Topology of Moduli Spaces of Topological Theories and Applications to Codes
Explore moduli spaces of topological theories, their homotopy types, and applications to Hastings-Haah floquet codes in quantum error correction and quantum gravity.
Symplectic Geometry of Teichmueller Spaces for Surfaces with Boundary - Lecture 3
Explore symplectic geometry of Teichmueller spaces for surfaces with boundary in this advanced mathematics lecture by Eckhard Meinrenken, part of a workshop on operator algebras and non-commutative geometry.
Cohomology of Moduli Spaces of Curves
Explore the intricate cohomology of curve moduli spaces with Hannah Larson, delving into advanced algebraic geometry concepts and their applications.
Constructing Polylogarithms on Higher-Genus Riemann Surfaces
Generalization of elliptic polylogarithms to higher-genus Riemann surfaces, exploring homotopy-invariant iterated integrals, modular tensors, and connections to Enriquez-Zerbini polylogarithms and Fay identities.
Quantum Complexity of Clique Homology
Explore the quantum mechanical structure in topology, connecting complexity theory to QMA hardness and examining implications for quantum algorithms and PCPs.
Homological Mirror Symmetry: Recent Developments and Future Directions
Explore recent advancements in Homological Mirror Symmetry, surveying new results and opening avenues for future development and collaboration in mathematics.
Topological Complexity of Monotone Symplectic Manifolds
Explore topological complexity in 4D spherically monotone manifolds, focusing on Kodaira dimension estimation and its implications for symplectic geometry.
Homological Mirror Symmetry: Recent Developments and Future Directions
Explore recent advancements in Homological Mirror Symmetry, surveying new results and opening avenues for future development and collaboration in this transformative field of mathematics.
Incidences and Tilings in Linear Geometry
Explore how classical incidence geometry theorems connect to surface tilings, unveiling a unified framework for generating new theorems and expanding existing ones in this insightful lecture.
Geometric Objects Associated to Planar Bipartite Graphs
Explore topological and geometric data associated with planar bipartite graphs, including knots, cluster varieties, and critical varieties, and their interconnections.
Combinatorial Approach to Categorical Möbius Inversion and Magnitude
Explore categorical Möbius inversion and magnitude through a combinatorial lens, uncovering new interpretations of Möbius coefficients and their implications for magnitude homology.
Some Stories of Graphs and Geometry
Explore fascinating connections between graphs and geometry, uncovering intriguing mathematical insights and their applications in various fields.
Cohomology Classes in the RNA Transcriptome
Explore how cohomology classes in single-cell sequencing data can model transient biological processes, using persistent cohomology and differential forms to infer gene expression dynamics.
Homological Percolation in a Torus
Explore homological percolation on tori, examining phase transitions in higher dimensions using algebraic topology. Discover new perspectives on percolation beyond traditional giant components.
Chern Classes and Indices of Vector Fields on Singular Varieties
Explore Chern classes and vector field indices on singular varieties, examining fundamental invariants in geometry and topology and their evolving theory for non-smooth spaces.
Universally Counting Curves in Calabi-Yau Threefolds
Explore enumerative geometry through a new perspective on curve counting in complex threefolds, focusing on the Grothendieck group of 1-cycles and its implications for the MNOP conjecture.
Cohomology Rings of Character Varieties
Explore cohomology rings of character varieties, including P=W conjecture proof and zero-dimensional COHA computation. Discover connections to Hilbert scheme of C^2 for punctured sphere case.
How to Enhance Categories and Why - Localization and Homotopical Enhancement
Exploring alternative techniques for enhancing localized categories using Grothendieck's derivator concept, offering a conceptually clearer approach than infinity-categories or quasicategories.
Milnor Spheres - 60 Years Later
Explore Milnor Spheres through a category theory lens, examining recent findings and insights in this seminar on classical differential topology by Ludmil Katzarkov.
Chinese Remainder Theorem and Carlson's Theorem for Monoidal Triangulated Categories
Explore Carlson's connectedness theorem generalization for monoidal triangulated categories, including a Chinese remainder theorem version and Balmer support properties.
Stable Module Category for Finite Group Schemes over Commutative Noetherian Rings
Explore finite group schemes, tensor triangular analysis, and Balmer spectrum calculations in stable module categories, based on recent advancements in cohomology and representation theory.