Modular Regulators and Multiple Modular Values
Explore recent advancements in computing Goncharov regulator integrals for K_4 classes on modular curves, relating them to multiple modular values and single L-values of modular forms.
Integer Points on Mordell Curves
Explore integer solutions on Mordell curves, a fascinating topic in number theory. Gain insights into this complex mathematical concept through clear explanations and examples.
Equivariant Birational Geometry
Explore new results and constructions in equivariant birational geometry, delving into advanced mathematical concepts and their applications in this specialized field.
Fractal Dimensions of Critical Loci in Algebraic Geometry
Explore fractional dimensions in mathematics, focusing on critical loci of holomorphic functions. Discover theories from algebraic geometry, singularity theory, and more, with the smallest non-zero dimension at 1/3.
Chern Classes and Indices of Vector Fields on Singular Varieties
Explore Chern classes and vector field indices on singular varieties, examining fundamental invariants in geometry and topology and their evolving theory for non-smooth spaces.
Universally Counting Curves in Calabi-Yau Threefolds
Explore enumerative geometry through a new perspective on curve counting in complex threefolds, focusing on the Grothendieck group of 1-cycles and its implications for the MNOP conjecture.
The Shape of a Minimal Resolution
Explore the intricacies of minimal free resolutions, delving into open questions and recent findings on their shape. Survey both established and innovative methods in this mathematical exploration.
Proof of the Geometric Langlands Conjecture
Explore recent breakthroughs in the geometric Langlands conjecture, including its proof in characteristic zero settings, framework, obstacles, and solutions in this advanced mathematics lecture.
Cohomology Rings of Character Varieties
Explore cohomology rings of character varieties, including P=W conjecture proof and zero-dimensional COHA computation. Discover connections to Hilbert scheme of C^2 for punctured sphere case.
G-modules: Stable Categories and Subcoalgebras - Lecture on Affine Group Scheme Representations
Explore affine group scheme representations, stable module categories, and support theory for G-modules. Discover filtrations associated with subcoalgebras of coordinate algebras in this advanced mathematics lecture.
Stable Module Category for Finite Group Schemes over Commutative Noetherian Rings
Explore finite group schemes, tensor triangular analysis, and Balmer spectrum calculations in stable module categories, based on recent advancements in cohomology and representation theory.
Interpolation Categories for Finite Linear Groups
Exploration of representation stability for complex representations of finite linear groups, focusing on interpolation categories and their applications in algebraic geometry.
Hodge Theory for Poisson Varieties and Nonperturbative Quantization
Explore Hodge theory for Poisson varieties and nonperturbative quantization, focusing on K-theory and mixed Hodge structures to simplify complex calculations in deformation quantization.
Equivariant Geometry of Cubics - Applications to Cubic Threefolds and Fourfolds
Explore applications of new invariants in equivariant birational geometry to cubic threefolds and fourfolds, advancing understanding in algebraic geometry and related fields.
Wobbly Fixed Points, Equivariant Multiplicities and U(p,q)-Higgs Bundles
Explores geometry of Higgs bundle moduli spaces, focusing on nilpotent cone fixed points and their classification. Analyzes U(p,q)-Higgs bundles and compares results with equivariant multiplicities.
Local-Global Principles for Norm One Tori and Multinorm Tori Over Semi-Gl
Explore local-global principles for norm one tori and multinorm tori over semi-global fields, delving into advanced algebraic number theory and geometric applications.
Support Varieties for Lie Superalgebras - Lecture 1
Explore support varieties for Lie superalgebras in positive characteristic, examining their use in studying non-semisimple tensor categories and addressing open questions in this 40+ year research area.
Support Variety Theory for Algebraic Supergroups
Explore algebraic supergroups and support variety theory in this advanced mathematics lecture, focusing on representations and Frobenius symmetric monoidal tensor categories.
From Representation Rigidity to Profinite Rigidity by Alan Reid
Explore rigidity concepts in group theory, from representation to profinite, with applications in geometry and number theory. Gain insights into Zariski-dense subgroups and their implications.
Tannakian Formalism for Stacks
Explores Tannakian formalism for stacks, discussing representation categories of affine group schemes and characterizing symmetric monoidal Grothendieck categories equivalent to quasi-coherent sheaves on stacks.
Twistor Spaces and Compact Manifolds Admitting Kähler and Non-Kähler Structures
Explore twistor spaces and compact manifolds with dual Kähler and non-Kähler structures. Discover historical examples and new findings in higher dimensions using quaternion twistor spaces of hyperkähler manifolds.