Colloquia
Department of Mathematics and Statistics
Texas Tech University
In this talk, I will describe two projects that use fluid-structure interaction techniques for modeling human cardiac physiology. The first project is focused on abnormal coronary vessels in children. The goal is to perform a sort of model validation, where we determine whether models calibrated to data in a "resting" state can predict a quantity of interest in a "stress" state (e.g. exercise). The second project is focused on the creation of a model for the human heart that includes the four valves, the four chambers, the blood, and most of the great vessels. I will demonstrate that this model is able to capture aspects of normal adult cardiac physiology, including realistic pressure volume loops and valve dynamics.
Bio: Charles Puelz is an Assistant Professor of Mathematics at the University of Houston. He obtained his PhD from Rice University and did postdoctoral work at the University of North Carolina and the Courant Institute. His interests include the development of useful numerical methods and computer models that can be used to help treat congenital heart disease.
This Departmental Colloquium was sponsored by the TTU Chapter of SIAM.
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At each point on a surface in three-dimensional Euclidean space, the mean curvature is defined as the average of the two principal curvatures. A surface with constant mean curvature is called a constant mean curvature (CMC) surface, and when this constant is zero, the surface is referred to as a minimal surface. Surfaces defined mathematically often harmonize with our daily experiences. For instance, soap bubbles and soap films formed while washing are real-life examples of CMC surfaces and minimal surfaces, respectively. Due to their property of minimizing area under given conditions, these surfaces possess mathematically beautiful structures and offer various applications.
In this talk, I will discuss the mathematical properties and applications of minimal surfaces and surfaces with constant mean curvature and their extensions.
This Departmental Colloquium is sponsored by the Geometry, PDE and Mathematical Physics seminar group.
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In this talk, we present some of our recent work on stochastic Kolmogorov systems. The motivation stems from dealing with important issues of ecological and biological systems. Focusing on environmental noise, we aim to address such fundamental questions: "what are the minimal conditions for long-term persistence of a population, or long-term coexistence of interacting species". Some optimal control problems are also mentioned. [The talk reports some of our joint work with N.T. Dieu, H. Du, D.H. Nguyen, and N.N Nguyen.]
This Departmental Colloquium was sponsored by the Statistics seminar group.
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In 1948/1949 Claude Shannon wrote two papers [Sha48, Sha49] which became the foundation of modern information theory. The papers showed that information can be compressed up to the entropy, that data can be transmitted error free at a rate below the capacity and that there exist provable secure cryptographic systems. These were all fundamental theoretical results. The challenge remained to build practical systems which came close to the theoretical optimal systems predicted by Shannon.
In this overview talk we will explain how the first two challenges concerning coding theory have resulted in practical solutions which are very close to optimal. Then we explain why the gap between the practical implementation of cryptographic protocols with the theoretical result of Shannon is largest.
[Sha48] C.E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27, (1948), 379--423 and 623--656.
[Sha49] C.E. Shannon, Communication theory of secrecy systems, Bell System Tech. J. 28, (1949), 656--715.
Biography: Joachim Rosenthal received a Diploma in mathematics from the University of Basel in 1986 and his Ph.D. in mathematics from Arizona State University in 1990. From 1990 to 2006, he was with the University of Notre Dame, USA, where he held the Endowed Chair of applied mathematics and a Concurrent Professor of electrical engineering. Since 2004, he has been a Professor of applied mathematics with the University of Zurich. He is a fellow of IEEE, a fellow of SIAM and an Honorary Professor at Universidad del Norte, Colombia. He currently serves as President of the Swiss Mathematical Society.
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Coding theory plays a crucial role in modern communication devices. The lecture will provide an overview to the mathematical constructions and decoding techniques used in coding theory. First we will show how techniques from algebra and algebraic geometry led to the construction of block codes with large distance and efficient decoding techniques. Second, we will cover classes of different type of codes such as LDPC codes and convolutional codes. The latter can be seen as discrete linear systems defined over a finite field and techniques from systems theory play an important role in their construction.
Please attend the second of this year's three Dayawansa Memorial Lecture Series at 4 PM (UT-5) in the Experimental Sciences Building 1, room 120.
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Public key cryptography has been at the center of modern cryptography. It is not only used for the exchange of secret keys but also for the authentication of entities on the Internet, for digital signatures and for the construction of digital currencies.
Until a few years ago most public key systems were based on the hardness of factoring integers or on the hardness of the discrete logarithm problem in an elliptic curve. With the realization that a quantum computer would make many practically used public key cryptographic systems obsolete it became an important research topic to design public key systems which are expected to be secure even if a powerful quantum computer would exist.
This new area of research is called post-quantum cryptography and there has been in the last couple of years a lot of effort to come up with new standards to be used in everyday applications. The National Institute of Standards and Technology (NIST) currently conducts a standardization process.
The main part of the lecture will overview this recent development and will explain the underlying mathematical problems.
Please attend the second of this year's three Dayawansa Memorial Lecture Series at 4 PM (UT-5) in the Experimental Sciences Building 1, room 120.
This presentation may be viewed in the TTU Mediasite catalog via eraider login.
Fifty Years of Math pdf abstract
This Departmental Colloquium is sponsored by the Applied Math seminar group.
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