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Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips Complexes
Description:
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.
Last Updated:
2022-09-06
Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips Complexes
Lecture (Remotely)
Creator:
Kalisnik, Sara (ETH Zürich)
Created:
2022-08-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-09-06
Lecture (Remotely)
Decomposition of topological Azumaya algebras in the stable range
Description:
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.
Last Updated:
2022-09-06
Decomposition of topological Azumaya algebras in the stable range
Path induction and the indiscernibility of identicals
Description:
Mathematics students learn a powerful technique for proving theorems about an arbitrary natural number: the principle of mathematical induction. This talk introduces a closely related proof technique called "path induction," which can be thought of as an expression of Leibniz's "indiscernibility of identicals": if x and y are identified, then th...
Creator:
Riehl, Emily (Johns Hopkins University)
Created:
2022-08-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-09-06
Path induction and the indiscernibility of identicals
Persistent homology and its fibre (Remotely)
Description:
Persistent homology is a main tool in topological data analysis. So it is natural to ask how strong this quantifier is and how much information is lost. There are many ways to ask this question. Here we will concentrate on the case of level set filtrations on simplicial sets. Already the example of a triangle yields a rich structure with the Möb...
Creator:
Tillmann, Ulrike (University of Oxford)
Created:
2022-08-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-09-06
Persistent homology and its fibre (Remotely)
Ramification in Higher Algebra
Description:
I will review the theory of ramification in number theory and then show that being totally ramified or unramified is equivalent to a natural condition in higher algebra. This leads to a much simplified calculation of THH of a ring of integers in a number field, relying on ramified descent (a kind of weaker etale descent).
Creator:
Berman, John (University of Massachusetts)
Created:
2022-08-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-09-06
Ramification in Higher Algebra
Toward conjectures of Rognes and Church--Farb--Putman (Lecture Remotely)
Description:
In this talk I will give an overview of two related projects. The first project concerns the high-degree rational cohomology of the special linear group of a number ring R. Church--Farb--Putman conjectured that, when R is the integers, these cohomology groups vanish in a range close to the virtual cohomological dimension. The groups SL_n(R) sati...
Creator:
Wilson, Jenny (University of Michigan)
Created:
2022-08-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-09-06
Toward conjectures of Rognes and Church--Farb--Putman (Lecture Remotely)
Effective constructions in algebraic topology and topological data analysis
Description:
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.
Last Updated:
2022-09-06
Effective constructions in algebraic topology and topological data analysis
Motivic Euler characteristics and the Motivic Segal-Becker theorem (Remotely)
Description:
A well-known and very useful result in algebraic topology is the statement that the Euler characteristic of G/N(T) in singular cohomology is 1, where G is a compact Lie group and N(T) is the normalizer of a maximal torus. In the presence of a transfer map as constructed by Becker and Gottlieb the above result shows that in any generalized cohomo...
Creator:
Joshua, Roy (The Ohio State University)
Created:
2022-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-09-06
Motivic Euler characteristics and the Motivic Segal-Becker theorem (Remotely)
Persistent cup-length
Description:
Cohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by softwares, such as Ripser. The cup product operation which is available at cohomology level gives rise to a graded ring structure that extends the usual vector space structure and is ...
Creator:
Zhou, Ling (The Ohio State University)
Created:
2022-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-09-06
Persistent cup-length
Tracking Topological Features Across Neural Stimulus Spaces
Creator:
Giusti, Chad (University of Delaware)
Created:
2022-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-09-06
Tracking Topological Features Across Neural Stimulus Spaces
Witness complexes and Lagrangian duality
Description:
I'll discuss a method for approximating the super-level set persistent homology of a Gaussian kernel density estimator for a point cloud data set, which is related to the witness complex. Instead of selecting elements of the data set, the witnesses are generated using quadratic programming, and the shifted Voronoi diagram (aka the power diagram)...
Creator:
Carlsson, Erik (University of California, Davis)
Created:
2022-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-09-06
Witness complexes and Lagrangian duality
Braids and Hopf algebras
Description:
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.
Last Updated:
2022-09-06
Braids and Hopf algebras
Homology crowding in configuration spaces of disks
Description:
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.
Last Updated:
2022-09-06
Homology crowding in configuration spaces of disks
Limits of Dense Simplicial Complexes
Description:
We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued functions on unit cubes of increasing dimension, each corresponding to a dimension of the abstract simplici...
Creator:
Segarra, Santiago (Rice University)
Created:
2022-08-01
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-09-06
Limits of Dense Simplicial Complexes
Topological explorations of neuron morphology
Description:
To understand the function of neurons, as well as other types of cells in the brain, it is essential to analyze their shape. Perhaps unsurprisingly, topology provides us with tools ideally suited to performing such an analysis. In this talk I will present a selection of the results of a long-standing collaboration with Lida Kanari of the Blue Br...
Creator:
Kathryn Hess-Bellwald, Kathryn (École Polytechnique Fédérale de Lausanne (EPFL))
Created:
2022-08-01
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-09-06
Topological explorations of neuron morphology
Great Spangled Fritillary
Description:
F1: dorsal view of one old faded adult butterfly with wings spread out; F2: a life sized individual on an Echinacea flower
Creator:
McFarland, Terry
Created:
2022-06-25
Contributed By:
University of Minnesota Libraries, Andersen Horticultural Library.
Last Updated:
2022-08-15
Great Spangled Fritillary
Luu Nhat Tam Ngyuen
Description:
Luu Nhat Tam Ngyuen moved to the U.S. with her mom and dad in 2019. Unfortunately, her sister was not able to join them because of her age. Luu Nhat Tam is the only person who can speak English in her family.
Creator:
Nguyen, Luu Nhat Tam
Contributor:
Rolland, Isabella
Created:
2022-05-09
Contributed By:
University of Minnesota, Immigration History Research Center
Last Updated:
2022-05-11
Luu Nhat Tam Ngyuen
Lillian Gamm
Description:
Lillian Gamm arrived at Ellis Island from Russia on April 19, 1910. While living in Manhattan, she worked hard as a bookkeeper, raised a family, and pursued her dreams.
Creator:
Feldman, Jonah
Contributor:
Rolland, Isabella
Created:
2022-05-02
Contributed By:
University of Minnesota, Immigration History Research Center
Last Updated:
2022-05-11
Lillian Gamm
Sarah Reyes
Description:
Sarah Reyes was born in the Phlippines and moved to the U.S. when she was in middle school. Though she faced a lot of racial discrimination in her first years of being here, she eventually found a Filipino American community that she is proud to be a part of now.
Creator:
Haakonsen, Malia
Contributor:
Rolland, Isabella
Created:
2022-05-02
Contributed By:
University of Minnesota, Immigration History Research Center
Last Updated:
2022-05-11
Sarah Reyes