromov-Witten Invariants - Part 17

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Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their relevance to superstring theory.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
IMSA

Donaldson-Thomas and Gromov-Witten Invariants - Part 16

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Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their relevance to superstring theory.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
IMSA

Donaldson-Thomas and Gromov-Witten Theories - Part 14

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Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their connections to superstring theory.
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1 Lesons
1 hour 23 minutes
On-Demand
Free-Video
IMSA

Donaldson-Thomas and Gromov-Witten Theories - Part 13

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Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their relevance to superstring theory.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
IMSA

Donaldson-Thomas and Gromov-Witten Theories - Part 12

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Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their relevance to superstring theory.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
IMSA

Donaldson-Thomas and Gromov-Witten Theories - Part XI

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Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their connections to superstring theory.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
IMSA

Donaldson-Thomas and Gromov-Witten Theories - Part 10

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Explore moduli spaces of algebraic curves and coherent sheaves, their invariants, and connections to geometry, topology, and string theory. Includes computations of Gromov-Witten and Donaldson-Thomas invariants.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
IMSA

Donaldson-Thomas and Gromov-Witten Theories - Part 9

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Explore moduli spaces of algebraic curves and coherent sheaves, their invariants, and connections to geometry, topology, and string theory. Includes computations of Gromov-Witten and Donaldson-Thomas invariants.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
IMSA

Donaldson-Thomas and Gromov-Witten Theories - Part 8

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Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their connections to superstring theory.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
IMSA

Donaldson-Thomas and Gromov-Witten Theories - Part 7

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Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their relevance to superstring theory.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
IMSA

Donaldson-Thomas and Gromov-Witten Theories - Part VI

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Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their connections to superstring theory.
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1 Lesons
1 hour 38 minutes
On-Demand
Free-Video
ICTP Mathematics

AGRA IV - Diophantine Equations with Few Solutions - Lecture 2

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Exploración avanzada de ecuaciones diofantinas con soluciones limitadas, enfocándose en técnicas analíticas y algebraicas para abordar problemas complejos en teoría de números.
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1 Lesons
58 minutes
On-Demand
Free-Video
ICTP Mathematics

Tautological Rings of Moduli Spaces of Curves - Lecture 3

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Explore advanced concepts in algebraic geometry, focusing on tautological rings and their relation to moduli spaces of curves in this in-depth mathematical lecture.
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1 Lesons
1 hour
On-Demand
Free-Video
ICTP Mathematics

P=W via H_2

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Exploration of Lie algebra H_2 and its action on cohomology of moduli spaces, connecting natural filtrations and tautological operations to unify mathematical concepts.
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1 Lesons
1 hour 41 minutes
On-Demand
Free-Video
ICTP Mathematics

Algebraic Curves Defined by Singular Instanton Homology

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Explore singular instanton homology's role in defining algebraic curves, delving into advanced mathematical concepts at the intersection of geometry and topology.
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1 Lesons
53 minutes
On-Demand
Free-Video
IMSA

Cohomology of Hurwitz Spaces

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Explore the cohomology of Hurwitz spaces, focusing on branched covers of the affine line and their connections to braided Hopf algebras and a new family of braided operads.
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1 Lesons
1 hour
On-Demand
Free-Video
Insights into Mathematics

Quadratic Curvature for Algebraic Curves - Differential Geometry Lecture 15

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Explores advanced formulas for curvature of algebraic surfaces in 3D space, focusing on the normal paraboloid as key to encoding quadratic metrical information and curvatures in general situations.
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1 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

The Number Theory Revival - From Diophantus to Fermat

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Explore the revival of number theory, from Diophantus to Fermat, covering key concepts like combinatorics, algebraic curves, and famous theorems in this comprehensive mathematical journey.
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10 Lesons
57 minutes
On-Demand
Free-Video
Insights into Mathematics

Complex Numbers and Curves in 19th Century Mathematics

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Explore complex numbers, algebraic curves, and their intersection with projective geometry and topology. Discover how these concepts revolutionized 19th-century mathematics and laid the foundation for modern algebraic geometry.
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1 Lesons
58 minutes
On-Demand
Free-Video
Insights into Mathematics

Quadratic Curvature for Algebraic Curves - Differential Geometry Lecture 14

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Explores quadratic curvature for algebraic curves, extending from parabolas to general conics. Discusses connections between curvature and foci, emphasizing the power of formulas in differential geometry.
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1 Lesons
33 minutes
On-Demand
Free-Video
Insights into Mathematics

Projective View of Conics and Quadrics - Differential Geometry Lecture 9

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Explore projective geometry's application to conics and quadrics, using homogeneous coordinates to unify the study of algebraic curves and surfaces in plane and space.
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1 Lesons
39 minutes
On-Demand
Free-Video
IMSA

