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#Higgs Bundles

Showing: 22 courses
BunG Seminar

BunG and Higgs Bundles - Moduli Stacks and Geometric Langlands - Talk 4

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Delve into advanced mathematical concepts of moduli stacks, exploring tangent/cotangent stacks, Higgs bundles, and their role in Geometric Langlands through expert analysis of BunG framework.
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1 Lesons
1 hour 45 minutes
On-Demand
Free-Video
IMSA

Higgs Bundles on Elliptic Surfaces and Logarithmic Transformations

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Explore Higgs bundles on elliptic surfaces and their transformations, examining vector bundles' importance in mathematics and the impact of logarithmic transformations on these structures.
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11 Lesons
1 hour 7 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Representations of Fuchsian Groups, Parahoric Group Schemes by Vikraman Balaji

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Explore advanced mathematical concepts including Fuchsian groups, parahoric schemes, and root systems. Delve into complex algebraic structures and their representations in this in-depth lecture on geometric group theory.
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17 Lesons
1 hour 32 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Higgs Bundles - Lecture 1

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Explore complex geometric concepts in Higgs bundles, including Riemann surfaces, theorems, and constructions. Gain insights into advanced mathematical topics through examples, exercises, and proofs.
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21 Lesons
1 hour 18 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

An Introduction to Spectral Data for Higgs Bundles

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Explore spectral data for Higgs bundles, a key concept in algebraic geometry and mathematical physics, with insights on integrable systems and moduli spaces.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
IMSA

Asymptotics in Hitchin's Moduli Space

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Explores asymptotic behavior in Hitchin's moduli space, comparing different notions of ideal points at infinity and examining the extension of the nonabelian Hodge correspondence between partial compactifications.
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1 Lesons
53 minutes
On-Demand
Free-Video
IMSA

Wobbly Fixed Points, Equivariant Multiplicities and U(p,q)-Higgs Bundles

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Explores geometry of Higgs bundle moduli spaces, focusing on nilpotent cone fixed points and their classification. Analyzes U(p,q)-Higgs bundles and compares results with equivariant multiplicities.
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1 Lesons
58 minutes
On-Demand
Free-Video
IMSA

Higgs Bundles and the Topology of Higher Teichmüller Spaces

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Explore advanced mathematical concepts in topology, focusing on Higgs bundles and their role in understanding higher Teichmüller spaces for non-compact real Lie groups.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
IMSA

Components of Higgs Bundle Moduli Spaces - A Legacy of Hitchin's Ideas

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Explore Higgs bundle moduli spaces, their components, and the lasting impact of Hitchin's groundbreaking ideas in this mathematical lecture by Steven Bradlow.
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1 Lesons
48 minutes
On-Demand
Free-Video
IMSA

Higgs Bundles, Convex Cocompact Subgroups of SU(1,n), and Slodowy Slices

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Explore Higgs bundles, SU(1,n) subgroups, and Slodowy slices. Discover connections between stable Higgs bundles and holonomy groups, focusing on SU(1,n) representations and complex hyperbolic manifolds.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Equivariant Minimal Surfaces in Symmetric Spaces via Higgs Bundles - Lecture 3

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Explore equivariant minimal surfaces in symmetric spaces using Higgs bundles. Advanced mathematical concepts for researchers in geometry and topology.
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1 Lesons
1 hour 34 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Equivariant Minimal Surfaces in Symmetric Spaces via Higgs Bundles - Lecture 2

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Explore equivariant minimal surfaces in symmetric spaces using Higgs bundles. Advanced mathematical concepts for researchers in geometry and related fields.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Equivariant Minimal Surfaces in Symmetric Spaces via Higgs Bundles - Lecture 1

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Explore equivariant minimal surfaces in symmetric spaces using Higgs bundles. Expert-led lecture delves into advanced mathematical concepts, ideal for researchers in differential geometry.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

P=W via H2 - Moduli Space of Stable Twisted Higgs Bundles

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Explore the cohomology of stable twisted Higgs bundles moduli space through $H_2$ Lie algebra action, unifying weight and perverse filtrations via tautological classes and Hecke operators.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Motivic Invariants of Moduli of Irregular Parabolic Higgs Bundles and Bundles

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Explore motivic integration and its application to Donaldson-Thomas invariants in moduli stacks of semistable irregular parabolic Higgs bundles and connections on projective curves.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Institute for Advanced Study

Non Abelian Hodge Theory in Positive Characteristic

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Explore non-abelian Hodge theory in positive characteristic with Siqing Zhang, delving into advanced mathematical concepts and their applications.
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1 Lesons
19 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Heegaard Branes and Exact Results for Non-perturbative Complex Chern-Simons Theory

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Explore Heegaard branes in moduli spaces of Higgs bundles and their applications in mathematics, from geometric Langlands to low-dimensional topology and complex Chern-Simons theory.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Local Systems and Higgs Bundles in p-adic Geometry

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Explore the algebraic nature of local systems and Higgs bundles in p-adic geometry, drawing parallels to complex varieties and characteristic p counterparts.
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1 Lesons
1 hour 9 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
IMSA

On Coassociative ALE Fibrations and Higgs Bundles

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Explores G2-manifolds fibered by ALE spaces, connecting gauge theory and Hitchin's equations to Donaldson's program on coassociative K3 surface fibrations in G2-manifolds.
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1 Lesons
48 minutes
On-Demand
Free-Video
IMSA

Spinor-valued Higgs Bundles - Theory and Applications

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Explore spinor-valued Higgs bundles with Nigel Hitchin, examining their unique properties and implications for Riemann surface geometry. Gain insights into Dirac equations and vector bundle theory.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
BunG Seminar

Moduli Spaces in p-adic Non-abelian Hodge Theory

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Delve into p-adic non-abelian Hodge theory through geometric moduli spaces, exploring Higgs bundles, pro-étale vector bundles, and their relationships to Simpson correspondence.
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1 Lesons
2 hours 11 minutes
On-Demand
Free-Video