Stony Brook Mathematics Courses

Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds

Explore the interaction between hyperbolic geometry and homology cobordism in low-dimensional topology using monopole Floer homology to study subgroups of the homology cobordism group.

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

Supersymmetry and Trace Formulas: From Atiyah-Singer to Jacobi-Poisson and Selberg

Explore supersymmetry's mathematical origins and applications, from Atiyah-Singer formula to Jacobi-Poisson and Selberg trace formulas, in this advanced mathematics colloquium.

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

Supersymmetry and Trace Formulas: From Atiyah-Singer to Jacobi-Poisson and Selberg - Part 1

Explore supersymmetry's mathematical origins and applications, from Atiyah-Singer formula to Jacobi-Poisson and Selberg trace formulas, in this advanced mathematics colloquium.

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

The High-Degree Rational Cohomology of the Special Linear Group

Explore high-degree rational cohomology of SL_n(Z) and SL_n(R) for number rings. Examine Steinberg modules and associated simplicial complexes to understand special linear group cohomology.

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

Positivity, Representations, and Non-Commutative Hyperbolic Geometry

Explore total positivity in matrices, its generalization to split real Lie groups, and a new notion of positivity in flag varieties with applications to higher Teichmüller spaces.

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

Local-Global Principles for Homogeneous Spaces Over Arithmetic Function Fields

Explore local-global principles for homogeneous spaces over arithmetic function fields, focusing on function fields of curves over complete discretely valued fields and related patching methods.

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

Mirror Structure Constants via Non-Archimedean Analytic Disks

Explore mirror structure constants for smooth affine log Calabi-Yau varieties using non-archimedean analytic disks, generalizing previous constructions and discussing positivity, integrality, and potential extensions.

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

Nonabelian Mixed Hodge Structures

Explore nonabelian mixed Hodge structures, their relation to rational homotopy, and applications to character varieties and schematic homotopy types. Examine weights from noncompact bases and parabolic structures.

• YouTube
• 1 hour 38 minutes
• Self-Paced
• Free Video

Quantitative Ell-Adic Sheaf Theory

Explore quantitative bounds for étale cohomology groups and their applications in algebraic geometry. Learn about complexity measures for sheaves and how they interact with various functors.

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

Counting Curves in Calabi-Yau Threefolds

Explore enumerative invariants and a universal approach to counting curves in Calabi-Yau threefolds. Discover how cluster formalism aids computations and potentially simplifies conjectural identities between invariants.

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

Computing the Weil Representation of Superelliptic Curves

Explore the Weil representation of superelliptic curves, focusing on local Galois representations and stable reductions in algebraic geometry.

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

Non-free Curves and Geometric Manin's Conjecture - Lecture

Explore non-free curves on varieties, their classification, and implications for Geometric Manin's Conjecture in Fano fibrations. Gain insights into algebraic geometry and number theory.

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

A Finiteness Theorem for Gromov-Hyperbolic Groups

Explore a finiteness theorem for Gromov-hyperbolic groups, delving into δ-hyperbolic, torsion-free, non-cyclic marked groups with bounded entropy. Gain insights into the proof and key concepts.

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

Non-Archimedean Pluripotential Theory and K-stability - Lecture 3

Explore non-Archimedean pluripotential theory and K-stability in this advanced mathematics lecture, part of a series connecting complex and non-Archimedean geometry.

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

Combinatorial Approximations to the Continuum for Fluid Computation

Explore combinatorial approximations in fluid computation, featuring insights from Dennis Sullivan and Ruth Lawrence-Naimark in this geometry and analysis workshop.

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