A New Perspective on Exotic Manifolds - Spherical Duality and Torus Links

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Explore exotic manifolds through spherical duality and torus links. Discover new perspectives on homotopy spheres, O(3)-actions, and connections to singularity theory and mirror symmetry.
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1 Lesons
41 minutes
On-Demand
Free-Video
Fields Institute

Exploring the Real Parameter Space

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Delve into enumerative geometry with Margaret Regan as she investigates real parameter spaces, offering insights into this fascinating mathematical realm.
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1 Lesons
53 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
M-Seminar, Kansas State University

An Irregular Deligne-Simpson Problem

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Explore connections on algebraic curves with prescribed singularities, focusing on G-connections with regular and irregular singularities, using rational Cherednik algebras.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Geometry from Donaldson-Thomas Invariants

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Explore Donaldson-Thomas invariants in 3-Calabi-Yau categories to define geometric structures on stability condition spaces, focusing on hyperkähler structures and moduli-theoretic constructions.
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1 Lesons
1 hour 25 minutes
On-Demand
Free-Video
Isaac Newton Institute for Mathematical Sciences

Hasse Principle for Simply Connected Groups - Kirk Lecture

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Explore the Hasse principle for simply connected groups, its significance in number fields, and recent progress in function fields of curves over p-adic fields.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institute for Advanced Study

KP Solutions from Algebraic Curves and the Positive Grassmannian

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Explore KP solutions derived from algebraic curves and the positive Grassmannian in this advanced mathematical talk by Yelena Mandelshtam.
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1 Lesons
19 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Algebraic Curves with Many Rational Points over Finite Fields

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Explore algebraic curves with many rational points over finite fields, focusing on maximum curves, automorphisms, and their applications in coding theory.
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15 Lesons
49 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Graded Lie Algebras and Families of Algebraic Curves

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Explore graded Lie algebras and their connection to algebraic curve families. Gain insights into natural questions, philosophy, and Thorne's construction in this mathematical symposium talk.
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10 Lesons
51 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Computing Ceresa Classes of Curves

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Explore computational methods for Ceresa classes of curves in algebraic geometry, focusing on arithmetic and geometric aspects.
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1 Lesons
1 hour
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

On ODEs Satisfied by Modular Forms

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Explore ODEs satisfied by modular forms, their invariance under Lie groups, and associated algebraic curves. Extend results to Jacobi forms and examine examples from classical modular forms.
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9 Lesons
1 hour 1 minute
On-Demand
Free-Video
IPhT-TV

Moduli Space of Curves and Its Intersection Theory - Lecture 2

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Explore advanced concepts in algebraic geometry, focusing on moduli spaces of curves and their intersection theory in this in-depth lecture.
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1 Lesons
1 hour 53 minutes
On-Demand
Free-Video
IPhT-TV

Moduli Space of Curves and Its Intersection Theory - Lecture 1

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Explore the moduli space of curves and its intersection theory in this advanced mathematical lecture by Nitin Kumar Chidambaram.
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1 Lesons
1 hour 51 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Isolated and Parameterized Points on Algebraic Curves

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Explore isolated and parameterized points on algebraic curves, examining their behavior in families and implications for elliptic curve arithmetic. Gain insights into curve geometry and its connection to arithmetic properties.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
BIMSA

Sparsity of Rational Points on Curves - What is Known and What is Expected

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Explore the known results and open questions surrounding the sparsity of rational points on curves, gaining insights into this mathematical concept.
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1 Lesons
49 minutes
On-Demand
Free-Video
BIMSA

Recent Progress in Geometric Langlands - ICBS 2024

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Explore recent advancements in geometric Langlands theory, including verified conjectures and related questions in algebraic geometry and representation theory.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
BIMSA

Algebraic Curves and Minimal Surfaces

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Explore algebraic curves and minimal surfaces with Prof. Sebastian Heller, delving into Riemann surfaces, harmonic maps, and experimental mathematics.
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1 Lesons
51 minutes
On-Demand
Free-Video
ICTP Mathematics

Hopf-Galois Extensions and Applications

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Explore Hopf-Galois theory, its applications in field extensions, and arithmetic properties derived from algebraic curves. Gain insights into this generalization of classical Galois theory.
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1 Lesons
55 minutes
On-Demand
Free-Video
Max Planck Science

Riemann's Theta Function: From Algebraic Geometry to Water Wave Physics

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Explore Riemann's theta function's role in mathematics, from geometry to cryptography, and its connection to water wave physics through the KP equation.
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1 Lesons
18 minutes
On-Demand
Free-Video
Institute for Advanced Study

Maximal Mumford Curves and Graph Embeddings in Real Algebraic Geometry

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Explore the geometric properties of MM-curves, focusing on real stable curves, hyperplane arrangements, and graph embeddings in relation to Mumford curves and their deformations.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video