Collapses and Z-Compactifications of CAT(0) Cube Complexes Mr. Daniel Gulbrandsen University of Wisconsin-Milwaukee Dissertator We extend the notion of collapsibility to non-compact cube complexes and prove collapsibility of locally-finite CAT(0) cube complexes. Namely, we construct such a cube complex X... Read More

Random quotients of hyperbolic groups and Property (T) Mr. Prayagdeep Parija University of Wisconsin-Milwaukee Dissertator How does a random quotient of a group look like? Gromov looked at the density model of quotients of free groups. The density parameter d... Read More

Combinatorial Problems Related to Optimal Transport and Parking Functions Mr. Jan Kretschmann University of Wisconsin-Milwaukee Dissertator In the first part, we show contributions to optimal transport through work on the discrete Earth Mover's Distance (EMD). We provide a new formula... Read More

Coarse Homotopy Extension Property and its Applications Mr. William Braubach University of Wisconsin-Milwaukee A pair (X, A) has the homotopy extension property if any homotopy of A can be extended to a homotopy of X. The main goal of this... Read More

Markov Chain Model of Three-Dimensional Daphnia Magna Movement Ms. Helen Kafka University of Wisconsin-Milwaukee Daphnia magna make turns through an antennae-whipping action. This action occurs every few seconds, hence, during the intervening time, the animal either remains in place or... Read More

Bayesian Change Point Detection In Segmented Multi-Group Autoregressive Moving-Average Data For The Study Of COVID-19 In Wisconsin Mr. Russell Latterman University of Wisconsin-Milwaukee Changepoint detection involves the discovery of abrupt fluctuations in population dynamics over time. We take a Bayesian... Read More

Utilizing ARMA Models for Non-Independent Replications of Point Processes Mr. Lucas Fellmeth University of Wisconsin-Milwaukee The use of a functional principal component analysis (FPCA) approach for estimating intensity functions from prior work allows us to obtain component scores of replicated... Read More

Adding a Third Normal to CLUBB Mr. Sven Bergmann University of Wisconsin-Milwaukee The Cloud Layers Unified By Binormals (CLUBB) model uses the sum of two normal probability density function (pdf) components to represent subgrid variability within a single grid layer... Read More

Contraction Rates For McKean-Vlassov Stochastic Differential Equations Mr. Dan Noelck University of Wisconsin-Milwaukee This work focuses on the contraction rates for McKean-Vlasov stochastic differential equations (SDEs), McKean-Vlasov Stochastic differential delay equations (SDDEs), and path dependent McKean-Vlasov stochastic differential equations. Under... Read More

A Finite Element Block Modified Backward Euler Method For Solving A One-Dimensional Poisson-Nernst-Planck Ion Channel Model Mr. Silas Winnemoeller University of Wisconsin-Milwaukee In this thesis, a finite element block modified backward Euler method is introduced to solve a one-dimensional Poisson-Nernst-Planck... Read More