## Events

### Department of Mathematics and Statistics

### Texas Tech University

We will introduce a pre-Schwarzian and a Schwarzian derivative for locally univalent pluriharmonic mappings in ${\mathbb C}^n$ and prove some basic theorems for these operators. For example, we will characterize the case when the pre-Schwarzian derivative is holomorphic and, also, show that the pre-Schwarzian is stable only with respect to rotations of the identity, among other theorems.

Along the way we will make some observations related to the dilatation of pluriharmonic mappings and to the dilatation of their affine transformations. These will reveal some differences between the theories in the plane and in higher dimensions.

Let $R$ be a commutative local ring to which we associate the subcategory $\mathbf{K_{tac}}(R)$ of the homotopy category of $R$-complexes, consisting of the totally acyclic complexes. When $R$ is a hypersurface ring of finite CM type we can show that this category has only finitely many non-isomorphic, indecomposable objects. We will use these objects and the idea of approximation, to classify totally acyclic complexes over certain complete intersection rings using the defined notion of Arnold-tuples.

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https://zoom.us/j/95294234500?pwd=dDVrS1pPNi9OR3pJNnZZRDkvWTZZUT09

Meeting ID: 952 9423 4500

Passcode: 677809

Prostate cancer is a common cancer among males in the United States and is frequently treated by intermittent androgen deprivation therapy. This therapy requires a patient to alternate between periods of androgen suppression treatment and no treatment. Prostate-specific antigen levels are used to track relative changes in tumor volume of prostate cancer patients undergoing intermittent androgen deprivation therapy. During this therapy, there is a pause between treatment cycles. We use dynamic equations to estimate prostate-specific antigen levels and construct a novel time scale model to account for both continuous and discrete time simultaneously. This allows us to account for breaks between treatment cycles. Using empirical data sets of prostate-specific antigen levels, a known biomarker of prostate cancer, across multiple patients, we fit our model and use least squares to estimate two parameter values. We compare our model to the data and find a resemblance on treatment intervals similar to our time scale. We then use several different time scales to construct variations of our novel model.

This seminar is held in conjuction with the **Applied Math** seminar group.

In order to facilitate the notion of local diffeomorphisms in a cohesive infinity topos, one need an additional structure called “elastic subtopos”, where all the cohesion modalities factor thorough this sub-infinity-topos. In this talk, I will discuss how this viewpoint subsumes (some) familiar constructions of classical differential geometry.