Events
Department of Mathematics and Statistics
Texas Tech University
Persistent homology is a tool in topological data analysis for learning about the geometrical/topological structures in data by detecting different dimensional holes and summarizing their appearance disappearance scales in persistence diagrams. However, quantifying the uncertainty present in these summaries is challenging. In this talk, I will present a Bayesian framework for persistent homology by relying on the theory of point processes. This Bayesian model provides an effective, flexible, and noise-resilient scheme to analyze and classify complex datasets. A closed form of the posterior distribution of persistence diagrams based on a family of conjugate priors will be provided. The goal is to introduce a supervised machine learning algorithm using Bayes factors on the space of persistence diagrams. This framework is applicable to a wide variety of datasets. I will present an application to a materials science problem.
The Statistics seminar may be attended online at 4:00 PM CST (UTC-6) via this Zoom link.
Meeting ID: 915 4575 0834
Passcode: 552577
The cobordism hypothesis tells us that the process of freely adding adjoints to the $k$-morphisms of a symmetric monoidal $(\infty,n)$-category can be roughly described as follows: treat one such $k$-morphism as an $n$-framed $k$-dimensional cube and change the framing appropriately to obtain its left/right adjoint. At the very least, this description is correct if we start with the the commutative monoid generated by a single object. But what happens with more complicated examples? Motivated by work of Dawson-Paré-Pronk, we explicitly construct the functor that freely adds right adjoints to the morphisms of an infinity-category; we also extend the construction to arbitrary dimensions and speculate on what its universal property should be. This is based on joint work with Martina Rovelli.See PDF abstract.
Watch online via this Zoom link.
We will give an overview of the Number Field Sieve, which is the fastest known algorithm for factoring integers on a digital computer.
Abstract: We will discuss two topics. First, we consider the application of implicit Runge-Kutta (IRK) methods to systems of implicit ordinary differential equations (ODEs). We are interested in the situation when stiffness arises. We present some results about sufficient conditions ensuring local contractivity, hence convergence, of modified Newton iterations for stiff ODEs with step size conditions independent of stiffness. Second we consider systems of differential-algebraic equations (DAEs) of index two. We present some modifications to standard IRK methods to obtain superconvergence of non-stiffly accurate IRK methods, such as Gauss and Radau IA methods. We also discuss the development of starting approximations for the internal stages of those methods.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this
Direct Link that embeds meeting ID and passcode
or
- Choice #2: Log into zoom, then join by manually inputting the meeting ID and passcode ...
* Meeting ID: 915 2866 2672
* Passcode: applied
 | Thursday
Nov. 13
6:30 PM
MA 108
|
| Mathematics Education
Math Circle
Erhan Guler
Mathematics and Statistics, Texas Tech University
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Math Circle Fall Flyer
Abstract pdf
abstract noon CST (UTC-6)
Zoom link available from Dr. Brent Lindquist upon request.