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.
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.
Embeddings of Kac-Moody Affine Grassmannian Slices
Explorez les développements récents dans la théorie des représentations géométriques, en se concentrant sur les tranches de Grassmanniennes affines de type Kac-Moody et leur construction via les branches de Coulomb.
The Method of Gauge Transform II
Explorez la méthode de transformation de jauge et son application aux problèmes spectraux périodiques et ergodiques avec Jeffrey Galkowski.
Quantitative Global Theory of One-Frequency Quasiperiodic Operators - Part II
Explorez la théorie quantitative globale des opérateurs quasipériodiques à une fréquence, en examinant la réductibilité et ses implications dans les problèmes spectraux.
Quantitative Global Theory of One-Frequency Quasiperiodic Operators - Part I
Explore quantitative global theory of one-frequency quasiperiodic operators, covering dynamic approaches, prototypical models, and applications in spectral problems.
The Method of Gauge Transform - Lecture 4
Explorez la méthode de transformation de jauge et ses applications dans les problèmes spectraux périodiques et ergodiques avec Jeffrey Galkowski de l'University College London.
Spherical Functions and Mirror Symmetry
Explore spherical functions and mirror symmetry in mathematics, bridging quantum physics and the Langlands Program through innovative interdisciplinary approaches.
Highlights from the History of Probability
Explore key milestones in probability theory, from Hilbert's problems to martingales, with insights on Brownian motion, Central Limit Theorem, and stochastic processes.
Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 4
Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.
Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 2
Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.
Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 1
Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.
The Method of Gauge Transform - Lecture 3
Explore advanced mathematical concepts in periodic and ergodic spectral problems, focusing on the Gauge transform method.
S-duality and Lie Super-algebras
Explore geometric realization of quantum simple Lie super-algebras, S-duality, and connections to geometric Langlands correspondence and relative Langlands duality.