Scalar Curvature Rigidity in Manifolds
Explore scalar curvature rigidity in manifolds, examining known solutions and current research questions using spinorial techniques.
Scalar Curvature Rigidity and Extremality in Dimension 4
Explore scalar curvature rigidity in 4D using Finsler-Thorpe trick and twisted spinor methods. Discover area-extremal properties of 4-manifolds with nonnegative sectional curvature.
Recent Inequalities on the Mass-to-Capacity Ratio
Explore new inequalities for mass-to-capacity ratio on manifolds with nonnegative scalar curvature, revealing proofs of positive mass theorem and applications in geometry.
The World of Shadows - From Plato to Thom
Explore the philosophical and mathematical journey from Plato's shadows to Thom's theories, guided by renowned mathematician Mikhail Gromov.
The Geometric Ideas of René Thom Related to Manifolds with Singularities
Explore René Thom's groundbreaking papers on transversality, cobordism, and manifolds with singularities, revealing their geometric insights and impact on mathematical understanding.
Twisted K-theory in Motivic Homotopy Theory
Explore algebraic K-theory of vector bundles twisted by Brauer class, its role in motivic homotopy theory, and a new approach to the motivic spectral sequence for twisted K-theory.
Efimov K-theory and Its Applications to Complex Geometry - Lecture 2
Explore Efimov's extended algebraic K-theory, its broader categorical context, and applications to complex geometry in this advanced mathematics lecture.
Prismatic Cohomology of Commutative Ring Spectra
Explore motivic filtrations on trace invariants of commutative ring spectra and their extension to prismatic cohomology, as presented by Arpon Raksit from MIT.
A Homotopical Approach to Crystalline Cohomology
Explore a homotopical approach to crystalline cohomology, focusing on higher homotopies for canonical lifts and easier global definition through gluing.
Anosov Representations - Lecture 3
Explore Anosov representations, their characterizations, domains of discontinuity, and connections to convex projective geometry. Discover recent developments and potential research directions.
Geometric Structures Associated to Anosov Representations
Explore geometric structures linked to Anosov representations, focusing on domains of discontinuity and their quotients as smooth fiber bundles over closed hyperbolic manifolds.
Anosov Representations - Lecture 2
Explore Anosov representations, their characterizations, domains of discontinuity, and connections to convex projective geometry in this advanced mathematical lecture.
Regularising Manifolds Using Ricci Flow
Explore Ricci flow's applications in deforming and regularizing manifolds, including its use in identifying topology and proving geometric theorems.
Heegaard Branes and Exact Results for Non-perturbative Complex Chern-Simons Theory
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.
Holomorphic Floer Theory and Resurgence - Lecture 3
Explore holomorphic Floer theory and its connection to resurgence, examining the Riemann-Hilbert correspondence and its implications for perturbative expansions in mathematics and physics.
A Conjectural Reciprocity Law for Realizations of Motives
Explore a conjectural reciprocity law connecting realizations of motives, drawing parallels to classical number theory and expanding on Hodge theory's comparison isomorphisms.
Geometry, Arithmetic, and Dynamics of Discrete Groups - Lecture 4
Explore advanced concepts in discrete group theory, focusing on geometric, arithmetic, and dynamic aspects with Professor Nikolay Bogachev from the University of Toronto.
Gauss Realisability Conditions - From Error Correction to Formalization
Explore Gauss Realisability conditions, their applications in error correction, and the journey towards formalization in mathematics, offering insights into advanced mathematical concepts.
Hodge Theory and Lagrangian Fibrations in Holomorphic Symplectic Manifolds
Explore Hodge theory and Lagrangian fibrations in holomorphic symplectic manifolds. Delve into conjectures, isomorphisms, and decomposition theorems in this advanced mathematical discourse.
Enumerative Geometry Through Sheaves
Explore enumerative geometry, sheaf counting, and their applications in algebraic geometry. Discover new approaches to generalized Donaldson-Thomas invariants on Calabi-Yau threefolds.
Real Loci of Non-Real Varieties - Mathematics Department Colloquium
Explore cooriented submanifolds in real algebraic geometry, focusing on their properties, intersections, and linking numbers. Gain insights into the geometry of pencils and real projective spaces.