Erwin Schrödinger International Institute for Mathematics and Physics (ESI) Courses

On Katz' Nilpotence Conjecture, p-Determinants, and q-Generalization

Delve into advanced mathematical concepts exploring Katz' nilpotence conjecture, examining p-determinants and their q-generalizations through expert analysis and theoretical frameworks.

• YouTube
• 1 hour 41 minutes
• On-Demand
• Free Video

On Abel's Problem and Gauss Congruences

Delve into advanced mathematical concepts exploring Abel's problem and Gauss congruences, examining their relationships and implications in differential equations and number theory.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Video

The Arithmetic of Power Series and Applications to Periods

Explore the mathematical foundations of power series arithmetic and their relationship to periods, focusing on singular differential equations and their applications.

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

Towards a Kontsevich-Zagier Type Conjecture for Holonomic Series

Delve into advanced mathematical concepts exploring holonomic series and their relationship to the Kontsevich-Zagier conjecture through rigorous theoretical analysis.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Ice Clouds Over the Asian Monsoon and Their Role in the Global Climate

Explore the formation and impact of ice clouds in the Asian Summer Monsoon system, examining their crucial role in climate patterns and water vapor transport through aircraft-based observations and simulations.

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

Extending Hölder's Result on the Differential Transcendence of the Gamma Function

Delve into advanced mathematical concepts exploring Hölder's theorem and its extension to the differential transcendence properties of the Gamma function through rigorous analysis.

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

Arithmetic Algebraization Theorems and the Analogy Between Number Fields and Function Fields

Delve into advanced mathematical concepts exploring arithmetic algebraization theorems and their relationship with number fields through expert analysis and theoretical frameworks.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video

First Order Differential Equations in Characteristic Zero and Characteristic p

Explore advanced mathematical concepts of first-order differential equations across characteristic zero and characteristic p, with insights from leading mathematician Marius van der Put.

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

Higher Dimensional Katz Theory

Explore advanced mathematical concepts in higher dimensional Katz theory through rigorous analysis and theoretical frameworks within singular differential equations.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Picard-Fuchs Equations and Modular Forms - Applications and Theory

Explore the intricate relationship between Picard-Fuchs equations and modular forms, examining their mathematical applications and theoretical foundations in algebraic differential equations.

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

G-Functions of Differential Order 2

Delve into advanced mathematical concepts exploring G-functions of differential order 2, focusing on algebraicity and transcendence properties in singular differential equations.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Differential Galois Theory and the Algebraicity of Solutions - Part 3

Delve into advanced concepts of Differential Galois Theory, exploring algebraicity of solutions and their applications in singular differential equations with mathematician Michael Singer.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

Differential Equations, Geometry and Arithmetic - Lecture 3

Delve into advanced mathematical concepts exploring the intricate relationships between differential equations, geometry, and arithmetic through expert analysis and theoretical frameworks.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

Competing Magnetisms and Onset of Static Magnetic Order in Sr2RuO4

Explore competing magnetic instabilities in Sr2RuO4, their link to superconductivity, and the onset of static magnetic order under strain using first-principles and self-consistent renormalization theories.

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

Exotic Phenomena Due to Multipolar Superexchange Interactions in f-Electron Systems

Explore exotic phenomena in f-electron systems, focusing on hidden orders, multipolar interactions, and their impact on material properties in NpO2, PrO2, URu2Si2, and UTe2.

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