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.
P-adic Height Pairings of Geodesics on Modular Curves
Explore p-adic height pairings of real quadratic geodesics on modular curves, their relation to real quadratic singular moduli, and insights from triple product period interpretation.
Prequantization of a Non-Exact Courant Algebroid
Explore advanced mathematical concepts in geometric structures, focusing on prequantization techniques for non-exact Courant algebroids in this in-depth lecture by Gavin Hurd.
Numerical Approach to Polylogarithms on Higher-Genus Riemann Surfaces
Explore numerical evaluation of polylogarithms on genus-two Riemann surfaces using Schottky parametrization and averaging over genus-one differential forms, advancing particle physics research.
Sums of Weighted Lattice Points of Polytopes
Explore connections between polytopes and algebraic combinatorics, focusing on sums of weighted lattice points and their computational implications in estimating maximal weighted lattice points.
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.
Petr's Miracle: The Lost Theorem of Polygon Transformation - Mathologer Masterclass
Explore the fascinating Petr-Douglas-Neumann theorem, its history, and mathematical implications. Discover how this remarkable result was overlooked for a century and its connections to other geometric concepts.
Mechanism Synthesis and Applied Enumerative Geometry
Explore applied enumerative geometry in mechanism synthesis, uncovering innovative approaches to design and optimize mechanical systems for various engineering applications.
What is Symplectic Geometry?
Explore symplectic geometry fundamentals in this engaging lecture, covering key concepts, applications, and recent developments in this fascinating mathematical field.
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.
Random Matrix Statistics in the Uniform Spanning Tree
Explore random matrix statistics in uniform spanning trees, focusing on branch behavior, scaling limits, and connections to Dyson Brownian motion and Loewner evolution.
Superport Networks: Generalizing Kirchhoff's Matrix-Tree Theorem
Exploration of multiport networks, generalizing Kirchhoff's theorem with novel mathematical approaches. Insights into electrical engineering applications and superport network theory.
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.
Planar Site Percolation via Tree Embeddings
Explore planar site percolation and tree embeddings in infinite graphs. Discover novel proofs for Bernoulli percolation and confirm a 1996 conjecture by Benjamini and Schramm.
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.