Events
Department of Mathematics and Statistics
Texas Tech University
A differential graded (DG) algebra is the confluence of a graded
associative algebra and a complex. An example of a prototypical
DG-algebra is the Koszul complex. The algebra structure of the Koszul
complex is inherited by its homology, making both the Koszul complex
and its homology an incredibly useful tool in algebra. There is much
that can be learned about the properties of a ring from its resulting
DG-algebra resolution. In this talk we will examine a spectrum of
properties that can be gleaned from a DG-algebra resolution,
specifically the Koszul complex. We will use this to create a basic
framework for the purpose of examining the relationship between a ring
and the algebra structure of its resulting DG-algebra resolution.
Follow the talk via this Zoom link
Meeting ID: 944 0908 4315
Passcode: 015259
A new heuristic mathematical model was proposed for accurate forecasting of prices of stock options. This new technique uses the Black-Scholes equation supplied by new intervals for the underlying stock and new initial and boundary conditions for option prices. The Black-Scholes equation was solved in the positive direction of the time variable. This ill-posed initial boundary value problem was solved by the so-called Quasi-Reversibility Method (QRM). In our current work, we used the geometric Brownian motion to provide an explanation of that effectivity using computationally simulated data for European call options. We also provide a convergence analysis for QRM. The key tool of that analysis is a Carleman estimate. This talk emphasizes convergence analysis.
We present a pseudo-reversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. Once trained,the normalizing flow model can directly generate samples of the SDE's final state without simulating trajectories. Notably, the model requires only a single training session, after which it can accommodate a range of initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we introduce a conditional pseudo-reversible normalizing flow for quantifying forward and inverse uncertainty propagation. The convergence analysis in the Kullback–Leibler divergence and numerical experiments will be provided.
Please attend this week's Statistics seminar at 4 PM (UT-6) Monday via this Zoom link.
Meeting ID: 976 6926 2940
Passcode: 690064
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs and faculty welcome from any discipline.
See the pdf flyer for this semester's schedule.
Categorical spectra, developed by Stefanich, are a directed version of spectra where the suspension of pointed ∞-groupoids is replaced by that of pointed ω-categories. They are very useful for capturing stability phenomena in iterated categorifications, or for defining “∞-vector spaces”. In this talk, I will explain that they can be understood as a weak version of Lessard's ℤ-categories, a kind of category with arrows in all negative as well as positive dimensions, which allows for a more direct study of their structure.For a closed embedded submanifold $\Sigma^n$ of a closed Riemannian manifold $(M^{n+k}, g)$, with $k < n + 2$, we define extrinsic global conformal invariants of $\Sigma$ by renormalizing the volume associated to the unique singular Yamabe metric with singular set $\Sigma$. For odd $n$, the renormalized volume is an absolute conformal invariant, while for even $n$, there is a conformally invariant energy term given by the integral of a local Riemannian invariant. We also compute the derivatives of these quantities with respect to variations of the submanifold. We compare these results with their counterparts in the CCE and the classical singular Yamabe contexts.
For even-dimensional submanifolds, the notion of energy extends to most codimensions without the dimensionality constraint when viewed from a formal standpoint, allowing for an introduction of a larger class of conformal invariants. Even in the exceptional codimensions, interesting behaviors arise.
This talk is based on my doctoral work under the supervision of Stephen McKeown.
Available online via this Zoom link.
Abstract. Mathematical models of complex physical and biological systems play a crucial role in understanding real world phenomena and making predictions. Examples include models of weather systems, ocean circulation, ice-sheet dynamics, porous media flow, or spread of infectious diseases. Models governing complex systems typically include parameters that are uncertain and need to be estimated using indirect measurements. This is done by solving an inverse problem that uses the model and measurement data to estimate the unknown parameters. Optimal experimental design (OED) comprises a critical component of parameter estimation: it provides a rigorous framework to guide acquisition of data, using limited resources, to construct model parameters with minimized uncertainty. In this talk, we consider OED for inverse problems governed by partial differential equations (PDEs) with infinite-dimensional inversion parameters. Our focus will be the problem of finding an optimal placement of sensors where data are collected. I will discuss some mathematical and computational aspects of such optimal sensor placement problems, some of the recent advances in the field, as well as some interesting research questions.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 979 1333 6658
* Passcode: Applied (Note the capital letter "A")
abstract 2 PM CST (UT-6)
Zoom link available from Dr. Brent Lindquist upon request.
