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#Dirac Operator

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Santa Fe Institute

Topology Shapes Dynamics of Higher-order Networks

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Exploring how higher-order network interactions influence non-linear dynamics, synchronization, and percolation in complex systems like brain networks and climate patterns.
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1 Lesons
56 minutes
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Free-Video
Centre de recherches mathématiques - CRM

Spectral Analysis of Dirac Operators with a Purely Imaginary Dislocation

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Explore spectral analysis of Dirac operators with imaginary dislocation, covering Green functions, pseudospectra, and effects of matrix potentials on essential and discrete spectra.
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1 Lesons
55 minutes
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Free-Video
Centre de recherches mathématiques - CRM

The Moduli Space of Twisted Laplacians and Random Matrix Theory

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Explore the convergence of spectral number variance for twisted Laplacians to random matrix theory ensembles, extending Rudnick's work to break time-reversal symmetry and include Dirac operators.
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1 Lesons
1 hour 1 minute
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Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Maria Esteban - Spectral Results and Open Problems for Dirac-Coulomb Operators With Charge Distributions

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Explore spectral results and open problems for Dirac-Coulomb operators with general charge distributions, focusing on self-adjoint extensions, eigenvalue characterizations, and electron stability conditions.
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21 Lesons
49 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Curvature of the Determinant Line Bundle for Noncommutative Tori

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Explore differential geometry of curved noncommutative tori, including spectral invariants and curvature of determinant line bundle for Dirac operators on noncommutative two tori.
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18 Lesons
55 minutes
On-Demand
Free-Video
ICTP Mathematics

Families of Dirac Operators and Applications

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Explore advanced concepts in geometry and topology, focusing on families of Dirac operators and their applications in mathematical physics and differential geometry.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Fields Institute

A Fixed-Point Formula for Dirac Operators on Lie Groupoids

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Explore fixed-point formulas for Dirac operators on Lie groupoids, delving into advanced mathematical concepts and their applications in geometric analysis.
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1 Lesons
51 minutes
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Hausdorff Center for Mathematics

Dirac Operators Built from Quantum Riemannian Geometries

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Explore quantum Riemannian geometries and their application in constructing Dirac operators, delving into advanced mathematical concepts at the intersection of quantum theory and geometry.
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1 Lesons
1 hour 6 minutes
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Free-Video
Fields Institute

Homological Methods in Random Noncommutative Geometry

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Explore homological methods in random noncommutative geometry, covering fuzzy spectral triples, Dirac operators, and connections to random matrix theory and BV formalism.
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21 Lesons
53 minutes
On-Demand
Free-Video
ICTP Condensed Matter and Statistical Physics

Topology and Dynamics of Higher-Order Networks - Lecture 2: Introduction to Algebraic Topology on Networks and Simplicial Complexes

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Explore algebraic topology on networks and simplicial complexes, focusing on Hodge Laplacians and Dirac operators in higher-order networks. Gain insights into topological signals and their applications.
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1 Lesons
2 hours
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Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

One-Loop Renormalizability of the Spectral Action Using Cyclic Cocycles

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Explore one-loop renormalizability of the spectral action principle using cyclic cocycles, uncovering its cyclic structure and connections to ribbon graphs in non-commutative geometry.
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1 Lesons
44 minutes
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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Continuum Limits for Discrete Dirac Operators on 2D Square Lattices

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Explore continuum limits of discrete Dirac operators on 2D square lattices, focusing on convergence in strong resolvent sense and implications for complex analysis and quantum theory.
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1 Lesons
41 minutes
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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Geometrically Induced Discrete Eigenvalues of Dirac Operators with Lorentz Scalar Delta-Shell Interactions

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Explore geometrically induced discrete eigenvalues of Dirac operators with Lorentz scalar δ-shell interactions on broken lines, revealing novel spectral properties in quantum theory.
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1 Lesons
29 minutes
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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Schrödinger Operators with Oblique Transmission Conditions in R2

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Explore Schrödinger operators with oblique transmission conditions, examining self-adjointness, spectral properties, and connections to Dirac operators with delta-potentials in quantum theory.
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1 Lesons
29 minutes
On-Demand
Free-Video
Prague Mathematical Physics Seminar

Cubic and Non-cubic Dirac Operators - Applications in Algebraic and Differential Geometry

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Explore algebraic Dirac operators, their cohomology, and applications in differential geometry. Delve into Vogan's construction and its generalizations.
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1 Lesons
1 hour 7 minutes
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Free-Video
Institute for Mathematical Sciences

Hypoelliptic Laplacian and the Trace Formula

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Explore geometric formulas for semisimple orbital integrals, connecting heat equation methods to Selberg's trace formula through Laplacian deformations and Fokker-Planck operators.
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1 Lesons
1 hour 1 minute
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Global Noncommutative Geometry Seminar

