Events
Department of Mathematics and Statistics
Texas Tech University
The Mahler measure is defined as the geometric mean of a polynomial over the unit circle. This quantity is of importance in analysis and number theory. We show that it grows exponentially fast if we iterate a polynomial in the sense of complex dynamics. The exact base of that exponential growth is described by an integral over the invariant measure for the Julia set of the polynomial we iterate. We also provide sharp bounds for such integrals by using some results from complex function theory.
This Analysis seminar may be attended Monday the 7th at 4:00 PM CST (UT-6) via this Zoom link.
Meeting ID: 972 0263 8160
Passcode: 549916
In this talk we will discuss how ideas from noncommutative geometry put forward by Kontsevich can be used as a framework to study matrix models. We will explore the case of the Gaussian Unitary Ensemble from this perspective and determine some of its large N behavior.The mixture model represents the presence of subpopulation within a population, and it doesn't require that an observed data set identify the sub-population to which an individual observation belongs. So, population simulated from multivariate normal mixture models can be classified into sub-populations using several existing supervised machine learning models. This research generated multivariate normal mixture datasets with 1000, 2000, 5000, and 10000 observations with four groups. Each dataset had three different mean vectors, which follow the uniform distribution and three different covariance matrices generated from the Identity, Toeplitz and Equi-correlation matrix. A total of nine combinations of mean vector and covariance matrix were used to generate the datasets. So, in total, 36 datasets were generated. And classification was performed using supervised machine learning methods on those datasets, and accuracy was assessed using the test dataset after portioning the datasets into training data and test data. This research used multinomial logistic regression, support vector machine, K nearest neighborhood classifier, decision tree, bagging, and boosting to classify the multivariate normal mixture datasets. Finally, the accuracy of those methods was calculated and compared on the simulated datasets.
Please attend this week's Statistics seminar at 3 PM (UT-6) Wednesday the 9th via this Zoom link.
Meeting ID: 994 3003 6245
Passcode: 487707
The Hecke eigenvalues of classical modular forms are realized in the
Fourier expansions of eigenforms. For Siegel modular forms, the
relationship between Hecke eigenvalues and Fourier coefficients is
more complicated. In this talk, I will present joint work with Brooks
Roberts and Ralf Schmidt in which we develop a theory of stable
Klingen vectors inside of paramodular representations with sufficient
ramification that has many beautiful consequences, including a
generalization of Andrianov's rationality result for a certain
Dirichlet series of Fourier coefficients.
Follow the talk via this Zoom link
Meeting ID: 952 4925 1386
Passcode: 853016
Calcium dynamics in neurons containing an endoplasmic reticulum are governed by diffusion-reaction equations on interface-separated domains. Interface conditions are typically described by systems of ordinary differential equations that provide fluxes across the interfaces. For the model with ODE-flux boundary condition, we prove the existence, uniqueness, and boundedness of the solution. Then we propose and analyze an efficient implicit-explicit finite element scheme which is implicit for the parabolic operator and explicit for the nonlinear terms. We show that the stability does not depend on the spatial mesh size. Also, the optimal convergence rate in H^1 norm is obtained. We further develop a stable high-order multi-step scheme to overcome the instability and low accuracy of the previous method. Parallel algorithms are implemented for coupled PDEs on interface-separated domains. The newly designed scheme is used to solve large-scale 3D calcium models on neurons. To our knowledge, we are the first to obtain the 3D full-cell simulations with endoplasmic reticulum inside.
Please attend this week's Applied Math seminar at 4 PM Wednesday via this Zoom link.
Meeting ID: 976 3095 1027
Passcode: applied
We will review the main site FEmb_d of smooth families of d-manifolds and their fiberwise open embeddings and how it is used in the geometric cobordism hypothesis.This study examines the impact of ESG ratings on mutual fund holdings, stock returns,
corporate investment, and corporate ESG practices, using panel event studies.
Looking specifically at changes in the MSCI ESG rating, we document that rating downgrades
reduce ownership by mutual funds with a dedicated ESG strategy, while upgrades increase it.
We find a negative long-term response of stock returns to downgrades and a slower and weaker
positive response to upgrades.
Regarding firm responses, we find no significant effect of up- or downgrades on capital
expenditure.
We find that firms adjust their ESG practices following rating changes, but only in the
governance dimension.
These results suggest that ESG rating changes matter in financial markets, but so far have
only a limited impact on the real economy.