Events
Department of Mathematics and Statistics
Texas Tech University
I will describe a specific connection between geometry and dynamics. More than twenty years ago, G. Perelman posted three papers on arxiv solving the Poincare conjecture, one of the seven Millennium Prize Problems. The key mechanism in his proof is the theory of Ricci flows, smoothly deforming shapes and measurements, and understandings of their singularity models in dimension three. Here we are interested in analogous models with complex structures in real dimension four. That is the geometry. We'll show that such a model can be formulated as an integrable Hamiltonian system, which originally was invented to describe the dynamics of classical mechanics. This striking perspective gives insight into a fundamental conjecture towards generalizing Perelman's work to higher dimensions. This talk is also a trailer for Math 6332, Geometric Mechanics, in the Fall.
Joint seminar with the Geometry, PDE and Mathematical Physics group
Two-dimensional chiral conformal field theories (CFTs) admit three distinct mathematical formulations: vertex operator algebras (VOAs), conformal nets, and Segal (functorial) chiral CFTs. With the broader aim to build fully extended Segal chiral CFTs, we start with the input of a conformal net.
In this talk, we focus on presenting three equivalent constructions of the category of solitons, i.e. the category of solitonic representations of the net, which we propose is what theory (chiral CFT) assigns to a point. Solitonic representations of the net are one of the primary class of examples of bicommutant categories (a categorified analogue of a von Neumann algebras). The Drinfel’d centre of solitonic representations is the representation category of the conformal net which has been studied before, particularly in the context of rational CFTs (finite-index nets). If time permits, we will briefly outline ongoing work on bicommutant category modules (which are the structures assigned by the Segal Chiral CFT at the level of 1-manifolds), hinting towards a categorified analogue of Connes fusion of von Neumann algebra modules.
(Bicommutant categories act on W*-categories analogous to von Neumann algebras acting on Hilbert spaces.)This paper investigates the heterogeneous selection of house price spillover channels among metropolitan areas in the United States. I propose a Bayesian approach to incorporating shrinkage on groups of spatial dependence parameters in a heterogeneous higher-order spatial dynamic panel model. Results from Monte Carlo experiments demonstrate that including group-level shrinkage would lead to better finite-sample performance in estimating the spatial dependence parameters when there exists group-structured sparsity in the true model. Empirical results using the Bayesian approach show that the geographic proximity, followed by the migration channel, makes the greatest contributions to the correlation pattern in regional house price growth.
Please virtually attend this week's Statistics seminar at 3:00 PM (UT-5) via this zoom link.
Meeting ID: 976 7035 1114
Passcode: 038528
Abstract: We revisit the possibility of finite-time, dispersive blow up for nonlinear equations of Schrödinger type. This mathematical phenomena needs to be distinguished from the usual blow-up appearing in the case of NLS with focusing nonlinearities, as it is in essence a linear phenomena based on “concurrence”. The latter is one of the conceivable explanations for oceanic and optical rogue waves. We extend the results existing in the literature in several ways. In one direction, the theory is broadened to include the Davey-Stewartson and higher order equations. In another, dispersive blow up is shown to obtain for nonlinear Schrödinger equations in spatial dimensions larger than one and for more general power-law nonlinearities.
When: 4:00 pm (GMT -5)
Where: room 011 Math (Math Basement)
Zoom details:
- Choice #1: use this
Direct Link that embeds meeting ID and passcode.
- Choice #2: Start session with this link or however you commonly log into your Zoom account, then Join using the Meeting ID and Passcode below:
* Meeting ID: 979 1333 6658
* Passcode: Applied (note the capital letter "A")
 | Thursday
Apr. 24
6:30 PM
MA 108
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| Mathematics Education
Math Circle
Álvaro Pámpano
Mathematics and Statistics, Texas Tech University
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Math Circle Spring Poster
abstract noon CDT (UT-5)
Zoom link available from Dr. Brent Lindquist upon request.