Institute for Advanced Study Courses

Malle's Conjecture for Function Fields

Delve into Malle's conjecture for function fields, exploring a quantitative version of the inverse Galois problem and homological stability results for Hurwitz spaces with Ishan Levy.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Kinematic Flow and the Emergence of Time

Delve into the theory of initial conditions of the universe and explore a bootstrap approach to primordial cosmology, focusing on kinematic flow and how time evolution emerges from static differential equations.

• YouTube
• 1 hour 26 minutes
• Self-Paced
• Free Video

Erdős Unit Distance Problem and Graph Rigidity

Delve into the Erdős Unit Distance Problem and its connection to graph rigidity theory, exploring a new approach to this long-standing mathematical challenge.

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

Simulating Time With Square-Root Space

Delve into a groundbreaking simulation technique that improves on a 50-year-old algorithm, showing how multitape Turing machines running in time t can be simulated in O(t√log t) space.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Howe Duality Over Finite Fields

Explore Howe duality's complete decomposition of oscillator representations under tensor embeddings of symplectic and orthogonal groups over finite fields.

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

A Further Look at the Oscillator Semigroup and the eta Correspondence for Dual Pairs Over Finite Fields

Explore advanced oscillator semigroup theory and eta correspondence for dual pairs over finite fields with Yale's Roger Howe in this specialized group theory seminar.

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

A Look at Representations of SL(2,q) Via the Lens of Size - Motivations, Rank, Eta Correspondence

Explore harmonic analysis for finite classical groups through SL(2,q) representations, introducing frequency concepts and rank-based character analysis methods.

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

The Relation Between the Geodesic Flow and Finite-Area Holomorphic Quadratic Differentials on Infinite-Genus Riemann Surfaces

Explore the connection between geodesic flows and holomorphic quadratic differentials on infinite Riemann surfaces, examining ergodicity conditions through Fenchel-Nielsen parameters.

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

Ahlfors Currents and Symplectic Non-Hyperbolicity

Explore Ahlfors currents as a framework for studying complex lines in symplectic geometry, generalizing rational curve theory through topological methods and extending Bangert's theorem.

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

No Exponential Quantum Speedup for SIS^inf Anymore

Discover efficient classical algorithms for the Short-Integer-Solution problem that eliminate exponential quantum speedup, challenging previous quantum computational advantages.

• YouTube
• 2 hours 8 minutes
• Self-Paced
• Free Video

Looking for Black Holes in all the Wrong Places

Explore tidal disruption events to discover supermassive black holes in unexpected locations like dwarf galaxies and wandering positions, using advanced optical surveys and accretion physics.

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

Refined THH Over ku and Habiro Cohomology

Explore advanced algebraic geometry through refined topological Hochschild homology over ku, connecting to Habiro cohomology and Scholze's work on varieties over rationals.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

From Symplectic Weyl Laws to Homeomorphism Groups and Beyond

Explore how Floer theory and symplectic topology reveal the non-simplicity of area-preserving homeomorphism groups, extending classical invariants to continuous settings.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

From Morse Homology to Symplectic Weyl Laws

Explore symplectic Weyl laws and three-manifold invariants rooted in Morse theory, with applications to periodic point density and the Closing Lemma.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Motivic Action Conjecture for Doi-Naganuma Lifts

Explore the motivic action conjecture for Doi-Naganuma lifts, examining hidden degree-shifting actions in cohomology of locally symmetric spaces and Hilbert modular forms.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video