From Braid Groups to Artin Groups - Lecture 1
Explore Artin groups, including braid groups and free groups. Discover algebraic and geometric characterizations, current knowledge, and new approaches to challenging problems in this field.
Subgroups of Hyperbolic Groups, Finiteness Properties and Complex Hyperbolic Lattices
Explore finiteness properties of subgroups in hyperbolic groups and complex hyperbolic lattices, focusing on cocompact arithmetic lattices with positive first Betti number.
Extension of Bershadsky-Polyakov Type Algebras
Explore toroidal shifted algebras and deformed W-algebras, focusing on extensions of Bershadsky-Polyakov type algebras in quantum symmetries.
Diagrammatics in Categories - Lecture 4
Explorez les catégories diagrammatiques en algèbre à travers des exemples concrets et leur formalisme spécifique. Développez votre compréhension des applications dans divers domaines.
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.
Affine W-algebras - Lecture 3
Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
Affine W-algebras - Lecture 2
Explore affine W-algebras through quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
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.
Spectral Methods Meets Asymmetry: Two Recent Stories - Lecture 4
Explore spectral methods for asymmetric data matrices, covering top-K ranking and matrix de-noising. Learn advantages over traditional approaches in data analysis and estimation.
Free Resolutions of Powers of Square-Free Monomial Ideals
Explore free resolutions of square-free monomial ideals and their powers, focusing on combinatorial methods and discrete topology. Gain insights into this central problem in commutative algebra.
Minimal Surfaces and the Isoperimetric Inequality
Explore the generalization of the isoperimetric inequality to submanifolds in Euclidean space, focusing on minimal submanifolds and their sharp isoperimetric properties.
Isolated and Parameterized Points on Algebraic Curves
Explore isolated and parameterized points on algebraic curves, examining their behavior in families and implications for elliptic curve arithmetic. Gain insights into curve geometry and its connection to arithmetic properties.
Corona Rigidity in Operator Theory and C*-Algebras
Explore corona rigidity in operator theory, examining extensions of Weyl-von Neumann theorem and its implications for C*-algebras, Calkin algebra, and isomorphisms of quotients.
Degeneracy Loci in Geometry and Combinatorics
Explore degeneracy loci in geometry, tracing their history and examining modern formulas connecting geometric concepts with Schubert polynomial combinatorics.
The Steklov Spectrum of Convex Euclidean Polygons
Explore upper bounds and inverse problems for Steklov eigenvalues of convex polygons. Discover how generic n-gons can be determined by their Steklov spectra using powerful spectral invariants.
On the Direct Summand Conjecture and Beyond
Explore the direct summand conjecture's history, proof, and impact on commutative algebra and mixed characteristic birational geometry.
Functoriality and Sheaf Property for Wrapped Fukaya Categories
Explore functorial and sheaf-theoretic properties of wrapped Fukaya categories, surveying key results and insights in this advanced mathematical topic.