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

Conformal Field Theory - Virasoro Algebra, Wess-Zumino-Witten Models, and W-Algebras

Dive into advanced conformal field theory through Virasoro algebra, W-algebras, Wess-Zumino-Witten models, and boundary conditions in this comprehensive mathematical physics workshop.

• YouTube
• 20 hours 2 minutes
• Self-Paced
• Free Video

Adjoint L-Values and the Tate Conjecture

Explore a strategy to prove the Tate conjecture on algebraic cycles for quaternionic Shimura varieties using twisted adjoint L-value formulas and theta base-change lifts.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

On a Family of Poincaré Series

Explore a specialized mathematical family of Poincaré series in this advanced workshop lecture on automorphic forms and Eisenstein series applications.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

On Quaternionic Representations and Exceptional Theta Lifts

Explore quaternionic representations in exceptional Lie groups E_6, E_7, E_8 and their role in theta correspondence with applications to automorphic forms and functorial liftings.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

A New Relative Trace Formula and Central Values of Standard L-Functions

Explore advanced connections between automorphic forms and L-functions through new relative trace formulas, featuring joint work on global conjectures and endoscopic comparisons.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Strict Reverse Mathematics - Part III

Explore advanced concepts in Strict Reverse Mathematics, examining base theory requirements and fundamental strictly mathematical statements in this specialized mathematical logic lecture.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Return of the Goodstein

Explore advanced mathematical concepts in reverse mathematics through Goodstein sequences and their foundational implications in this specialized workshop lecture.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

A Trip to Goodstein Island

Explore the Goodstein principle's unprovability in Peano arithmetic through Bachmann-Howard Hardy hierarchy normal forms, revealing independence from ID2 theory in this advanced mathematics lecture.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Higman's Lemma for Better Quasi-Orders is Provable in ATR₀

Explore advanced proof theory showing Higman's lemma for better quasi-orders is provable in ATR₀, featuring innovative iterated ideal orders and Nash-Williams theorem equivalence.

• YouTube
• 55 minutes
• Self-Paced
• Free Video

How to Treat Goodstein Sequences via Well Partial Orders

Explore an abstract framework for analyzing Goodstein sequences using well partially ordered direct limits, revealing proof-theoretic complexity bounds and connections to the Ackermann function.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

The Barrier Ramsey Theorem

Explore generalizations of Ramsey's theorem using barrier-based largeness notions, achieving surprisingly tight bounds unlike classical finite cases.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Incompleteness Theorems for Observables in General Relativity

Explore how descriptive set theory reveals fundamental limitations in defining observables within general relativity's diffeomorphism-invariant framework.

• YouTube
• 1 hour
• Self-Paced
• Free Video

The Reverse Mathematics of the Mountain Pass Theorem

Explore the equivalence between the Mountain Pass Theorem and WKL over RCA, examining critical point existence in Hilbert spaces through reverse mathematics analysis.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

The Fractal Goodstein Principle

Explore a novel Goodstein process using hierarchical base representations that achieves Bachmann-Howard strength while avoiding non-elementary functions in natural number notation systems.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

The Reverse Mathematics of the Mountain Pass Theorem - Part II

Explore the equivalence between the Mountain Pass Theorem and WKL over RCA, covering deformation lemmas, minimax principles, and constructive counterexamples in reverse mathematics.

• YouTube
• 58 minutes
• Self-Paced
• Free Video