Events
Department of Mathematics and Statistics
Texas Tech University
Over an algebraically closed field, the {\it double point
interpolation} problem asks for the vector space dimension of the
projective hypersurfaces of degree $d$ singular at a given set of
points. After being open for 90 years, a series of papers by
J. Alexander and A. Hirschowitz in 1992--1995 settled this question in
what is referred to as the Alexander-Hirschowitz theorem. In this
talk, we use commutative algebra to prove analogous statements in the
{\it weighted projective space}, a natural generalization of the
projective space. I will also introduce an inductive procedure for
weighted projective planes, similar to that originally due to
A. Terracini from 1915, to demonstrate the only example of a weighted
projective plane, with mild assumptions, where the analogue of the
Alexander-Hirschowitz theorem holds {\it without any
exceptions}. Furthermore, I will give interpolation bounds for an
infinite family of weighted projective planes.
Follow the talk via this Zoom link
Meeting ID: 944 0908 4315
Passcode: 015259
Various changing phenomena around us can be described as dynamical systems. A dynamical system could be deterministic or random, continuous or discrete time. Each of the four combinations are different mathematical objects and have their own theoretical study. They may however be compared based on the collection of sample-paths they generate. This talk will present some old and new connections between these four kinds of dynamics, and the space of sample paths.
This paper considers linear panel data models with latent group structures when the number of groups is unknown. I propose a novel, penalty-free procedure to estimate the number of groups. Based on two newly designed measurements of within-group dissimilarity, two estimators are proposed by maximizing the dissimilarity ratio. Compared to existing methods, the estimators do not require any penalty parameters, making them easy to compute in practice. Their consistency is established, and the proof employs novel techniques beyond the standard uniform law of large numbers. Numerical studies based on synthetic and real-world data confirm the effectiveness of the proposed methods.
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday via this Zoom link.
Meeting ID: 960 7440 0300
Passcode: 607793
Abstract. Instantaneous time mirrors (ITMs) were recently introduced by M. Fink and collaborators as a new avenue for time reversal. The latter allows for the focusing of waves, whether acoustic, electromagnetic or elastic, and has found many important applications in medical imaging, non-destructive testing, and telecommunications for instance. The main practical difficulty of standard time reversal is the recording/reversal process which necessitates a quite complex apparatus. ITMs offer on the contrary a simplified experimental alternative that does not require any measurements, provided there is some control over the medium of propagation. We will review in this talk the basics of the time reversal of waves introduced in the nineties, and discuss the recent ITMs and some of their mathematical properties.
When: 3:30 pm (Lubbock's local time is CDT, 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")
Math Circle Fall Poster