This seminar at Colorado State University is for those interested in topology and its applications, broadly interpreted.
Fall 2024, co-organized by Alex Elchesen and Amit Patel. Tuesdays at 4pm in Weber 201
August 27, organizational meeting
Spring 2024, co-organized by Alex Elchesen and Amit Patel. Tuesdays at 4pm in Weber 201
January 30, Alex Elchesen, Summary of the paper "Spectra of Combinatorial Laplace Operators on Simplicial Complexes".
February 6, Tatum Rask, Spectra of Combinatorial Laplace Operators on Simplicial Complexes, Part 2.
February 13, Joe Geisz, Toward a Spectral Theory of Cellular Sheaves.
February 20, Michael Kardos, Cheeger’s Inequality and the Graph Laplacian.
February 27, Michael Kardos, Cheeger’s Inequality and the Graph Laplacian, Part 2.
March 26, Amit Patel, Persistent Homology and the Hodge-Laplacian.
April 23, Jacob Cleveland, The Morse Inequlaities via Laplacians on CW Complexes!
April 30, Jae Hwang Lee, Quantum Cohomology and Quantum Module.
Fall 2023, co-organized by Alex Elchesen and Amit Patel. Tuesdays at 4pm in Weber 201
Auguest 29, organizational meeting
September 5, Alex Elchesen, Circular Chromatic Numbers of Borsuk Graphs and Anti-Vietoris-Rips Complexes.
September 12, Tatum Rask, An Introduction to Poset Topology.
October 3, Mason Faldet, An Anecdote of Lie Groups Being Useful.
October 10, Jacob Cleveland, Persistence of a Self Map .
October 17, Michael Moy, Sheaf Laplacians, Heat Equations, and Cohomology.
October 24, Joe Geisz, Topological Fractal Dimensions: Discreetness, Connectedness, and Beyond.
October 31, Amit Patel, Mobius Homology and Multiparameter Persistence Diagrams.
November 7, Ignacio Rojas Rojas, Summer Exploration on Boolean Algebras, Spaces and Stone Duality.
November 14, Kristina Moen, Everything Everywhere All at Once: Universal Properties, Kan Extensions, and Adjoints.
November 28, Page Wilson, Homology as a Tool for Graph Embeddings.
December 5, Aziz Guelen, Orthogonal Möbius Inversion and Grassmannian Persistence Diagrams
Spring 2023, co-organized by Henry Adams and Alex Elchesen. Tuesdays at 4pm in Weber 201.
January 24, organizational meeting
January 31, Alex Elchesen, A Categorical Framework for Persistence Diagrams and the Wasserstein Distances. Dinner at Nick's
February 7, Michael Moy, Michael's perspective on persistence modules. Dinner at Post
February 14, Nate Mankovich, Chordal Distance Averaging on Flag Manifolds and its Applications. Dinner at Thai Station
February 21, Adam Jaffe, Statistical Estimation of Fréchet Mean Sets. Dinner at The Colorado Room.
