Introduction to Minimal Surfaces
Explore zero mean curvature surfaces in Euclidean 3-space, their mathematical aspects, and natural occurrences as idealized soap films. Recommended: Review complex analysis concepts.
Two Mathematicians, Their Work and Career Experiences - Radhika Ganapathy and Purvi Gupta
Explore cyclotomic fields in number theory and convexity in complex analysis through lectures by two accomplished mathematicians, offering insights into their research and career experiences.
Symmetric Spaces by Pralay Chatterjee
Explore symmetric spaces in this advanced lecture on geometry, groups, and dynamics. Delve into modern research aspects and connect with cutting-edge theories in the field.
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.
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.
Extensions in MHM and Hain's Biextension Line Bundle - Part 2
Explores biextension line bundles, their extensions, and algebraic structures. Presents a formula for Q-line bundles, building on Hain and Pearlstein's work on normal functions and complex manifolds.
Extensions in MHM and Hain's Biextension Line Bundle - Part 1
Explore complex manifolds, biextension line bundles, and normal functions in algebraic geometry. Discover formulas for Q-line bundle extensions and their topological invariants.
Quantum Representations and Bogomolov-Katzarkov Surfaces
Exploring quantum representations and their application to Bogomolov-Katzarkov surfaces, addressing the Shafarevich conjecture on holomorphic convexity in algebraic geometry.
Geometric Recursion - Lecture II
Explore geometric recursion's relation to topological recursion, focusing on mapping class group invariant functions and their applications in moduli spaces and Gromov-Witten invariants.
Mirrors of Curves and Their Fukaya Categories II
Exploración avanzada de la simetría especular homológica para curvas, enfocándose en la geometría simpléctica de sus espejos y las categorías de Fukaya. Incluye discusiones sobre modelos de Landau-Ginzburg y geometría tropical.
Perverse Sheaves on Varieties with Large Fundamental Group
Explore perverse sheaves on Kähler manifolds, focusing on a generalization of the Singer-Hopf conjecture and its proof using Shafarevich conjecture ideas. Joint work with Donu Arapura presented.
Mixed Hodge Structures on Cohomology Jump Ideals
Explore mixed Hodge structures on cohomology jump ideals in representation varieties, extending Goldman and Millson's work to non-compact Kähler manifolds and variations of mixed Hodge structures.
On Nilpotent Quotients of Quasi-Kähler Groups
Exploration of nilpotent quotients of quasi-Kähler groups, focusing on smooth complex quasi-projective manifolds and their quasi-Albanese maps, with implications for holomorphic convexity and special manifolds.
Extension Data of Global Families of Mixed Hodge Structures - Applications to Shafarevich Conjecture
Extension data analysis in mixed Hodge structures: capturing global family invariants and proving Shafarevich's Conjecture in the nilpotent case through monodromy and level 1-2 extensions.
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.
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.
An Introduction to Auxiliary Polynomials in Transcendence Theory - Lecture III
Explore transcendence theory, Baker's Theorem, and the structural rank conjecture. Learn complex analysis and commutative algebra techniques for proving lower bounds on logarithmic matrices.
An Introduction to Auxiliary Polynomials in Transcendence Theory - Lecture II
Explore advanced transcendence theory concepts, focusing on auxiliary polynomials and their applications in proving Baker's Theorem and the Masser-Waldschmidt theorem on logarithmic matrices.
An Introduction to Auxiliary Polynomials in Transcendence Theory
Explore transcendence theory, focusing on Baker's Theorem and the structural rank conjecture. Learn complex analysis and commutative algebra techniques for proving key results in number theory.