# Working Groups

### Topological Data Analysis Seminar

**Thursday, Mar 21, 2019, MC 105B, 3:30-4:30** - Michael Lesnick (SUNY/Albany), Computational aspects of 2-parameter persistent homology.

**Abstract:** In topological data analysis, one associates to the data a filtered topological space, whose structure we then examine using persistent homology. However, in many settings, a single filtered space is not a rich enough invariant to encode the interesting structure of the data. This motivates the study of multi-parameter persistence, which associates to the data a topological space simultaneously equipped with two or more filtrations. The homological invariants of these “multi-filtered spaces,” called persistence modules, are much richer than their 1-D counterparts, but also far more complicated. As such, adapting the usual 1-parameter persistent homology methodology for data analysis to the multi-parameter setting requires new ideas. For the past few years, I have been working with several collaborators on RIVET, a practical software tool for the visualization and analysis of 2-parameter persistent homology. One key new feature of RIVET is a fast algorithm for computing minimal presentations in the 2-parameter persistence setting; this is joint work with Matthew Wright. Perhaps surprisingly, the computational cost of the algorithm turns out to be similar to that of the standard algorithm for computing 1-parameter persistent homology. In this talk, I’ll introduce 2-parameter persistent homology, RIVET, and (time permitting) our algorithm for computing minimal presentations.

### Data Security Seminar

**Thursday, Mar 22, 2018** - Aleksander Essex (Electrical & Computer Engineering), Computing threshold functions under encryption

CBC news article about Aleks' work: http://www.cbc.ca/news/canada/london/london-ontario-online-voting-1.4598787

**Thursday, Apr 5, 2018** - Chris Hall (Mathematics), An Overview of Blockchains

Spatio-Temporal Statistics Reading Group

** Spring 2018 Schedule**

#### 2/1/2018

Zhou Lan: Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing

Gelfand, Alan E., Athanasios Kottas, and Steven N. MacEachern. "Bayesian nonparametric spatial modeling with Dirichlet process mixing." Journal of the American Statistical Association 100.471 (2005): 1021-1035.

#### 3/1/2018

Yawen Guan: A Multiresolution Gaussian Process Model

Nychka, Douglas, et al. "A multiresolution Gaussian process model for the analysis of large spatial datasets." Journal of Computational and Graphical Statistics 24.2 (2015): 579-599.

#### 3/15/2018

Arnab Hazra: Nonparametric Bayesian models for a spatial covariance

Reich, Brian J., and Montserrat Fuentes. "Nonparametric Bayesian models for a spatial covariance." Statistical methodology 9.1 (2012): 265-274.

#### 4/5/2018

Indranil Sahoo: Characterizing spatial processes on Spheres

Hitczenko, Marcin, and Michael L. Stein. "Some theory for anisotropic processes on the sphere." Statistical Methodology 9.1 (2012): 211-227.

#### 4/12/2018

Whitney Huang: Spatial Point Process

Gelfand, Alan E., et al., eds. Handbook of spatial statistics. CRC press, 2010.

** Fall 2017 Schedule**

#### 9/7/2017

Whitney Huang: Introduction to Spatial Statistics

Charpters 2-4 Handbook of Spatial Statistics

#### 9/21/2017

Maggie Johnson: Hierarchical Modeling with Spatial Data

Charpters 7 Handbook of Spatial Statistics

#### 10/19/2017

Yuan Tian: Introduction to Extreme Value Analysis

Charpters 3-4 An introduction to statistical modeling of extreme values

#### 11/2/2017

Zhou Lan: Low-Rank Representations for Spatial Processes

Charpters 8 Handbook of Spatial Statistics

#### 11/16/2017

Alexandra Larsen: Continuous Parameter Spatio-Temporal Processes

Charpters 23 Handbook of Spatial Statistics

### Cryptography Research Group

Please visit the Westen Cryptography Research Group website for more information: https://sites.google.com/view/westerncrypto

### Homotopy Type Theory Electonic Seminar Talks

Please visit the Homotopy Type Theory Electonic Seminar Talks website for more information: https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html