Monodromy Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Non-Archimedean Motives IV

Explore advanced non-Archimedean motives over adic spaces, covering six-functor formalism, continuity properties, and applications to p-adic cohomology theories.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Non-Archimedean Motives III

Explore advanced non-Archimedean motives over adic spaces, focusing on six-functor formalism, continuity properties, and applications to p-adic cohomology theories.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Non-Archimedean Motives II

Explore advanced non-Archimedean motives over adic spaces, six-functor formalism, and applications to p-adic cohomology theories including rigid and de Rham cohomologies.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Non-Archimedean Motives I

Explore non-Archimedean motives over adic spaces, their six-functor formalism, and applications to p-adic cohomology theories including rigid and de Rham cohomologies.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

BIMSA

D-Modules and Singularities - Bernstein-Sato Ideals and Monodromy for Polynomial Mappings

Explore recent findings connecting D-modules with singularities, focusing on Bernstein-Sato ideals and monodromy in polynomial mappings.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Wolfram

New Algorithms: Numerical Solution of Large Systems of Nonlinear Equations Using Monodromy

Explore a novel algorithm using monodromy to solve large systems of analytic nonlinear equations, developed during a Wolfram internship.

• YouTube
• 20 minutes
• On-Demand
• Free Video

Galileo Galilei Institute

Modularity and Monodromy

Explore the intricate relationship between modularity and monodromy in mathematics, delving into advanced concepts and their applications in number theory and algebraic geometry.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Monodromy in Bi-parameter Persistence Modules

Delve into the algebraic formalization of monodromy behavior in bi-parameter persistence modules, exploring how non-trivial monodromy relates to module presentations and direct sum decompositions.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Monodromy of Lagrangian Fibrations

Explore advanced algebraic geometry through hyperkähler manifolds and their Lagrangian fibrations, examining monodromy properties and Hodge structure variations in higher dimensions.

• YouTube
• 35 minutes
• On-Demand
• Free Video

IMSA

Braid Monodromy and Divisibility of Alexander Polynomials of Real Singular Curves

Explores Alexander polynomials in algebraic geometry, focusing on braid monodromy symmetries of real plane curves and their impact on divisibility relations for Alexander invariants.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

QuantumTopology

Quantum Cluster Algebras and Character Varieties of SL-2, R-Monodromy Problem

Explore quantum cluster algebras, character varieties, and SL(2,R)-monodromy problems through shear coordinates, local kernels, and quantum flips on Riemann surfaces.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Fields Institute

Numerical Computation of Monodromy Action Over R

Explore numerical computation of monodromy action over real numbers, focusing on a new piece-wise approach for analyzing real solution sets, with applications in kinematics and mechanism calibration.

• YouTube
• 37 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry Part 1

Explores the Riemann-Hilbert correspondence in complex and p-adic geometry, discussing its historical context, mathematical foundations, and recent developments in prismatic cohomology.

• YouTube
• 46 minutes
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 57 minutes
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 33 minutes
• On-Demand
• Free Video