Hausdorff Center for Mathematics Courses

Introduction to Fukaya Categories - James Pascaleff

Explore Floer cohomology and Fukaya category fundamentals, including Lagrangian intersection theory, Floer differential, A∞ operations, and Gromov compactification in symplectic geometry.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Introduction to A-Infinity Structures - Bernhard Keller

Explore A-infinity algebras, modules, and derived categories. Learn about topological origins, minimal models, and twisted objects in this advanced mathematics lecture.

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

An Introduction to Modified Traces

Explore fundamental invariants in representation theory, focusing on modified traces as replacement invariants in non-semi-simple settings. Learn basic properties and applications through examples.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Introduction to A-Infinity Structures - Bernhard Keller

Explore A-infinity algebras, modules, and derived categories. Learn about topological origins, minimal models, and twisted objects in this advanced mathematical lecture.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Introduction to A-Infinity Structures - Bernhard Keller

Explore A-infinity algebras, their modules, and derived categories. Learn about topological origins, definitions, morphisms, bar construction, and Kadeishvili's theorem on minimal models.

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

Deformations of Path Algebras of Quivers With Relations

Explore deformation theory of path algebras using reduction systems. Learn about L-infinity algebras, formal deformations, and Poisson structure quantization. Accessible to non-experts with examples.

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

Deformations of Path Algebras of Quivers with Relations

Explore deformation theory of path algebras using reduction systems. Learn to describe all deformations by systematically modifying relations, with applications in representation theory and algebraic geometry.

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

Deformations of Path Algebras of Quivers With Relations - Lecture I

Explore path algebras of quivers with relations in representation theory and algebraic geometry. Learn about deformation theory using reduction systems to systematically deform relations.

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

Mathematik für alle - in Zeiten von Corona, Folge 8: Teilbarkeit durch 11

Entdecken Sie faszinierende Regeln zur Teilbarkeit durch 11 und erweitern Sie Ihr mathematisches Verständnis in diesem unterhaltsamen und lehrreichen 20-minütigen Video.

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

Mathematik für alle - in Zeiten von Corona, Folge 7: Des Rätsels Lösung

Entdecken Sie die Schönheit der Mathematik und ihre Relevanz in der heutigen Welt. Prof. Kreck führt Sie durch elementare Beweise und zeigt, wie mathematisches Denken den Verstand schult und gegen Irrationalität wappnet.

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

Osama Khalil- Diophantine Approximation on Fractals and Homogeneous Flows

Explore Diophantine approximation on fractals and homogeneous flows, examining exceptional sets and their connections to recurrence behavior. Discover new results on Hausdorff dimension of divergent orbits and self-similar measure projections.

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

Equidistribution of Linear Random Walks on the Torus

Explores quantitative equidistribution for linear random walks on the torus, presenting recent progress relaxing the proximality assumption in Bourgain et al.'s work. Joint research with Nicolas de Saxcé.

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

Equidistribution of Expanding Translates of Curves in Homogeneous Spaces

Explores equidistribution of expanding translates of non-degenerate real-analytic curves in semisimple group spaces, extending previous work and applying to Diophantine approximation on matrices.

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

Mathematik für alle - in Zeiten von Corona, Folge 2: Es gibt unendlich viele Primzahlen

Entdecken Sie die faszinierende Welt der Primzahlen und lernen Sie, warum es unendlich viele davon gibt. Ein spannender Einblick in die Schönheit und Logik der Mathematik für Neugierige jeden Alters.

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

Spectral Gaps of Random Covers of Hyperbolic Surfaces

Explore spectral gaps in random hyperbolic surfaces, including Laplacian resonances and a probabilistic version of Selberg's 3/16 theorem, using transfer operators and zeta functions.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video