Topology Shapes Dynamics of Higher-order Networks
Exploring how higher-order network interactions influence non-linear dynamics, synchronization, and percolation in complex systems like brain networks and climate patterns.
Spectral Analysis of Dirac Operators with a Purely Imaginary Dislocation
Explore spectral analysis of Dirac operators with imaginary dislocation, covering Green functions, pseudospectra, and effects of matrix potentials on essential and discrete spectra.
The Moduli Space of Twisted Laplacians and Random Matrix Theory
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.
Maria Esteban - Spectral Results and Open Problems for Dirac-Coulomb Operators With Charge Distributions
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.
Curvature of the Determinant Line Bundle for Noncommutative Tori
Explore differential geometry of curved noncommutative tori, including spectral invariants and curvature of determinant line bundle for Dirac operators on noncommutative two tori.
Families of Dirac Operators and Applications
Explore advanced concepts in geometry and topology, focusing on families of Dirac operators and their applications in mathematical physics and differential geometry.
A Fixed-Point Formula for Dirac Operators on Lie Groupoids
Explore fixed-point formulas for Dirac operators on Lie groupoids, delving into advanced mathematical concepts and their applications in geometric analysis.
Dirac Operators Built from Quantum Riemannian Geometries
Explore quantum Riemannian geometries and their application in constructing Dirac operators, delving into advanced mathematical concepts at the intersection of quantum theory and geometry.
Homological Methods in Random Noncommutative Geometry
Explore homological methods in random noncommutative geometry, covering fuzzy spectral triples, Dirac operators, and connections to random matrix theory and BV formalism.
Topology and Dynamics of Higher-Order Networks - Lecture 2: Introduction to Algebraic Topology on Networks and Simplicial Complexes
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.
One-Loop Renormalizability of the Spectral Action Using Cyclic Cocycles
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.
Continuum Limits for Discrete Dirac Operators on 2D Square Lattices
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.
Geometrically Induced Discrete Eigenvalues of Dirac Operators with Lorentz Scalar Delta-Shell Interactions
Explore geometrically induced discrete eigenvalues of Dirac operators with Lorentz scalar δ-shell interactions on broken lines, revealing novel spectral properties in quantum theory.
Schrödinger Operators with Oblique Transmission Conditions in R2
Explore Schrödinger operators with oblique transmission conditions, examining self-adjointness, spectral properties, and connections to Dirac operators with delta-potentials in quantum theory.
Cubic and Non-cubic Dirac Operators - Applications in Algebraic and Differential Geometry
Explore algebraic Dirac operators, their cohomology, and applications in differential geometry. Delve into Vogan's construction and its generalizations.
Hypoelliptic Laplacian and the Trace Formula
Explore geometric formulas for semisimple orbital integrals, connecting heat equation methods to Selberg's trace formula through Laplacian deformations and Fokker-Planck operators.
Equivariant Local Index Theory for Lie Groupoids
Explore equivariant local index theory for Lie groupoids, covering motivation, key concepts, and advanced mathematical techniques in noncommutative geometry.
Spectra of Laplace and Dirac Operators on Noncompact Manifolds
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.
Positive Mass Theorem for Asymptotically Flat Manifolds with Isolated Conical Singularities
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.
A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Part 1
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.
A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Lecture 2
Explore a stable algebraic version of Gromov's angle shrinking problem and its application to dihedral rigidity conjecture, focusing on Fredholm index computation.