Hidden Structures on de Rham Cohomology of P-adic Analytic Varieties
Dive into hidden structures on de Rham cohomology of p-adic analytic varieties. Explore Hodge filtration, Frobenius, and monodromy in this advanced mathematical colloquium.
Hodge Theory of Abelian Covers of Algebraic Varieties
Explore Hodge Theory of Abelian Covers in algebraic varieties, covering Alexander modules, multivariables, and transformations. Gain insights into advanced mathematical concepts and their applications.
Periods of Algebraic Cycles and Hodge Loci - Part 1
Explore periods of algebraic cycles and Hodge loci in this advanced mathematics lecture, part of the GADEPs conference on Noether-Lefschetz and Hodge loci.
Teoria de Hodge: Variedade de Fermat I - Aula 17
Explore a Teoria de Hodge aplicada à variedade de Fermat, aprofundando-se em conceitos avançados de geometria algébrica e topologia.
Teoria de Hodge: Gauss-Manin Connection - Aula 16
Explore a conexão de Gauss-Manin na Teoria de Hodge, aprofundando-se em conceitos avançados de matemática pura aplicada ao doutorado.
Teoria de Hodge: Hodge Loci - Aula 19
Explore Hodge loci in advanced mathematics, delving into complex algebraic geometry and Hodge theory concepts for doctoral-level understanding.
Teoria de Hodge da Variedade de Fermat - Aula 18
Explore a Teoria de Hodge aplicada à variedade de Fermat, aprofundando-se em conceitos avançados de geometria algébrica e topologia.
A Data-Driven Finite Element Exterior Calculus
Explore data-driven finite element exterior calculus for developing reduced-order models of multiphysics systems, combining machine learning with traditional finite element methods for robust surrogate modeling.
Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry
Explore p-adic geometry through Riemann-Hilbert correspondence, covering local systems, Galois representations, Hodge theory, and cohomology in this advanced mathematics lecture.
Unitary Representations of Reductive Lie Groups
Explore unitary representations of reductive Lie groups using Hodge theory, including progress on a conjecture. Joint work with Kari Vilonen presented by Harvard's Wilfried Schmid.
Minimal Exponents of Singularities
Explore advanced mathematical concepts like minimal exponents, Bernstein-Sato polynomials, and their connections to D-modules, Hodge theory, and birational geometry in this in-depth lecture.
Fixed Points in Toroidal Compactifications and Essential Dimension of Covers
Explores essential dimension in algebraic objects, focusing on congruence covers of Shimura varieties. Presents new geometric approaches and fixed point theorems, extending incompressibility results to exceptional types.
A Non-Archimedean Definable Chow Theorem
Explore non-archimedean algebraization theorems and their applications in Diophantine geometry, focusing on a p-adic analogue of the definable Chow theorem.
Log Symplectic Pairs and Mixed Hodge Structures
Explores log symplectic pairs, their connection to hyperkaehler variety degenerations, and classification of pure weight pairs. Discusses analogies with log Calabi-Yau surfaces and implications for mixed Hodge structures.
O-Minimality and Hodge Theory - Definable GAGA + Griffiths Conjecture
Explore o-minimal geometry, definable GAGA, and Griffiths Conjecture in algebraic geometry. Learn about definable analytic spaces, Oka coherence, and their applications to period maps and variations of mixed Hodge structures.
Mixed Period Maps: Definability and Algebraicity
Explore definable analytic spaces and their applications in algebraic geometry, focusing on period maps and mixed Hodge structures. Learn about o-minimal geometry and its role in proving key conjectures.
Holomorphic Bisectional Curvature and Applications to Deformations and Rigidity of Mixed Hodge Structure
Explore holomorphic bisectional curvature in Hodge theory, focusing on mixed Hodge metrics, rigidity results, and applications to geometric examples.
Period Mapping at Infinity
Explore Hodge theory's global study of period mapping at infinity, including new invariants, moduli space implications, and geometric insights for singular varieties.
A Homological Interpretation of Higher Du Bois and Higher Rational Singularities
Explore homological interpretations of higher Du Bois and rational singularities, focusing on hypersurfaces and characteristic classes. Gain insights into advanced algebraic geometry concepts.
Hodge Theory, Between Algebraicity and Transcendence
Explore recent advances in Hodge theory, comparing algebraic structures and bounding transcendence using o-minimal geometry. Gain insights into complex algebraic varieties and their applications.
Robert Ghrist - Laplacians and Network Sheaves
Explore cellular sheaves, Laplacians, and their applications in social networks and opinion dynamics. Learn about decentralized methods for computing sheaf cohomology and analyzing consensus and polarization.