Homotopy Groups of Spheres
Explore continuous maps between spheres, their abelian group structures, and connections to key problems in topology with Zhouli Xu from UC San Diego.
Geometric Variational Problems: Regularity vs Singularity Formation
Explore techniques for existence, regularity, and singularity formation in geometric problems, focusing on harmonic maps, Yang-Mills connections, and nematic liquid crystals. Learn about new gluing methods for parabolic flows.
Uniform Volume Doubling and Functional Inequalities on Lie Groups
Explore functional inequalities on Lie groups, focusing on uniform volume doubling and its implications for SU(2) and related structures. Gain insights into heat kernel estimates and measure contracting properties.
Towards a Mathematical Theory of 3D Mirror Symmetry
Explore the mathematical implications of 3D mirror symmetry, connecting quantum field theory dualities to algebraic geometry and symplectic topology. Uncover links to geometric Langlands and symplectic duality.
On Exotic Embeddings of Submanifolds in 4-Manifolds
Explore exotic embeddings of submanifolds in 4-manifolds, focusing on phenomena that survive stabilizations. Delve into advanced 4-dimensional topology concepts and recent research findings.
Chain Level String Bracket and Punctured Holomorphic Discs
Explore Audin's conjecture and its generalization to Liouville manifolds. Discover connections between holomorphic discs and string topology operations, focusing on chain level string brackets.
Billiards in Conics Revisited
Explore optical properties of conics, billiard reflections, and geometric consequences. Delve into classic results, Ivory's lemma, Poncelet Porism, and related theorems in projective geometry.
Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds
Explore the interaction between hyperbolic geometry and homology cobordism in low-dimensional topology using monopole Floer homology to study subgroups of the homology cobordism group.
The High-Degree Rational Cohomology of the Special Linear Group
Explore high-degree rational cohomology of SL_n(Z) and SL_n(R) for number rings. Examine Steinberg modules and associated simplicial complexes to understand special linear group cohomology.
Positivity, Representations, and Non-Commutative Hyperbolic Geometry
Explore total positivity in matrices, its generalization to split real Lie groups, and a new notion of positivity in flag varieties with applications to higher Teichmüller spaces.
Local-Global Principles for Homogeneous Spaces Over Arithmetic Function Fields
Explore local-global principles for homogeneous spaces over arithmetic function fields, focusing on function fields of curves over complete discretely valued fields and related patching methods.
Mirror Structure Constants via Non-Archimedean Analytic Disks
Explore mirror structure constants for smooth affine log Calabi-Yau varieties using non-archimedean analytic disks, generalizing previous constructions and discussing positivity, integrality, and potential extensions.
Nonabelian Mixed Hodge Structures
Explore nonabelian mixed Hodge structures, their relation to rational homotopy, and applications to character varieties and schematic homotopy types. Examine weights from noncompact bases and parabolic structures.
Quantitative Ell-Adic Sheaf Theory
Explore quantitative bounds for étale cohomology groups and their applications in algebraic geometry. Learn about complexity measures for sheaves and how they interact with various functors.
Counting Curves in Calabi-Yau Threefolds
Explore enumerative invariants and a universal approach to counting curves in Calabi-Yau threefolds. Discover how cluster formalism aids computations and potentially simplifies conjectural identities between invariants.
Computing the Weil Representation of Superelliptic Curves
Explore the Weil representation of superelliptic curves, focusing on local Galois representations and stable reductions in algebraic geometry.
Non-free Curves and Geometric Manin's Conjecture - Lecture
Explore non-free curves on varieties, their classification, and implications for Geometric Manin's Conjecture in Fano fibrations. Gain insights into algebraic geometry and number theory.
A Finiteness Theorem for Gromov-Hyperbolic Groups
Explore a finiteness theorem for Gromov-hyperbolic groups, delving into δ-hyperbolic, torsion-free, non-cyclic marked groups with bounded entropy. Gain insights into the proof and key concepts.
Non-Archimedean Pluripotential Theory and K-stability - Lecture 3
Explore non-Archimedean pluripotential theory and K-stability in this advanced mathematics lecture, part of a series connecting complex and non-Archimedean geometry.
Conjugate Points and the MC Criterion in Volume-Preserving Diffeomorphisms - Lecture
Explore conjugate points on volume-preserving diffeomorphisms, focusing on the MC criterion and its applications in fluid dynamics and Riemannian geometry.
The Formulation of the Navier-Stokes Equations on Riemannian Manifolds
Explore advanced formulations of Navier-Stokes equations on Riemannian manifolds, focusing on Ebin and Marsden's approach and recent developments in this complex field of fluid dynamics.