The Geometric Ideas of René Thom Related to Manifolds with Singularities
Explore René Thom's groundbreaking papers on transversality, cobordism, and manifolds with singularities, revealing their geometric insights and impact on mathematical understanding.
New Perspectives on Borel Summation - Lecture 3
Explore new perspectives on Borel summation through Airy-Lucas functions, examining their properties, linear ODEs, and thimble integral expressions. Gain insights from both ODE and integral equation approaches.
New Perspectives on Borel Summation - Lecture 4
Explore Airy-Lucas functions through Borel summation, focusing on thimble integrals and hypergeometric Laplace transforms. Gain insights into Stokes phenomenon reflections in the Borel plane.
New Perspectives on Borel Summation - Lecture 1
Explore new perspectives on Borel summation, focusing on linear ODEs and integrals over Lefschetz thimbles, to understand when divergent series solutions produce holomorphic solutions.
Twisted K-theory in Motivic Homotopy Theory
Explore algebraic K-theory of vector bundles twisted by Brauer class, its role in motivic homotopy theory, and a new approach to the motivic spectral sequence for twisted K-theory.
Prismatic Cohomology Relative Delta-Rings
Explore prismatic cohomology's evolution, comparing absolute and relative variants, and delve into a new generalization bridging the two approaches.
Efimov K-theory and Its Applications to Complex Geometry - Lecture 2
Explore Efimov's extended algebraic K-theory, its broader categorical context, and applications to complex geometry in this advanced mathematics lecture.
Motivic Cohomology of Schemes - Lecture 3
Explore advanced motivic cohomology theory for equicharacteristic schemes, covering cdh topology, K-theory filtration, and applications to algebraic geometry and zero cycles.
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.
Introduction to Prismatic Cohomology - Lecture 4
Explore prismatic cohomology, focusing on prismatization and the prismatic logarithm in advanced algebraic geometry and number theory.
Localizing Invariants and Algebraic K-theory - Lecture 3
Explore localizing invariants in algebraic K-theory, including Thomason's insights, descent properties, and recent developments in the field.
Introduction to Prismatic Cohomology - Lecture 3
Explore prismatic cohomology, covering general results, prismatization, and the prismatic logarithm in this advanced mathematics lecture by Johannes Anschütz.
Introduction to Prismatic Cohomology - Lecture 2
Explore prismatic cohomology, focusing on general results and derived concepts. Delve into prismatization as a tool for understanding this advanced mathematical theory.
A Homotopical Approach to Crystalline Cohomology
Explore a homotopical approach to crystalline cohomology, focusing on higher homotopies for canonical lifts and easier global definition through gluing.
Introduction to Prismatic Cohomology - Lecture 1
Explore prismatic cohomology's foundations, including its applications in characteristic 0 and p, general results, prismatization, and the prismatic logarithm.
Localizing Invariants and Algebraic K-theory - Part 1
Explore localizing invariants in algebraic K-theory, from classical foundations to recent developments, with emphasis on descent properties and applications.
Orbit Counting Theorem for Cusped Hitchin Representations
Explore cusped Hitchin representations through orbit counting theorems, Bowen-Series coding, and Quint's Iwasawa cocycle. Gain insights into dynamics and potential applications.
Ghost Polygons, Poisson Bracket and Convexity in Anosov Representations
Explore Anosov representations, length functions, and Poisson brackets in moduli spaces. Discover combinatorial techniques and their applications to convexity in character varieties.
Thurston's Asymmetric Metrics for Anosov Representations
Explore Thurston's asymmetric metric and its generalization to Anosov representations, applying thermodynamical formalism to construct pressure metrics on representation spaces.
Dynamics Associated to Anosov Representations: Some Geometric Consequences - Lecture 2
Explore dynamical systems of Anosov representations, including Patterson-Sullivan theory, critical hypersurface, and directional-conicality. Examine dominated sequences and their impact on limit set regularity.
Transverse Groups: Metric and Flow Space Analysis
Explore transverse groups, their metric and flow spaces, and new results in this advanced mathematical talk on discrete group theory and hyperbolic geometry.