AGRA IV - Diophantine Equations with Few Solutions - Lecture 2
Exploración avanzada de ecuaciones diofantinas con soluciones limitadas, enfocándose en técnicas analíticas y algebraicas para abordar problemas complejos en teoría de números.
Tautological Rings of Moduli Spaces of Curves - Lecture 3
Explore advanced concepts in algebraic geometry, focusing on tautological rings and their relation to moduli spaces of curves in this in-depth mathematical lecture.
P=W via H_2
Exploration of Lie algebra H_2 and its action on cohomology of moduli spaces, connecting natural filtrations and tautological operations to unify mathematical concepts.
Algebraic Curves Defined by Singular Instanton Homology
Explore singular instanton homology's role in defining algebraic curves, delving into advanced mathematical concepts at the intersection of geometry and topology.
Cohomology of Hurwitz Spaces
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.
Quadratic Curvature for Algebraic Curves - Differential Geometry Lecture 15
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.
The Number Theory Revival - From Diophantus to Fermat
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.
Complex Numbers and Curves in 19th Century Mathematics
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.
Quadratic Curvature for Algebraic Curves - Differential Geometry Lecture 14
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.
Projective View of Conics and Quadrics - Differential Geometry Lecture 9
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.
A New Perspective on Exotic Manifolds - Spherical Duality and Torus Links
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.
Exploring the Real Parameter Space
Delve into enumerative geometry with Margaret Regan as she investigates real parameter spaces, offering insights into this fascinating mathematical realm.
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.
An Irregular Deligne-Simpson Problem
Explore connections on algebraic curves with prescribed singularities, focusing on G-connections with regular and irregular singularities, using rational Cherednik algebras.
Geometry from Donaldson-Thomas Invariants
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.
Hasse Principle for Simply Connected Groups - Kirk Lecture
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.
KP Solutions from Algebraic Curves and the Positive Grassmannian
Explore KP solutions derived from algebraic curves and the positive Grassmannian in this advanced mathematical talk by Yelena Mandelshtam.
Algebraic Curves with Many Rational Points over Finite Fields
Explore algebraic curves with many rational points over finite fields, focusing on maximum curves, automorphisms, and their applications in coding theory.
Graded Lie Algebras and Families of Algebraic Curves
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.
Computing Ceresa Classes of Curves
Explore computational methods for Ceresa classes of curves in algebraic geometry, focusing on arithmetic and geometric aspects.
On ODEs Satisfied by Modular Forms
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.