On the P=W Conjecture II
Exploration of the mirror P=W conjecture, its evidence in low dimensions, and potential verification methods using Lagrangian torus fibrations. Discusses work with Katzarkov-Przyjalkowski and Katzarkov-Pantev.
Blow Up Formulae and Invariants II - Dimension Theory
Explore numerical invariants in meromorphic connections, their relation to singularity theory, and applications to non-rationality criteria for Fano varieties.
Structural Aspects of Fukaya Categories of LG Models
Explore Fukaya categories of Landau-Ginzburg models, monodromy, and related functors in this expository talk, covering work by Abouzaid-Seidel, Hanlon, Sylvan, Jeffs, and others.
NC Spectra
Explore noncommutative spectra, their applications to nonrationality questions, and potential generalizations in this advanced mathematics lecture.
Hodge Ideals and Spectrum of Isolated Hypersurface Singularities - Spectrum
Explore the connection between Hodge ideals and spectrum in isolated hypersurface singularities, extending previous findings to advance understanding of these important mathematical concepts.
Hodge Ideals and Spectrum of Isolated Hypersurface Singularities - Overview
Explore the connection between Hodge ideals and spectrum in isolated hypersurface singularities, extending previous findings on multiplier ideals in algebraic geometry.
Differential Equations and Mixed Hodge Structures
Explores asymptotic Hodge theory, focusing on period-theoretic aspects through examples. Discusses motivic Gamma functions and their role in encoding invariants of variations of Hodge structures on P^1.
D-Modules and Toric Schobers
Exploring mirror symmetry using perverse sheaves of categories and schobers, with focus on B-side category in toric homological mirror symmetry and associated D-module characteristic cycles.
Model Theory: From Logic to Geometric Stability Theory and O-Minimality II
Explore model theory principles, focusing on o-minimality and stability theory, with applications to complex geometry and arithmetic aspects.
The P=W Conjecture in Genus Two and the Hodge Numbers of O'Grady 10
Exploration of moduli of sheaves, perverse filtrations, and the P=W conjecture in genus two curves, with insights on Betti and Hodge numbers of O'Grady 10 variety.
Hodge-Theoretic Aspects of Mirror Symmetry
Explores mirror symmetry for Fano varieties through Hodge theory, discussing Hodge diamond rotation, Katzarkov--Kontsevich--Pantev conjectures, and the mirror P=W conjecture in relation to mixed Hodge structures.
Higher Chow Cycles Arising from Some Laurent Polynomials
Exploration of higher Chow cycles from Laurent polynomials, focusing on Apéry constants in Fano threefolds and cubic fourfolds with planes, connecting to mirror symmetry and rationality problems.
Atiyah Class and Sheaf Counting on Local Calabi-Yau 4 Folds
Explore Donaldson-Thomas invariants of torsion sheaves in Calabi-Yau fourfolds, examining their relation to reduced DT theory and modularity predictions for elliptic K3 surfaces.
Tame Geometry and Hodge Theory II
Explores applications of tame geometry in Hodge theory, covering algebraization results, tameness of period maps, functional transcendence, and atypical intersection conjectures in complex algebraic geometry.
Degenerating Complex Variations of Hodge Structure
Explore complex variations of Hodge structure, focusing on adapting Schmid's analysis to arbitrary polarized variations and examining key results like Hodge norm estimates and limiting mixed Hodge structures.
Remarks on Degenerations of K-Trivial Varieties
Exploration of higher-dimensional analogues to K3 surface degenerations, focusing on Hyperkaehler manifolds and touching on Calabi-Yau cases. Insights into moduli space compactifications for these complex geometric structures.
Archimedean Height Pairings for Higher Cycles
Explore archimedean height pairings for higher cycles, their interpretation as mixed Hodge structure invariants, and asymptotic behavior in Hodge-Tate variations.
Non-Simplicial Quantum Toric Varieties
Explore the construction of quantum toric varieties linked to arbitrary fans on finitely generated subgroups of R^d, expanding mathematical understanding in algebraic geometry.
Irrational Toric Varieties and the Secondary Polytope
Explore irrational toric varieties, their connections to classical theory, and their relationship with secondary polytopes in algebraic geometry and combinatorics.
Basic Cohomology of Moment-Angle Manifolds
Explores basic cohomology of moment-angle manifolds, presenting a Davis-Januszkiewicz type formula for calculating de Rham and Dolbeault cohomology of canonical holomorphic foliations on complex moment-angle manifolds.
Intersection of Quadrics, Moment-Angle Manifolds, Complex and Quaternionic Manifolds and Convex Polytope
Explore LVM manifolds, toric manifolds, and their quaternionic extensions. Gain insights into the intersection of quadrics, moment-angle manifolds, and convex polytopes in complex and quaternionic settings.