Structure of Equivariant Derived Categories - ICBS 2024
Explore equivariant derived categories, their structure theorems, and applications to GIT quotients and hidden symmetries in algebraic geometry.
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.
Point Counting over Finite Fields and the Cohomology of Moduli Spaces of Curves
Explore algebraic geometry through point counting over finite fields and cohomology of moduli spaces of curves, resolving longstanding questions and confirming Langlands program predictions.
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.
T-Shift on Reduced Plabic Graphs and Legendrian Weaves
Explorez les T-shifts sur les graphes plabiques réduits et les tissages légendrien pour interpréter topologiquement la structure de cluster des strates positroïdes du grassmannien.
Monoidal Triangular Geometry with Applications to Representation Theory
Explorez la géométrie triangulaire monoïdale et ses applications à la théorie des représentations, en mettant l'accent sur les algèbres de Hopf de dimension finie et les catégories tensorielles finies.
Isoresidual Fibration: At the Crossroads of Complex Analysis, Flat Geometry and Combinatorics
Explore the intersection of complex analysis, flat geometry, and combinatorics through isoresidual fibration. Gain insights into moduli spaces and geometric structures on surfaces.
Schobers and Riemann-Hilbert Correspondence
Explore geometric representation theory, super groups, and non-commutative algebraic geometry with a focus on Schobers and Riemann-Hilbert correspondence.
From Quadratic Forms to Motivic Cohomologies
Explore the journey from quadratic forms to motivic cohomologies, delving into advanced mathematical concepts and their applications in algebraic geometry.
Algebraic Curves and Minimal Surfaces
Explore algebraic curves and minimal surfaces with Prof. Sebastian Heller, delving into Riemann surfaces, harmonic maps, and experimental mathematics.
Arithmeticity and FC-Subspaces of Hyperbolic Manifolds
Explore connections between geometry and arithmeticity of hyperbolic orbifolds using fc-subspaces. Learn about new arithmeticity criteria and applications to reflection groups and hyperbolic link complements.
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.
Ball Quotients and Algebraic Geometry - ICBS 2024
Explore ball quotients in algebraic geometry, focusing on moduli spaces, Kaehler metrics, and their connections to sporadic finite simple groups. Examine known examples and recent progress on the Allcock ball quotient.
Derived Approach to Highest Weight Categories
Explore highest weight categories in Representation Theory, examining their interpretation through exact categories, abelian envelops, and exceptional collections in derived categories.
Higher Gromov-Witten Invariants of Calabi-Yau Threefolds
Explore mixed-spin-p-fields method for Calabi-Yau quintics, its application to BCOV Feynman summation rule, and generalization to hypersurfaces in toric varieties.
Exotic Calabi-Yau Metric and Holomorphic Fibration
Explore complete Calabi-Yau metrics, from historical developments to recent constructions on C^3, with insights into collapsing metrics on Calabi-Yau 3-folds.
Metric SYZ Conjecture for Calabi-Yau Manifolds - ICBS 2024
Explore special Lagrangian torus fibrations on Calabi-Yau manifolds, focusing on recent progress and the Fermat family of hypersurfaces.
Structure in the Search for Structure - Algebraic Number Theory and Motivic Cohomology
Explore algebraic number theory through analogies between numbers and shapes, including quadratic reciprocity and linking numbers, leading to insights on Tate's 1966 conjecture.
A Finite Dimensional Proof of the Verlinde Formula
Explore a purely algebro-geometric proof of the Verlinde formula, examining recurrence relations for curve genus and parabolic points in generalized theta function spaces.
Locally Symmetric Varieties with Moduli Interpretation
Explore complex algebraic geometry, focusing on realizing moduli spaces as locally symmetric varieties through Hodge theory. Survey existing results and examine Calabi-Yau manifolds with complex hyperbolic ball periods.
New Geometric Structures in the Langlands Program
Explore new geometric structures in the Langlands program, including the moduli space of G-bundles on the curve, and their role in constructing the semi-simple local Langlands correspondence.