De Rham cohomology

Voisin Claire "From Analysis situs to the theory of periods"

Résumé The talk will focus on the pairing between singular homology and de Rham cohomology: Combinatorics of cells of a triangulation on one side, differential forms on the other side. The two aspects of the subject were already present in Poincaré's work, but the fact that this pairing i

From playlist Colloque Scientifique International Poincaré 100

A Gentle Approach to Crystalline Cohomology - Jacob Lurie

Members’ Colloquium Topic: A Gentle Approach to Crystalline Cohomology Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: February 28, 2022 Let X be a smooth affine algebraic variety over the field C of complex numbers (that is, a smooth submanifold of C^n which can

From playlist Mathematics

B. Bhatt - Prisms and deformations of de Rham cohomology

Prisms are generalizations of perfectoid rings to a setting where "Frobenius need not be an isomorphism". I will explain the definition and use it to construct a prismatic site for any scheme. The resulting prismatic cohomology often gives a one-parameter deformation of de Rham cohomology.

From playlist Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday

Vladimir Berkovich: de Rham theorem in non-Archimedean analytic geometry

Abstract: In my work in progress on complex analytic vanishing cycles for formal schemes, I have defined integral "etale" cohomology groups of a compact strictly analytic space over the field of Laurent power series with complex coefficients. These are finitely generated abelian groups pro

From playlist Algebraic and Complex Geometry

Olivia Dumitrescu - Lagrangian Fibration of the de Rham Moduli Space and Gaiotto Correspondence

There have been new developments in understanding Lagrangian fibrations of the de Rham moduli space in connection to Lagrangian stratifications of the Dolbeault moduli space through biholomorphic isomorphisms of the Lagrangian fibers. I will report recent results by different groups of aut

From playlist Resurgence in Mathematics and Physics

Florian Herzig: On de Rham lifts of local Galois representations

Find other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies,

From playlist Algebraic and Complex Geometry

Arthur Ogus - Prisms, prismatic neighborhoods, and p-de Rham cohomology

Correction: The affiliation of Lei Fu is Tsinghua University. Prismatic cohomology, as proposed by B. Bhatt and P. Scholze, provides a uniform framework for many of the cohomoogy theories involved in p-adic Hodge theory. I will focus on the crystalline incarnation of prismatic cohomology

From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021

Lars Hesselholt: Around topological Hochschild homology (Lecture 8)

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Introduced by Bökstedt in the late eighties, topological Hochschild homology is a manifestation of the dual visions of Connes and Waldhausen to

From playlist HIM Lectures: Junior Trimester Program "Topology"

Javier Fresán: Exponential motives

Abstract: I will sketch the construction - following ideas of Kontsevich and Nori - of a Tannakian category of exponential motives over a subfield of the complex numbers. It is a universal cohomology theory for pairs of varieties and regular functions, whose de Rham and Betti realizations

From playlist Algebraic and Complex Geometry

Lars Hesselholt: Around topological Hochschild homology (Lecture 7)

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Introduced by Bökstedt in the late eighties, topological Hochschild homology is a manifestation of the dual visions of Connes and Waldhausen to

From playlist HIM Lectures: Junior Trimester Program "Topology"

Philippe ELBAZ - Cohomology of arithmetic groups and number theory: geometric, ... 4

In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

De Rham Cohomology: PART 1- THE IDEA

Credits: Animation: I animated the video myself, using 3Blue1Brown's amazing Python animation library "manim". Link to manim: https://github.com/3b1b/manim Link to 3Blue1Brown: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw Beyond inspecting the source code myself, this channel

From playlist Cohomology

Lars Hesselholt: Around topological Hochschild homology (Lecture 1)

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Introduced by Bökstedt in the late eighties, topological Hochschild homology is a manifestation of the dual visions of Connes and Waldhausen to

From playlist HIM Lectures: Junior Trimester Program "Topology"

Lars Hesselholt: Around topological Hochschild homology (Lecture 3)

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Introduced by Bökstedt in the late eighties, topological Hochschild homology is a manifestation of the dual visions of Connes and Waldhausen to

From playlist HIM Lectures: Junior Trimester Program "Topology"

Akhil Mathew - Remarks on p-adic logarithmic cohomology theories

Correction: The affiliation of Lei Fu is Tsinghua University. Many p-adic cohomology theories (e.g., de Rham, crystalline, prismatic) are known to have logarithmic analogs. I will explain how the theory of the “infinite root stack” (introduced by Talpo-Vistoli) gives an alternate approach

From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021

Lars Hesselholt: Around topological Hochschild homology (Lecture 2)

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Introduced by Bökstedt in the late eighties, topological Hochschild homology is a manifestation of the dual visions of Connes and Waldhausen to

From playlist HIM Lectures: Junior Trimester Program "Topology"