Equivariant Local Index Theory for Lie Groupoids

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Explore equivariant local index theory for Lie groupoids, covering motivation, key concepts, and advanced mathematical techniques in noncommutative geometry.
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24 Lesons
56 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Spectra of Laplace and Dirac Operators on Noncompact Manifolds

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Explore spectra of Laplace and Dirac operators on complete manifolds, including types of spectra, results for special behaviors at infinity, and effects of additional potentials.
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1 Lesons
46 minutes
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Institut des Hautes Etudes Scientifiques (IHES)

Positive Mass Theorem for Asymptotically Flat Manifolds with Isolated Conical Singularities

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Explore recent advancements in positive mass theorem for asymptotically flat manifolds with isolated conical singularities, covering spin and non-spin settings, analysis techniques, and Geroch-type results.
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1 Lesons
45 minutes
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Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Part 1

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Explore Gromov's angle shrinking problem and its role in proving the dihedral extremality/rigidity conjecture through a new index theorem for manifolds with polyhedral boundary.
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1 Lesons
52 minutes
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Institut des Hautes Etudes Scientifiques (IHES)

A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Lecture 2

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Explore a stable algebraic version of Gromov's angle shrinking problem and its application to dihedral rigidity conjecture, focusing on Fredholm index computation.
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1 Lesons
51 minutes
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Institut des Hautes Etudes Scientifiques (IHES)

Index Theory and Applications to Scalar Curvature

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Explore index theorems for compact manifolds with boundary and their applications to scalar curvature geometry, focusing on Dirac operators and boundary value problems.
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1 Lesons
49 minutes
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Institut des Hautes Etudes Scientifiques (IHES)

Gromov's Rigidity Theorem for Polytopes with Acute Angles

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Explore recent developments in dihedral rigidity, focusing on Gromov's conjecture and Brendle-Wang's alternative smoothing construction for polytopes with acute angles.
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1 Lesons
59 minutes
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Centre de recherches mathématiques - CRM

Curvature Contribution to the Essential Spectrum of Dirac Operators with Critical Shell Interactions

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Explore the essential spectrum of 3D Dirac operators with critical shell interactions, examining how surface geometry influences spectral properties in quantum mechanics.
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1 Lesons
55 minutes
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Centre de recherches mathématiques - CRM

Scalar Curvature Rigidity of Polytopes

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Explore Riemannian metrics and scalar curvature positivity in differential geometry. Delve into Gromov's comparison principle for polytopes and recent advancements in verifying his conjecture.
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1 Lesons
58 minutes
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Free-Video
Centre de recherches mathématiques - CRM

Dirac Eigenvalue Optimization and Harmonic Maps

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Explore Dirac eigenvalue optimization, comparing it to Laplace eigenvalues and examining critical metrics' correspondence with harmonic maps to complex projective spaces.
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1 Lesons
53 minutes
On-Demand
Free-Video
ICTP Mathematics

Families of Dirac Operators and Applications

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Explore Dirac operators and their applications in geometry and topology, focusing on families and their mathematical significance in advanced theoretical frameworks.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Supersymmetry and Trace Formulas: From Atiyah-Singer to Jacobi-Poisson and Selberg

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Explore supersymmetry's mathematical origins and applications, from Atiyah-Singer formula to Jacobi-Poisson and Selberg trace formulas, in this advanced mathematics colloquium.
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1 Lesons
1 hour 4 minutes
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Free-Video
Stony Brook Mathematics

Supersymmetry and Trace Formulas: From Atiyah-Singer to Jacobi-Poisson and Selberg - Part 1

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Explore supersymmetry's mathematical origins and applications, from Atiyah-Singer formula to Jacobi-Poisson and Selberg trace formulas, in this advanced mathematics colloquium.
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1 Lesons
41 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Approximation of Dirac Operators with Delta-Shell Potentials

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Explore approximation of 2D Dirac operators with δ-shell potentials using squeezed potentials. Analyze convergence in norm resolvent sense for specific interaction strengths.
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1 Lesons
21 minutes
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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Feynman Propagators on Curved Spacetime

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Explore Feynman propagators on curved spacetime, their construction, and connection to quantum states. Delve into microlocal techniques and their application to wave and Dirac-type operators.
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1 Lesons
57 minutes
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Prague Mathematical Physics Seminar

Dirac Cohomology for Lie Superalgebras

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Explore Lie superalgebras, cohomology, and Dirac operators, focusing on gl(m|n) case and connections between Lie algebra and Dirac cohomology.
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1 Lesons
1 hour 12 minutes
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