Kirchhoff’s Theorem and Semi-Canonical Representatives for the Tropical Prym Variety
Explore Kirchhoff's theorem, metric graphs, and tropical Prym varieties. Delve into divisors, Jacobians, and double covers, gaining insights into advanced algebraic geometry concepts.
Neil Olver: On the Integrality Gap of the Prize Collecting Steiner Forest LP
Explores the integrality gap of the prize collecting Steiner forest LP, disproving the belief it was 2 and showing it's at least 9/4, with implications for approximation algorithms in combinatorial optimization.
Omer Bobrowski - Random Simplicial Complexes, Lecture I
Explore random simplicial complexes, their applications in data analysis, and key phenomena like connectivity and cycle formation. Includes introduction to algebraic topology and homology theory.
Andreas E. Feldmann - A -embedding of Low Highway Dimension Graphs into Bounded Treewidth Graphs
Explores embedding low highway dimension graphs into bounded treewidth graphs, with applications in transportation network optimization problems like Travelling Salesman and Facility Location.
Ahmad Abdi- Packing Odd T-Joins With at Most Two Terminals
Explore graph theory with Ahmad Abdi as he delves into packing odd T-joins, covering applications, proof strategies, and open questions in combinatorial optimization.
Zoltán Szigeti: On -2k,k--connected Graphs
Exploration of (2k,k)-connected graphs, focusing on orientation and construction methods. Covers arc-connectivity, vertex-connectivity, and splitting-off techniques for various graph structures.
On LP-Relaxations for the Tree Augmentation Problem
Explore LP-relaxations for tree augmentation, including dual-fitting algorithms, shadow-minimal solutions, and blocking trees. Gain insights into improved approximation techniques for combinatorial optimization problems.
Spectral Graph Theory - Lecture 1
Explore spectral graph theory, covering self-adjoint matrices, Rayleigh equalities, graph isomorphism, Cayley graphs, and automorphism groups. Gain insights into complex systems and network analysis.
Phylogenetic Algebraic Geometry
Explore phylogenetic algebraic geometry, its applications in species history reconstruction, and the use of algebraic and geometric perspectives to solve phylogenetic problems.
Chromatic Number of G-Borsuk Graphs
Explore G-Borsuk graphs, their chromatic numbers, and topological connections. Delve into G-actions, Hom-complexes, and random graph thresholds for a deeper understanding of this algebraic topology concept.
Computing Optimal Homotopies
Explore optimal curve similarity measures using homotopy-based approaches, examining structural properties, algorithms, and open questions in topology and computational geometry.
How Connected Are You? An Introduction to Graph Theory and Network Science by Hugo Touchette
Explore networks and graphs in everyday life, from social media to transportation systems. Learn about graph theory, network shapes, and their evolution and applications.
Data-Driven Discovery of Linear Dynamical Systems Over Graphs via Dynamical Sampling
Explore linear dynamical systems on graphs through data-driven discovery, focusing on efficient recovery of missing information and optimal sampling strategies for graph signal processing.
Oriented Cayley Graphs
Explore oriented Cayley graphs, quantum walks, and association schemes. Discover applications in algebraic graph theory and quantum information, with insights on special eigenvalues and Galois groups.
Eigenvalue Gaps and Continuous Walks
Explore eigenvalue gaps, continuous walks, and perfect state transfer in algebraic graph theory, with applications to quantum information and oriented graphs.
Reconfiguring Simple ST Hamiltonian Paths in Rectangular Grid Graphs
Explore reconfiguration of Hamiltonian paths in grid graphs, focusing on algorithms, mechanisms, and structures for path transformation using switch pairs and zipping techniques.
High Dimensional Expanders - Introduction and Motivation
Explore high-dimensional expanders, their applications in error-correcting codes, and the motivations behind this emerging field of mathematics and computer science.
X-Ramanujan Graphs
Explore X-Ramanujan graphs and their applications in computer science, focusing on advanced concepts beyond randomized rounding and the probabilistic method in graph theory.
Applied Topology for Discrete Structures
Explore topological concepts applied to discrete structures modeling real data, bridging network science and applied topology for innovative analysis of complex systems.
Multiscale Many-body Correlations and Structure in Chemistry Data
Integrating graphs, topology, and geometry to analyze complex chemistry data, providing insights into multiscale correlations and structures beyond traditional methods.
The Topological Complexity of Pure Graph Braid Groups Is Stably Maximal
Explore the topological complexity of configuration spaces in graphs, using group theoretic estimates for higher topological complexity instead of traditional cohomology approaches.