Algebraization of Low-Dimensional Topology - Part II
Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
Diagrammatics in Categories - Lecture 5
Explorez les catégories diagrammatiques en algèbre à travers des exemples concrets et leur formalisme spécifique, en laissant place à la généralisation.
Affine W-algebras - Lecture 5
Explore affine W-algebras construction, theory, and applications in vertex algebra. Delve into quantum Hamiltonian reduction, Virasoro minimal models, and tensor categories of W-algebra representations.
Affine W-algebras - Lecture 4
Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
Towards the Quantum Exceptional Series
Explore continuous families of planar algebras interpolating exceptional Lie algebras and their quantum counterparts. Discover a potential new exceptional knot polynomial through skein theoretic analysis.
Affine W-algebras - Part I
Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
W-algebras and Lax Operators - Lecture 5
Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures in quantum algebra and integrable systems.
W-algebras and Lax Operators - Lecture 3
Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures using advanced algebraic techniques.
Mathematics and Machines: Navigating New Frontiers
Explore the intersection of mathematics and machine learning, examining how computers transform mathematical research and their potential future impact on the field.
Integrating Mechanistic Models with Computational Statistics and Machine Learning - New Insights in Biology
Explore integrating mechanistic models with computational statistics and machine learning for new insights in cell and developmental biology. Tackle challenges in analyzing complex quantitative data.
Polyhedra with Vertices on a Quadric
Explore combinatorial types of polyhedra with vertices on quadrics, from Steiner's 1832 question to recent findings using ideal polyhedra in various geometries.
Interlacing Families and Ramanujan Graphs - #ICBS2024
Explore Ramanujan Graphs, interlacing families, and their connections to various mathematical fields. Gain insights into recent developments and open problems in graph theory.
Elliptic Cohomology and Enumerative Geometry
Explore the intersection of elliptic cohomology and enumerative geometry, focusing on stable envelopes and their role in understanding q-difference equations.
Causal Inference with Mendelian Randomization in Biomedical Studies
Explore Mendelian Randomization for causal inference in biomedical research. Learn innovative methods, overcome challenges, and gain insights into complex disease relationships through simulation and case studies.
Mock Modularity of Calabi-Yau Threefolds - ICBS 2024
Explore modular properties of generating functions for Donaldson-Thomas invariants in Calabi-Yau threefolds, their physical origins, and applications in string theory compactifications.
Linear Stability of Ricci Solitons - ICBS2024
Explore linear stability of compact shrinking Ricci solitons, including positive Einstein manifolds. Examine critical aspects, open problems, and recent research findings in Ricci flow and geometric analysis.
Entropy Analysis and Singularities of Solutions for Nonlinear Hyperbolic Conservation Laws
Explore entropy analysis and singularities in nonlinear hyperbolic conservation laws. Gain insights into open problems, minimal entropy conditions, and phenomena like cavitation and concentration.
Sheaves on Calabi-Yau 4-folds and Virtual Invariants - An Overview
Explore developments in enumerative geometry on Calabi-Yau 4-folds, including point counting, curve counting, and surface counting, with connections to string theory and physics.
Modularity of Donaldson-Thomas Invariants on Compact Calabi-Yau Threefolds
Explore Donaldson-Thomas invariants, their connection to BPS indices, and modular behavior in string theory. Gain insights into computational methods and applications to Gopakumar-Vafa invariants and topological string amplitudes.
Integrable Billiards and Rigidity - Lecture 1
Explore integrable billiards and the Birkhoff-Poritsky conjecture, focusing on Hopf-type rigidity and its extension to Twist symplectic maps and billiards.
Critical Well-Posedness for the Derivative Nonlinear Schrödinger Equation on the Line
Explore critical well-posedness for the derivative nonlinear Schrödinger equation on the line, focusing on recent advancements in resolving the problem in critical space.