Gauge Theory and the Analytic Approach to Geometric Langlands - Edward Witten
Explore gauge theory's role in geometric Langlands correspondence, comparing categorical and analytic approaches through quantum states, operators, and gauge theory interpretations.
Moduli Spaces of Bundles on Curves with Abelian Motives
Explore the mathematical theory behind abelian motives in bundle moduli spaces, examining motivic formulas and their relationship to cohomological phenomena on curves.
Moduli of Calabi-Yau Manifolds and Mirror Symmetry
Delve into advanced mathematical concepts exploring Calabi-Yau manifolds and mirror symmetry theory through expert insights from Kyoto University's mathematics department.
Mirror Symmetry for Young Students - Elementary Mathematics Explained
Explore mirror symmetry through visual mathematics, focusing on regular tilings and their symmetry lines. Ideal for teachers and parents to introduce geometric concepts to young learners.
A Tropical Approach to Homological Mirror Symmetry of Quadrics
Tropical geometry approach to homological mirror symmetry of quadrics, exploring new anti-canonical divisor and potential construction. Compares with previous work and discusses exceptional collections.
Homological Mirror Symmetry - Toward the Logarithmic Hilbert Scheme
Explore logarithmic geometry and its applications in mirror symmetry, focusing on the development of a logarithmic Hilbert scheme and its implications for degenerations and tropical mathematics.
Homological Mirror Symmetry - Moduli Space of Non-Archimedean Holomorphic Disks Pt. II
Explore non-Archimedean holomorphic disks in affine log Calabi-Yau varieties, covering boundary conditions, smoothness, dimension, and properness. Gain insights into non-Archimedean mirror symmetry and related theories.
Canonical Wall Structures via Punctured Gromov-Witten Theory
Exploration of canonical wall structures in logarithmic Calabi-Yau pairs using punctured Gromov-Witten theory, connecting intrinsic mirror construction with earlier approaches.
Mirror Symmetry for Character Varieties and Field Theory by Sergey Galkin
Explore mirror symmetry for character varieties, using threespace mirrors to construct SU(2) character variety mirrors on Riemann surfaces, with applications in topological field theory and random walks.
Tamas Hausel - Enhanced Mirror Symmetry for Langlands Dual Hitchin Systems
Explore enhanced mirror symmetry for Langlands dual Hitchin systems, covering topics from SYZ mirror symmetry to equivariant cohomology and Kirillov algebras.
The Rogers-Ramanujan Identities and the Icosahedron - Lecture 3
Explore the deep connections between Rogers-Ramanujan identities and the icosahedron, spanning number theory, modular forms, combinatorics, and more. Uncover the beauty and complexity of these mathematical gems.
Mirror Symmetry for Fano Orbifolds - Lecture 01
Explore mirror symmetry for Fano orbifolds, covering key concepts like differential operators and torque variety in this advanced mathematics lecture.
Mirror Symmetry and Big Algebras
Explore mirror symmetry in Hitchin systems, Kirillov algebras, and equivariant cohomology. Delve into conjectures on non-very stable flows and big commutative subalgebras in affine Schubert varieties.
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.
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.
Hilbert Schemes of Plane Curve Singularities and Matrix Factorizations
Explore connections between algebraic geometry and topology through plane curve singularities, Hilbert schemes, and matrix factorizations in this advanced mathematics lecture.
Mirror Symmetry and Cluster Varieties
Explore symplectic geometry of cluster varieties and their applications to mirror symmetry, including homological mirror symmetry for Gross-Hacking-Keel cluster varieties.
Homological Mirror Symmetry for Some Non-Kähler Elliptic Surfaces
Explore homological mirror symmetry for non-Kähler elliptic surfaces, including logarithmic transformations and potential applications to singular curves and mirror operations.
Homological Mirror Symmetry - Twisted Shklyarov Pairing & Applications
Explore twisted Shklyarov pairing in Hochschild homology, its applications to Lefschetz fibrations, mirror symmetry, and classical problems. Joint work with Paul Seidel presented.