February 28, Henry Adams, Vietoris-Rips metric thickenings. Dinner at Back Door Grill
March 7, Tatum Rask, Toroidal Coordinates: Decorrelating Circular Coordinates with Lattice Reduction. Dinner at Thai Pepper
March 21, Jacob Cleveland, Morse Information. Dinner at Los Tarascos
March 30 (Thursday), Cigole Thomas, Data learning using varieties. Dinner at Izakaya Jooa
April 11, Daniel Vargas-Rosario, Gromov-Hausdorff Distances Between n-Dimensional Spheres and (n + 1)-Dimensional Hypercubes
April 18, Bei Wang, Topology of Artificial Neuron Activations in Deep Learning: From Images to Word Embeddings
April 25, a double header! Dinner at Los Tarascos
James Meiss, Weighted Birkhoff Averages as a test for Chaos
May 2, Yariana Diaz, A framework to support the study of tame- and wild-type quivers in persistence theory
May 9, Alex McCleary, Interleavings and Optimal Transport. Dinner at Thai Pepper
Fall 2022, co-organized by Henry Adams and Alex Elchesen
August 23, organizational meeting
August 30, Henry Adams, Zigzag persistence and vineyards. Dinner at Avogadro's Number
September 6, Lander Ver Hoef, Persistent Homology to Support Image Analysis Tasks in Environmental Science. Dinner at The Colorado Room
September 13, Alex Smith, Data analysis via Topology and Geometry with Applications in Chemical Engineering. Dinner at Thai Pepper
September 20, Page Wilson, Knots and Permutations. Dinner at The Mayor of Old Town
September 27, Alex Elchesen, Optimal Transport and Persistence. Dinner at Back Door Grill
October 4, Michael Moy, The fundamental group, covering spaces, Galois connections, and duality. Dinner at DGT
October 10 (Monday at 12pm), Facundo Mémoli, Gromov-like distances between spheres
October 11, Kristina Moen, The Shape of Biological Data: Three Applications of Topological Data Analysis. Dinner at Thai Pepper
October 18, Tatum Rask, Möbius Inversion & Persistence. Dinner at Back Door Grill
Friday October 21, Jose Perea, Learning functions on the space of persistence diagrams. Dinner at Los Tarascos
October 25, Daniel Vargas-Rosario, Persistent Homology of Hypercubes. Dinner at Panda Express
November 1, Jacob Cleveland, An Invitation to Morse Theory. Dinner at Thai Pepper
November 8, Mason Faldet, A Preview of Smooth Manifolds with an Aim Towards de Rham Cohomology. Dinner at Post
November 15, Michael Catanzaro, Using persistence to study task modulation in fMRI
November 29, Sabari Kumar, Applications of Topological Data Analysis in Computational Chemistry. Dinner at Los Tarascos
December 6, Chris Peterson, Random Topology in Manifold Menageries
Spring 2022, Fall 2021, Spring 2021, Fall 2020: Please see www.aatrn.net for an online topology seminar co-hosted by CSU, meeting on Zoom. Please email Henry for more details.
Spring 2020, co-organized by Henry Adams and Amit Patel
January 28, organizational meeting
February 11, Alex Williams, Computing persistent homology
Wednesday February 12, Shmuel Weinberger. This is part of the AATRN Online Seminar.
February 18, Henry Adams, Persistent homology, zigzag persistence, and quiver representations
February 25, Michael DiPasquale, Multiparameter persistence
March 3, Hailun Zheng, Face numbers of centrally symmetric simplicial polytopes and spheres
March 10, Joshua Mirth, A statistical perspective on persistence
The remaining topology seminar meetings were cancelled due to COVID-19.
March 24, Chris Peterson, Stochastic topology
March 31, Eric Kehoe, The complex of pseudoultrametrics and iterated cycle structures
April 7, Brittany Carr, Radon's theorem and Tverberg's conjecture
April 14, Johnathan Bush, The topological Tverberg conjecture
April 21, Henry Adams at Topology Day in Boulder
Friday May 8, Hannah Alpert, Configuration spaces of hard objects
Fall 2019, co-organized by Henry Adams and Amit Patel
September 3, organizational meeting
September 10, Henry Adams, An introduction to matroids [Notes]
September 17, Alex McCleary, An introduction to matroids and greedoids [Björner Section 6]
September 24, Michael DiPasquale, Oriented matroids [Björner Section 7] and/or [appendix of MacPherson]
October 1, Amit Patel, Matroid bundles [Anderson]
October 8, Woojin Kim, Generalized persistence diagrams for persistence modules over posets
October 15, Amit Patel, Matroid bundles and the MacPhersonian [MacPherson]
October 22, Harrison Chapman, Knots, biology, (and data)
October 29, Mark Blumstein, Symmetries in data
November 5, Molly Moran, An introduction to geometric group theory
November 12, Markus Pflaum, Relative K-theory
November 19, Chris Peterson, A piece of Hilbert's 16th problem
December 10, Bryan Gillespie, Convexity in ordered matroids and the generalized external order
Spring 2019, co-organized by Henry Adams and Amit Patel
January 29, organizational meeting. Topics we discussed that were not claimed below included group representations in data analysis, Persistent cohomology and circular coordinates, and magnitude homology for metric spaces, and Finding optimal discrete Morse functions is NP-hard.
