Abstract: The Kaczmarz algorithm is a method for solving linear systems of equations that was introduced in 1937. The algorithm is a powerful tool with many applications in signal processing and data science that has enjoyed a resurgence of interest in recent years. We'll discuss some of the history of the Kaczmarz algorithm as well as describ...
Creator:
Weber, Eric (Iowa State University)
Created:
2022-04-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
If A is a finite-dimensional algebra with automorphism group G, then varieties of generating r-tuples of elements in A, considered up to G-action, produce a sequence of varieties B(r) approximating the classifying space BG. I will explain how this construction generalizes certain well-known examples such as Grassmannians and configuration spaces...
Creator:
Williams, Ben (University of British Columbia)
Created:
2022-08-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The Milnor–Moore theorem identifies a large class of Hopf algebras as enveloping algebras of the Lie algebras of their primitives. If we broaden our definition of a Hopf algebra to that of a braided Hopf algebra, much of this structure theory falls apart. The most obvious reason is that the primitives in a braided Hopf algebra no longer form a L...
Creator:
Westerland, Craig (University of Minnesota, Twin Cities)
Created:
2022-08-01
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Topological Azumaya algebras are topological shadows of more complicated algebraic Azumaya algebras defined over, for example, schemes. Tensor product is a well-defined operation on topological Azumaya algebras. Hence given a topological Azumaya algebra $\mathcal{A}$ of degree $mn$, where $m$ and $n$ are positive integers, it is a natural questi...
Creator:
Arcila-Maya, Niny (Duke University)
Created:
2022-08-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In order to incorporate ideas from algebraic topology in concrete contexts such as topological data analysis and topological lattice field theories, one needs effective constructions of concepts defined only abstractly or axiomatically. In this talk, I will discuss such constructions for certain invariants derived from the cup product on the coh...
Creator:
Medina-Mardones, Anibal (Max Planck Institute for Mathematics)
Created:
2022-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I will talk about equivariant homotopy theory and its role in the proof of the Segal conjecture and the Kervaire invariant one problem. Then, I will talk about chromatic homotopy theory and its role in studying the stable homotopy groups of spheres. These newly established techniques allow one to use equivariant machinery to attack chromatic com...
Creator:
Shi, XiaoLin (Danny) (University of Chicago)
Created:
2022-08-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I will share some reminiscences of my many years working with Gunnar. The career that I have had would not have been possible without his kindness, wisdom, and generosity.
Creator:
de Silva, Vin (Pomona College)
Created:
2022-08-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The Gromov-Hausdorff distance between two metric spaces is an important tool in geometry, but it is difficult to compute. For example, the Gromov-Hausdorff distance between unit spheres of different dimensions is unknown in nearly all cases. I will introduce recent work by Lim, Mémoli, and Smith that finds the exact Gromov-Hausdorff distances be...
Creator:
Adams, Henry (Colorado State University)
Created:
2022-08-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Configuration spaces of disks in a region of the plane vary according to the radius of the disks, and their topological invariants such as homology also vary. Realizing a given homology class means coordinating the motion of several disks, and if there is not enough space for the disks to move, the homology class vanishes. We explore how cluster...
Creator:
Alpert, Hannah (Auburn University)
Created:
2022-08-01
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.