IMSA Courses

Interpolation for Polynomials in Two Variables

1 rating

Explore advanced polynomial interpolation techniques in two variables, covering dimension counts, Picard groups, and conjectures like Segre's and Nagata's. Delve into cones, extremal rays, and the A-Conjecture.

• YouTube
• 53 minutes
• Self-Paced
• Conference Talk

Low Dimensional Topology and Circle-valued Morse Functions

1 rating

Explore taut foliations in 3-manifolds with Heegaard genus two, examining the connection between left-orderable fundamental groups and co-orientable taut foliations in closed, orientable, irreducible 3-manifolds.

• YouTube
• 1 hour
• Self-Paced
• Conference Talk

The $K(\pi, 1)$ Conjecture - Part 2

1 rating

Explore the recent proof of the classical K(π,1) conjecture for affine Artin groups, delving into its mathematical intricacies and implications for algebraic topology.

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

Coinduction for Comodule Algebras

1 rating

Explore coinduction for comodule algebras, focusing on constructing C_c(G)-comodule algebras from C(H)-comodule algebras for finite H, and its implications for crossed products and group cases.

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

Equivariant Birational Geometry of 3-Dimensional Projective Space

1 rating

Explore G-equivariant birational geometry of 3D projective space, focusing on finite group actions and their impact on fibrations into rational curves or surfaces.

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

Equivariant Birational Geometry of Linear Actions

Explore equivariant birational geometry of linear actions, focusing on Burnside group formalism and its applications in 2D and 3D projective spaces and smooth quadrics.

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

Computation in Unitary Equivariant Bordism

Explore explicit computations of the unitary equivariant bordism ring, presented by Bernardo Uribe on behalf of Dev Sinha. Gain insights into advanced mathematical concepts and recent research findings.

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

On the Second Homotopy Group of Spaces of Commuting Elements in Lie Groups

Explore the computation of the second homotopy group of Hom(Z^n, G) spaces, focusing on compact Lie groups. Learn about geometric generators and specific results for simply connected, simple groups.

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

Cohomology of Hurwitz Spaces

Explore the cohomology of Hurwitz spaces, focusing on branched covers of the affine line and their connections to braided Hopf algebras and a new family of braided operads.

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

Eugenia Ellis, Universidad de la República- Algebraic KK-Theory and the KH-Isomorphism Conjecture

Explore the connection between Davis-Lück homology and equivariant algebraic kk-theory, examining the KH-isomorphism conjecture's assembly map through homotopy theory and adjointness theorems.

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

A More Comprehensible Proof of the Reductive Shafarevich Conjecture

Explore a new, more comprehensible proof of the reductive Shafarevich conjecture in complex geometry, connecting non-abelian Hodge theories and presenting recent work on Shafarevich morphisms construction.

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

Sophie Kriz, University of Michigan - Some Computations on FI-Modules

Explores recent results on FI-modules in positive and mixed characteristic, including local cohomology computations and examples of simple generic FI-modules in positive characteristic.

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

Skein Exact Triangles in Equivariant Singular Instanton Theory

Explore knot signatures and singular instanton homology, focusing on skein exact triangles in equivariant theory. Uncover new insights into link invariants and their categorifications.

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

Low Dimensional Topology and Circle-valued Morse Functions

Explore Khovanov homology of torus braids, characterizing simplified complexes and their applications in quantum topology. Gain insights into recent advancements and conjectures in low-dimensional topology.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Conference Talk

Low Dimensional Topology and Circle-Valued Morse Functions

Explore the Kakimizu complex for genus one hyperbolic knots, examining its structure, dimensions, and examples across various dimensions in 3-sphere topology.

• YouTube
• 54 minutes
• Self-Paced
• Conference Talk