Feb 5, Michael DiPasquale, Steinitz' theorem and some relatives
Feb 26, Amit Patel is giving two lectures at the Boulder Topology Seminar
March 5, Jānis Lazovskis, Stratifications and sheaves for persistent homology
March 12, Érika Roldán Roa, Asymptotic behavior of the homology of random polyominoes
March 26, Henry Adams, The waist inequality [Notes/Slides, Reference by Larry Guth]
April 2, Amit Patel, Intersection homology & duality for pseudomanifolds I
April 9, Amit Patel, Intersection homology & duality for pseudomanifolds II
April 16, Topology day in Boulder, with talks by Satyan Devadoss and Ezra Getzler
April 23, Harrison Chapman, The Grunbaum-Hadwinger-Ramos Hyperplane Mass Partition Problem
April 30, John Bush, Metric thickenings, orbitopes, and Borsuk-Ulam theorems
Fall 2018, co-organized by Henry Adams and Amit Patel
August 21, organizational meeting
August 28, Bernd Sturmfels, Learning algebraic varieties from samples (AATRN seminar, at an unusual time 11:00am, in Morgan 172)
September 4, Joshua Mirth, Morse theory
September 11, Joshua Mirth, Discrete Morse theory
September 18, Grzegorz Muszynski, Towards topological pattern detection methods in spatiotemporal data
September 25, Amit Patel, Multidimensional persistence
October 2, Chris Peterson, Multiparameter persistence
October 9, Alex McCleary, Magnitude homology
October 16, Tanner Strunk, Applied vector bundles
October 23, Agnès Beaudry, The Linearization Conjecture
October 30, Mark Blumstein, Introduction to Lie groups and principal bundles
November 6, Mark Blumstein, Principal bundles and Chern-Weil theory
November 13, Henry Adams, Lovasz' proof of the Kneser conjecture
December 4, Ezra Miller (AATRN seminar, at an unusual time 11:00am, in Morgan 172)
Spring 2018, co-organized by Henry Adams and Amit Patel
January 30, Mark Blumstein, An introduction to equivariant cohomology I
February 6, Mark Blumstein, An introduction to equivariant cohomology II
February 20, Topology Day at CU Boulder
February 27, Tom Needham, Injectivity properties of distance distributions
March 6, Amit Patel, Applications of merge trees and Reeb graphs
March 20, Amit Patel, Homology with twisted coefficients
March 27, Greg Henselman, Combinatorics and Computation in Topological Data Analysis
April 10, Chad Topaz, Topological data analysis of collective motion
April 17, Amit Patel, Cosheaf homology
April 24, Henry Adams, An introduction to homotopy colimits [Notes]
May 1, Henry Adams, Using homotopy colimits to understand infinite simplicial complexes
Fall 2017, co-organized by Henry Adams and Amit Patel
September 5, Amit Patel, The theory of persistence I
September 12, Amit Patel, The theory of persistence II
September 19, Amit Patel, The theory of persistence III
September 26, Henry Adams, An introduction to Vietoris-Rips and Cech complexes I
October 3, Joshua Mirth, Metric thickenings of Euclidean submanifolds
October 10, Henry Adams, Vietoris-Rips complexes of the circle
October 31, Amit Patel, Tubular neighborhoods for Whitney stratified spaces
November 7, Henry Kvinge, An introduction to Khovanov homology I
November 14, Henry Kvinge, An introduction to Khovanov homology II
November 28, Dustin Sauriol, Leray spectral sequences I
December 5, Dustin Sauriol, Leray spectral sequences II