Index Theory and Applications to Scalar Curvature
Explore index theorems for compact manifolds with boundary and their applications to scalar curvature geometry, focusing on Dirac operators and boundary value problems.
Gromov's Rigidity Theorem for Polytopes with Acute Angles
Explore recent developments in dihedral rigidity, focusing on Gromov's conjecture and Brendle-Wang's alternative smoothing construction for polytopes with acute angles.
Curvature Contribution to the Essential Spectrum of Dirac Operators with Critical Shell Interactions
Explore the essential spectrum of 3D Dirac operators with critical shell interactions, examining how surface geometry influences spectral properties in quantum mechanics.
Scalar Curvature Rigidity of Polytopes
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.
Dirac Eigenvalue Optimization and Harmonic Maps
Explore Dirac eigenvalue optimization, comparing it to Laplace eigenvalues and examining critical metrics' correspondence with harmonic maps to complex projective spaces.
Families of Dirac Operators and Applications
Explore Dirac operators and their applications in geometry and topology, focusing on families and their mathematical significance in advanced theoretical frameworks.
Supersymmetry and Trace Formulas: From Atiyah-Singer to Jacobi-Poisson and Selberg
Explore supersymmetry's mathematical origins and applications, from Atiyah-Singer formula to Jacobi-Poisson and Selberg trace formulas, in this advanced mathematics colloquium.
Supersymmetry and Trace Formulas: From Atiyah-Singer to Jacobi-Poisson and Selberg - Part 1
Explore supersymmetry's mathematical origins and applications, from Atiyah-Singer formula to Jacobi-Poisson and Selberg trace formulas, in this advanced mathematics colloquium.
Approximation of Dirac Operators with Delta-Shell Potentials
Explore approximation of 2D Dirac operators with δ-shell potentials using squeezed potentials. Analyze convergence in norm resolvent sense for specific interaction strengths.
Feynman Propagators on Curved Spacetime
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.
Dirac Cohomology for Lie Superalgebras
Explore Lie superalgebras, cohomology, and Dirac operators, focusing on gl(m|n) case and connections between Lie algebra and Dirac cohomology.