Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds
Explore the interaction between hyperbolic geometry and homology cobordism using monopole Floer homology, focusing on subgroups generated by hyperbolic homology spheres.
Instantons, Suspension, and Surgery
Explore advanced concepts in gauge theory, including instantons, suspension, and surgery techniques for manifolds with boundary components and their applications in cobordism maps.
Instantons, Suspension, and Surgery - Part 1
Explore Dehn surgery number in 3-manifolds, using mod 2 instanton homology and Froyshov's q_3 invariant to prove existence of integer homology 3-spheres with arbitrarily large surgery numbers.
Smooth Closing Lemma for Area-Preserving Diffeomorphisms of Surfaces
Explore the smooth closing lemma for area-preserving diffeomorphisms on surfaces, featuring a proof based on Weyl formula and Seiberg-Witten Floer homology. Joint work with Cristofaro-Gardiner and Prasad.
Fillable Contact Structures From Positive Surgery
Exploring conditions for fillable contact structures from positive surgery on Legendrian knots, with applications to topological consequences and lens space surgeries.
PL-Surfaces in Homology 4-Balls
Exploration of PL-surfaces in homology 4-balls, discussing minimum genus of PL surfaces and their bounds in homology balls using Heegaard Floer homology. Joint research findings presented.
Nearly Parallel G2-Structures on 7-Manifolds - Associative 3-Folds in Aloff-Wallach Spaces
Explore nearly parallel G2-structures on 7-manifolds, focusing on Aloff-Wallach spaces and Sasaki-Einstein manifolds. Learn about associative 3-folds and their construction in these spaces.
Coassociative Fibrations in G2 Geometry
Explore G2 geometry in 7D spaces, focusing on coassociative submanifolds. Learn about their properties, deformation theory, and constructions forming fibrations with singular fibers in 7-manifolds.
Tight Contact Structures on Hyperbolic 3-Manifolds - IMSA Topology Seminar
Exploring tight contact structures on hyperbolic 3-manifolds via Dehn surgery on genus one fibered knots in lens spaces, with insights on classification and Stein fillability.
Quasipositive Surfaces and Decomposable Lagrangians in Topology - IMSA Seminar
Explore Legendrian links, knot Floer homology, and Lagrangian link cobordisms in topology. Learn about braiding techniques and the comultiplication property in this advanced mathematical seminar.
Intersection Cohomology of the Moduli Spaces of Stable Bundle I
Explore intersection cohomology of semistable bundle moduli spaces on Riemann surfaces, including Decomposition Theorem analysis and new formula for intersection Betti numbers.
Generalized Kaehler and Bihermitian Structures
Explore generalized Kaehler structures, their properties, and similarities to Kaehler case. Covers stability under deformations, Calabi-Yau problem, and period map in complex geometry.
Mapping Spaces and E_2 Algebras
Explore mapping spaces, spectral sequences, and E_2 algebras in topology. Discover connections between configuration spaces, cochains, and factorization homology in this advanced mathematical lecture.
Functions on Commuting Stacks via Mirror Symmetry
Explores complex reductive groups, commuting stacks, and G-local systems on tori. Utilizes mirror symmetry and Betti geometric Langlands to calculate global functions on commuting stacks.
A Splitting Formula for Punctured Gromov-Witten Invariants
Explore punctured Gromov-Witten theory and its role in mirror symmetry. Learn about a new formula for reconstructing invariants, generalizing Jun Li's degeneration formula.
Homological Mirror Symmetry for Theta Divisors
Exploring homological mirror symmetry for theta divisors in principally polarized abelian varieties, with insights from ongoing research in complex moduli and SYZ fibrations.
Lagrangian Intersections in Phase Tropical Hypersurfaces
Explore phase tropical hypersurfaces, their relation to complex hypersurfaces, and combinatorial analogs of Lagrangian spheres and thimbles. Discuss connections to mirror matrix factorization categories.
Derived Categories and Motives of Moduli Spaces of Vector Bundles on Curves
Explore derived categories and motives of moduli spaces of vector bundles on curves, their relationships, and recent developments in algebraic geometry.
Stability Structures in Holomorphic Morse-Novikov Theory
Explore complex symplectic manifolds, Floer theory, and Morse-Novikov theory. Delve into analytic questions of convergence and generalization to almost-complex cases in this advanced mathematical lecture.
Basic Remarks on Lagrangian Submanifolds of Hyper-Kähler Manifolds
Explore properties of Lagrangian subvarieties in hyper-Kähler manifolds, focusing on their interaction with Lagrangian fibrations and albanese dimension of Lagrangian surfaces.
Topological Invariants of Compact Singular Varieties
Explore topological invariants of compact singular varieties with José Seade from UNAM. Gain insights into advanced mathematical concepts and their applications in algebraic geometry.