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

The Casimir Energy as a Trace

Explore the Casimir effect's connection to spectral geometry and microlocal analysis. Learn to define Casimir energy as an operator trace and compute it using boundary layer operator determinants.

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

Relative Oscillation Theory and Essential Spectra of Sturm-Liouville Operators

Explore relative oscillation theory for Sturm-Liouville operators, examining perturbation results and essential spectra invariance in terms of real coefficients p, q, and r.

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

Improved Lieb-Thirring Type Inequalities for Non-Selfadjoint Schroedinger Operators

Explore improved Lieb-Thirring inequalities for complex-valued Schroedinger operators, focusing on eigenvalue analysis and sharpness in one-dimensional cases.

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

Spectral Approximation for Maxwell's Equations in Conductive Media

Explore spectral approximation for Maxwell's equations in conductive media, focusing on non-selfadjoint operators, spectral pollution, and domain truncation methods.

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

A New Approach to the Hot Spots Conjecture

Explore a novel approach to the hot spots conjecture in mathematics, focusing on eigenvalues of Neumann and Dirichlet Laplacians and recent advances in the field.

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

Spectral Properties of Soft Quantum Waveguides

Explore spectral properties of soft quantum waveguides, focusing on Schrödinger operators with attractive potentials along curved channels. Analyze discrete spectrum conditions and ground state optimization.

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

Singularity of Stationary Measures in Markov Chains

Explore stationary measures of compound Markov chains, focusing on examples using boundary processes of random walks on the modular group PSL(2,Z) and related classical constructions.

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

Constrained Stochastic Processes: From Brownian Motion to Run-and-Tumble Particles

Explore constrained stochastic processes, including Brownian motion, Lévy flights, and run-and-tumble particles. Learn effective dynamics for generating constrained trajectories in various scenarios.

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

Large Deviations and Large Biasing of Ground State Entanglement Entropy

Explore large deviations in charge resolved entanglement entropy, examining universal tail structures and their implications for ground state properties in many-body systems.

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

Homogenization of Markovian Processes and Application to Quantum Continuous Measurement

Explore Markovian processes with time scale separation, deriving effective dynamics on reduced state spaces. Apply to quantum systems with strong continuous measurement.

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

Current Fluctuations in Noninteracting Run-and-Tumble Particles in One Dimension

Explore current fluctuations in noninteracting run-and-tumble particles, focusing on flux distribution through origin and anomalous large-deviation form in active particles.

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

Localization Transition in the Discrete Non-Linear Schrödinger Equation

Explore the localization transition in the Discrete Nonlinear Schrödinger Equation, focusing on ensemble inequivalence, microcanonical entropy, and thermodynamic stability using large-deviation techniques.

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

Thermodynamics of Non-Additive Systems: The Example of the Thirring Model

Explore thermodynamics of non-additive systems through the Thirring model, examining ensemble inequivalence and equilibrium states in long-range interacting systems.

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

Measurement Incompatibility vs. Bell Non-locality: An Approach via Tensor Norms

Explore measurement incompatibility and quantum non-locality, analyzing their relationship through tensor norms and Bell inequalities in quantum theory.

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

Quantum Simulation of Conformal Field Theory

Explore quantum algorithms for simulating conformal field theory dynamics and local conformal transformations in scaling-symmetric systems.

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