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.
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.
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.
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.
On the Applications of Topology
Explore topological methods for analyzing complex data sets, focusing on persistent homology and mapper, with applications in computer vision, biology, and medicine.
Formalization of Infinity Category Theory
Explore ∞-category theory's formalization, unifying mathematics, computer science, and physics. Learn synthetic reasoning and the Yoneda Lemma in this advanced mathematical seminar.
Topology in 1930s America - A Tale of Two Camps
Explore the rivalry between point-set and combinatorial topology camps in 1930s America, examining their approaches, key figures, and impact on the mathematical research community.
From HoTT to HOTT - Exploring Homotopy Type Theory
Explore the evolution from Homotopy Type Theory (HoTT) to Higher-Order Type Theory (HOTT) in this insightful lecture by Michael Shulman.
Barry Mazur and the Infinite Cheese of Knowledge - A Mathematical Documentary
Explore the life and insights of influential mathematician Barry Mazur in this intimate documentary, capturing his wit, profound approach to mathematics, and enduring impact on the field.
Quantum Periods for Complements
Explore quantum periods for complements, focusing on polynomial-defined spectral curves and quantization of polynomial algebras. Gain insights into cohomological descriptions of WKB series.
Topological Invariants of Gapped States and 't Hooft Anomalies
Explore topological invariants of gapped ground-states in lattice systems, their interpretation as obstructions to gauging, and the role of locality in infinite-volume systems with rapidly decaying interactions.
Waists Measured via Urysohn Width in Riemannian Manifolds
Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.
Width, Scalar Curvature and Macroscopic Scalar Curvature
Explore the interplay between positive scalar curvature and macroscopic scalar curvature, examining Urysohn width and closed geodesics in PSC and PMSC spaces.
Analytic Stacks - Lecture 12
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
Analytic Stacks - New Foundations for Analytic Geometry - Lecture 11/24
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.
Birational Invariants from Gromov-Witten Theory - Lecture 4
Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of geometric objects like cubic 4-folds.
Analytic Stacks - New Foundations for Analytic Geometry
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
Graph Complex Action on Poisson Structures: From Theory to Computation
Explore graph complex action on Poisson structures, from theoretical foundations to computational applications using SageMath's gcaops package for advanced mathematical research.
Analytic Stacks - New Foundations for Analytic Geometry
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.