IMSA Courses

Moduli Spaces for Rational Elliptic Surfaces - of Index 1 and 2

Explore rational elliptic surfaces, their construction from pencils of curves, and recent developments in moduli space construction for surfaces with multiple fibers.

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

The Average Genus of a 2-Bridge Knot Grows Linearly with Respect to Crossing Number

Explore the linear growth relationship between Seifert genus and crossing number in 2-bridge knots using Chebyshev billiard table diagrams, building on previous research and experimental data.

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

Virtual Reductions and Intersection Theory on Moduli Space of Sheaves on Calabi-Yau 4 Folds

Explore virtual reductions of fundamental classes on moduli spaces of sheaves in Calabi-Yau 4-folds, examining applications to Donaldson-Thomas invariants and connections to threefold theories.

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

Braids and Line Arrangements - Old and New

Explore the interplay between braid groups, configuration spaces, and hyperplane arrangements, focusing on recent advances in understanding fundamental groups of complex line arrangement complements.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Braidings and Braid Equivalences

Explore braiding algorithms and braid equivalences for various knot types, including classical, virtual, and singular, with a focus on knotoids and braidoids.

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

Degeneration of Cubic Threefolds with Nodes

Explore the degeneration of cubic threefolds with nodes, focusing on intermediate Jacobians, Fano varieties, and Prym varieties. Gain insights into irrationality proofs and limiting behaviors.

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

Braids and Machine Learning

Explore the fascinating intersection of braids and machine learning, uncovering innovative applications and insights in mathematics and data science.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Braids and Line Arrangements

Explore the fascinating connection between braids and line arrangements in mathematics, with insights from expert Moshe Cohen in this engaging lecture.

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

Algebraic Definition of Braids and the Braid Group

Explore the algebraic foundations of braids and the braid group, delving into their mathematical properties and applications in topology and geometry.

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

Dancing with Braids

Explore the mathematical concept of braids through dance and movement, blending art and science in this innovative presentation by Nancy Scherich from ICERM.

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

Braids and Art

Explore the fascinating intersection of mathematics and art through the lens of braids, uncovering their significance in both fields and their role in advancing women in mathematics.

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

Multispectra

Explore new birational invariants in algebraic geometry with Professor Ludmil Katzarkov, delving into advanced mathematical concepts and their applications.

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

On the Rouquier Dimension of Wrapped Fukaya Categories

Explores Rouquier dimension of wrapped Fukaya categories, linking symplectic topology to algebraic geometry through homological mirror symmetry. Discusses applications to Lagrangian intersections and Lefschetz fibrations.

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

Homological Mirror Symmetry for Hypersurface Singularities II

Explores graded matrix factorizations of invertible polynomials and stability conditions in homological mirror symmetry for singularities, continuing from a previous lecture.

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

Homological Mirror Symmetry for Hypersurface Singularities

Explore homological mirror symmetry for hypersurface singularities, covering basic definitions, Berglund-Hubsch duality, known results, and detailed examples in this advanced mathematics lecture.

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