The New York Applied Topology Meeting Group is an informal meeting group composed of investigators at all career stages who are interested in topology and its applications in the sciences. Meetings take place roughly every two weeks at Columbia University Medical Center’s Irving Cancer Research Center. The meeting group is open to all.

For more information, or to inquire about speaking at an event, contact Mathieu Carrière at [mc4660 at cumc.columbia.edu].

# Upcoming Meetings

### 2020

**April 23rd (POSTPONED due to coronavirus outbreak)**

Multiple hypothesis testing with persistent homology (**M. Vejdemo-Johansson**)

*Multiple hypothesis testing requires a control procedure. Simply increasing simulations or permutations to meet a Bonferroni-style threshold is prohibitively expensive. **We adapt an False Discovery Rate (FDR) control approach to the topological setting, and show it to be compatible both with our null model approach and with previous approaches to hypothesis testing in persistent homology. **Furthermore, we observe that in order to attain enough structure for a Family-Wise Error Rate (FWER) control method, the testing needs an explicit noise model. Therefore, we propose a null model based approach to testing for acyclicity, coupled with a Family-Wise Error Rate (FWER) control method that does not suffer from these computational costs. **By extending a limit theorem for persistent homology on samples from point processes, we provide theoretical validation for our FWER and FDR control methods.*

**March 13th (POSTPONED due to coronavirus outbreak)**

Learning with Topological Priors and Constraints (**C. Chen**)

*In various contexts, it is challenging to incorporate global topological prior or constraints into an end-to-end training system. In this talk, we explain how topological information, e.g., the number of connected components and handles, can indeed be formulated as a differentiable penalty function through the theory of persistent homology. We show how the topological information can be effectively leveraged in different contexts. In biomedical image analysis, it helps training a topology-aware image segmentation network to segment fine-scale structures such as neurons with correct topology. In machine learning, topological information helps improving the generalization power and robustness of classifiers.*

### 2019

**December 10th, 10:00 AM**

Some topological aspects of time series (**S. Weinberger**)

*So much of our modern technology depends on the analysis of time series, and signal processing/harmonic analysis provide an advanced methodology for dealing with precisely timed numerical series. However, cycles that arise in biology and economics, do not seem to be so well clocked, and the combination of this with noise presents new challenges. I will try to explain some simple topological ideas motivated by these questions, and that are hopefully not completely useless.*

This year, the meeting group will start with a 1-day Symposium on Random Matrix Theory and its Applications. It will happen in Lerner Hall, room 477, Columbia University. Feel free to come and attend the presentations!

**November 1st, 9:30 AM — 5 PM**

**Symposium on Random Matrix Theory and its Applications**.

Speakers: **Andrew Blumberg** (University of Texas), **Luis Aparicio** (Columbia University), **Ivan Corwin** (Columbia University), **Mor Nitzan** (Harvard University), **Ben Landon** (MIT), **Alex Bloemendal** (Broad Institute),** Jeff Pennington** (Google Brain), **John Bloom** (Broad Institute)

Check the following link if you are interested!

# Past Meetings

### 2017

June 9th, 3:00 PM

Diffusion-Based Representations for Revealing Trajectory Structure and Gene Interactions in Noisy Single Cell Data (**K. Moon**)

May 12th, 3:00 PM

Cardiac Trabeculae Segmentation: An Application of Computational Topology (**C. Chen**)

Apr 28th, 3:00 PM

Creolizing the Web – Analyzing models for language acquisition -09876yqaop[(**A. Tamaskar**)

Apr 14th, 3:00 PM

A Higher-Dimensional Homologically Persistent Skeleton (**S. Kalisnik Verovsek**)

Mar 31st, 3:00 PM

Universality of the Homotopy Interleaving Distance: Towards a Persistent Homotopy Theory Foundation for Topological Data Analysis (**M. Lesnick**)

Mar 3rd, 3:00 PM

Persistent Homology of Asymmetric Networks (**F. Memoli**)

Feb 17th, 3:00 PM

Random geometric complexes and maximal persistence (**O****. Bobrowski**)

Feb 3, 3:00 PM

The shape of sparse statistical networks (**B. Cassidy**)

### 2016

Dec 9, 3:00 PM

The Convergence of Mapper (**L. Munch**)

Nov 11, 3:00 PM

Functional topology of brain altered states (**G. Petri**)

Oct 28, 3:00 PM

Concurrence topology: Review and extensions (**S. Ellis**)

Oct 14, 3:00 PM

Topological troubleshooting: using Mapper to find failure modes (**M. Vejdemo-Johansson**)

Sep 30, 3:00 PM

The mathematical study of random knotting (**M. Cohen**)

Sep 16, 3:00 PM

An Approximate Nerve Theorem (**P. Skraba**)

Jun 3, 3:00 PM

Topological analysis of motor cortex (**J. Seely**)

May 13, 3:00 PM

Single-cell, 42-plex cytokine analyses: from immune defense to hematologic malignancy (**R. Fan**)

Apr 29, 3:00 PM

Estimating Thresholding Levels for Random Fields via Euler Characteristics (**A. Monod**)

Apr 15, 3:00 PM

Persistent homology analyses of biological networks (**C. Giusti**)

Apr 4, 2:00 PM

Topological analysis of rat brain data (**N. Baas**)

Mar 18, 3:00 PM

“Concurrence Topology:” A new method for describing high-order statistical dependence in data (**S. Ellis**)

Mar 4, 3:00 PM

A topological measurement of protein compresibility (**V. Nanda**)

Mar 4, 1:00 PM

Genomic analysis and tumor evolution of adult diffuse glioma (**R. Verhaak**)

Feb 19, 3:00 PM

Database of dynamic signatures generated by regulatory networks (**K. Mischaikow**)

Feb 5, 3:00 PM

Applications of persistent homology to genomic data (**K. Emmett**)

Jan 22, 3:00 PM

Measuring intra-host HIV evolution using persistent homology (**D. Rosenbloom**)

### 2015

Dec 16, 3:30 PM

Introduction to Topological Data Analysis, Lecture 8 (**M. Lesnick**)

Dec 4, 3:00 PM

Topology of Instability of Maps, with applications to data analysis (**S. Ellis**)

Dec 2, 3:30 PM

Introduction to Topological Data Analysis, Lecture 7 (**M. Lesnick**)

Nov 20, 3:30 PM

Parametrized Homology and Parametrized Alexander Duality (**S. Kalisnik**)

Nov 20, 3:00 AM

Introduction to Topological Data Analysis, Lecture 6 (**M. Lesnick**)

Nov 11, 3:30 PM

Introduction to Topological Data Analysis, Lecture 5 (**M. Lesnick**)

Nov 9, 3:00 PM

Learning from persistence diagrams (**U. Bauer**)

Nov 6, 3:30 PM

Introduction to Topological Data Analysis, Lecture 4 (**M. Lesnick**)

Oct 30, 3:30 PM

Introduction to Topological Data Analysis, Lecture 3 (**M. Lesnick**)

Oct 23, 3:00 PM

Dynamics of 2D fluid simulations through persistent homology (**R. Levanger**)

Oct 21, 4:00 PM

Introduction to Topological Data Analysis, Lecture 2 (**M. Lesnick**)

Oct 16, 3:00 PM

Introduction to Topological Data Analysis, Lecture 1 (**M. Lesnick**)

Oct 9, 3:00 PM

Topology seminar (**B. Cassidy**)