Hausdorff Center for Mathematics Courses

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

Don Zagier: Holomorphic Quantum Modular Forms

Explore holomorphic quantum modular forms, their connections to number theory and quantum knot invariants, and applications in odd weight Eisenstein series and Maass cusp forms.

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

Thermodynamical Formalism and Markoff-Hurwitz Equations

Explore connections between Diophantine geometry and fractals through Markoff-Hurwitz equations, transfer operators, and thermodynamical formalism. Discover links to various mathematical areas.

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

Horocycle Flow on Moduli Spaces of Translation Surfaces

Explore the intricate dynamics of horocycle flow on moduli spaces of translation surfaces in this advanced mathematics lecture by Jon Chaika.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

The Transfer Operator Method

Explore the Transfer Operator Method in dynamical systems, focusing on its applications in topology and number theory within the context of advanced mathematical research.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Stochastic Quantization of Exponential Quantum Field Theory

Explores stochastic quantization of 2D scalar fields with exponential interaction, focusing on elliptic and parabolic Euclidean approaches and related random PDEs with multiplicative noise.

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