CSU Topology Seminar

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

  • Yulia Gel, Coupling Time-Aware Multipersistence Knowledge Representation with Graph Convolutional Networks for Time Series Forecasting

  • 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