Khovanov Homology and the Cinquefoil
Explore Khovanov homology's detection of the (2,5) torus knot through advanced Floer homology and recent developments in knot theory.
Categorified Traces and Colored SL_2 Knot Homology
Explore categorified traces and colored SL_2 knot homology in quantum topology, focusing on representation theory applications.
From Representation Theory to Topology: There and Back Again
Explorez les liens fascinants entre la théorie des représentations et la topologie quantique dans cette conférence approfondie.
Moduli Space of Curves and Its Intersection Theory - Lecture 2
Explore advanced concepts in algebraic geometry, focusing on moduli spaces of curves and their intersection theory in this in-depth lecture.
Moduli Space of Curves and Its Intersection Theory - Lecture 1
Explore the moduli space of curves and its intersection theory in this advanced mathematical lecture by Nitin Kumar Chidambaram.
Prismatic Cohomology of Commutative Ring Spectra
Explore motivic filtrations on trace invariants of commutative ring spectra and their extension to prismatic cohomology, as presented by Arpon Raksit from MIT.
A Conjectural Reciprocity Law for Realizations of Motives
Explore a conjectural reciprocity law connecting realizations of motives, drawing parallels to classical number theory and expanding on Hodge theory's comparison isomorphisms.
Hodge Theory and Lagrangian Fibrations in Holomorphic Symplectic Manifolds
Explore Hodge theory and Lagrangian fibrations in holomorphic symplectic manifolds. Delve into conjectures, isomorphisms, and decomposition theorems in this advanced mathematical discourse.
Enumerative Geometry Through Sheaves
Explore enumerative geometry, sheaf counting, and their applications in algebraic geometry. Discover new approaches to generalized Donaldson-Thomas invariants on Calabi-Yau threefolds.
Real Loci of Non-Real Varieties - Mathematics Department Colloquium
Explore cooriented submanifolds in real algebraic geometry, focusing on their properties, intersections, and linking numbers. Gain insights into the geometry of pencils and real projective spaces.
The High-Degree Rational Cohomology of the Special Linear Group
Explore high-degree rational cohomology of SL_n(Z) and SL_n(R) for number rings. Examine Steinberg modules and associated simplicial complexes to understand special linear group cohomology.
Nonabelian Mixed Hodge Structures
Explore nonabelian mixed Hodge structures, their relation to rational homotopy, and applications to character varieties and schematic homotopy types. Examine weights from noncompact bases and parabolic structures.
Quantitative Ell-Adic Sheaf Theory
Explore quantitative bounds for étale cohomology groups and their applications in algebraic geometry. Learn about complexity measures for sheaves and how they interact with various functors.
Topology in 1930s America - A Tale of Two Camps
Explore the rivalry between point-set and combinatorial topology camps in 1930s America, examining their approaches, key figures, and impact on the mathematical research community.
Quantum Periods for Complements
Explore quantum periods for complements, focusing on polynomial-defined spectral curves and quantization of polynomial algebras. Gain insights into cohomological descriptions of WKB series.
Birational Invariants from Gromov-Witten Theory - Lecture 4
Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of geometric objects like cubic 4-folds.
Analytic Stacks - New Foundations for Analytic Geometry
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
Graph Complex Action on Poisson Structures: From Theory to Computation
Explore graph complex action on Poisson structures, from theoretical foundations to computational applications using SageMath's gcaops package for advanced mathematical research.
Birational Invariants from Gromov-Witten Theory - Lecture 3
Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of geometric objects like cubic 4-folds.
Three Problems in the Mathematics of Deep Learning
Explore mathematical concepts behind aligning neural networks with classical programs, including polynomial functors, cohomology, and higher categories.
Integrality of the Betti Moduli Space
Explore the integrality of Betti moduli spaces for smooth projective varieties, examining representations of fundamental groups and their implications for algebraic geometry.