Differential Equations and Mixed Hodge Structures
Explore the interplay between differential equations and mixed Hodge structures, focusing on periods, kappa series, and motific gamma in number theory and algebraic geometry.
Applications of O-minimality to Hodge Theory - Lecture 4
Explore infinitesimal thickening, definable spaces, and cell decomposition in o-minimality, with applications to Hodge theory and Abelian shields.
Applications of O-minimality to Hodge Theory - Lecture 2
Explore o-minimality's applications to Hodge Theory, covering definable spaces, fundamental domains, and Hodge metrics in this advanced graduate-level lecture.
2-Selmer Groups, 2-Class Groups, and the Arithmetic of Binary Forms
Explore Selmer groups, class groups, and binary forms in number theory. Gain insights into elliptic curves, hyperelliptic Jacobians, and superelliptic equations in this advanced mathematics seminar.
Hilbert's 16th Problem and O-Minimality - Lecture 1
Explore the topology of cycles, limit cycles, and related mathematical concepts in this advanced graduate-level lecture on Hilbert's 16th problem and o-minimality.
From Multiple Polylogarithms to the Universal Vector Extension of an Elliptic Curve
Explore connections between polylogarithms and elliptic curves, delving into unipotent vector bundles, canonical extensions, and the universal vector extension. Gain insights into advanced number theory concepts.
O-minimality and the Pila-Wilkie Theorem - Lecture 1
Explore o-minimality, its foundations, and key theorems in this graduate-level lecture, emphasizing mathematical concepts and their applications in tame geometry.
Introduction to Contact Geometry by Dheeraj Kulkarni
Explore contact geometry fundamentals, including Frobenius theorem, contactomorphisms, and Gray stability theorem. Learn about symplectic structures and their relation to contact manifolds.
Out of the Closet and Into the Mirror
Explore algebraic geometry, Calabi-Yau varieties, and mirror symmetry with insights on finding the right mathematical community and research spaces for LGBTQ+ mathematicians.
Real Invariants in Arithmetic Geometry and Theta Series
Explore arithmetic geometry, theta series, and real invariants in this advanced mathematical lecture, focusing on Euclidean lattices, algebraic geometry, and chromological invariants.
On the Algebraicity of the Hodge Locus
Explore algebraic geometry and number theory with Bruno Klingler as he delves into the algebraicity of the Hodge locus, covering topics from universal families to arithmetic applications.
P-adic Etale Tate Twists and Syntomic Cohomology
Explore p-adic étale Tate twists and syntomic cohomology, delving into quasisyntomic structures, prismatic chromology, and the Italian Comparison Theorem in advanced algebraic geometry.
An Introduction to Spectral Data for Higgs Bundles
Explore spectral data for Higgs bundles, a key concept in algebraic geometry and mathematical physics, with insights on integrable systems and moduli 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.
Andras Szenes- Intersection Cohomology of the Moduli Spaces of Stable Bundle II
Exploration of intersection cohomology in moduli spaces of semistable bundles on Riemann surfaces, featuring new formulas for intersection Betti numbers and geometric insights.
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.
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.
Gromov-Hausdorff Convergence of Filtered A Infinity Categories
Explore Floer homology's dependence on Hamiltonian isotopy, its multiplicative structure, and connections to homological Mirror symmetry in formal deformation theory.