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Thomas Stelson Lecture Series
Thomas Stelson Lecture Series
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ItemRiemann, Boltzmann and Kantorovich Go to a Party(Georgia Institute of Technology, 20130419) Villani, Cedric ; Georgia Institute of Technology. School of Mathematics ; Institut Henri PoincaréThis talk is the story of an encounter of three distinct fields: nonEuclidean geometry, gas dynamics and economics. Some of the most fundamental mathematical tools behind these theories appear to have a close connection, which was revealed around the turn of the 21st century, and has developed strikingly since then.

ItemCryptography: From Ancient Times to a PostQuantum Age(Georgia Institute of Technology, 20180301) Pipher, Jill C. ; Georgia Institute of Technology. School of Mathematics ; Brown University. Dept. of MathematicsHow is it possible to send encrypted information across an insecure channel (like the internet) so that only the intended recipient can decode it, without sharing the secret key in advance? In 1976, well before this question arose, a new mathematical theory of encryption (publickey cryptography) invented by Diffie and Hellman made digital commerce and finance possible. The technology advances of the last 20 years bring new and urgent problems, including the need to compute on encrypted data in the cloud and to have cryptography that can withstand the speedups of quantum computers. In this lecture, Jill Pipher will discuss some of the history of cryptography and some of the latest ideas in "lattice" cryptography which appear to be quantum resistant and efficient.

ItemHow Quantum Theory and Statistical Mechanics Gave a Polynomial of Knots(Georgia Institute of Technology, 20140925) Jones, Vaughan ; Georgia Institute of Technology. School of Mathematics ; Vanderbilt University. Dept. of MathematicsWe will see how a result in von Neumann algebras (a theory developed by von Neumann to give the mathematical framework for quantum physics) gave rise, rather serendipitously, to an elementary but very useful invariant in the theory of ordinary knots in three dimensional space. Then we'll look at some subsequent developments of the theory, and talk about a thorny problem which remains open.

ItemMultiscale Modeling and Simulation: The Interplay Beween Mathematics and Engineering Applications(Georgia Institute of Technology, 20091026) Hou, Thomas Y. ; Georgia Institute of Technology. School of Mathematics ; California Institute of TechnologyMany problems of fundamental and practical importance contain multiple scale solutions. Composite and nano materials, flow and transport in heterogeneous porous media, and turbulent flow are examples of this type. Direct numerical simulations of these multiscale problems are extremely difficult due to the wide range of length scales in the underlying physical problems. Direct numerical simulations using a fine grid are very expensive. Developing effective multiscale methods that can capture accurately the large scale solution on a coarse grid has become essential in many engineering applications. In this talk, I will use two examples to illustrate how multiscale mathematics analysis can impact engineering applications. The first example is to develop multiscale computational methods to upscale multiphase flows in strongly heterogeneous porous media. Multiphase flows arise in many applications, ranging from petroleum engineering, contaminant transport, and fluid dynamics applications. Multiscale computational methods guided by multiscale analysis have already been adopted by the industry in their flow simulators. In the second example, we will show how to develop a systematic multiscale analysis for incompressible flows in three space dimensions. Deriving a reliable turbulent model has a significant impact in many engineering applications, including the aircraft design. This is known to be an extremely challenging problem. So far, most of the existing turbulent models are based on heuristic closure assumption and involve unknown parameters which need to be fitted by experimental data. We will show that how multiscale analysis can be used to develop a systematic multiscale method that does not involve any closure assumption and there are no adjustable parameters.

ItemThe Complexity of Random Functions of Many Variables(Georgia Institute of Technology, 20160831) Arous, Gérard Ben ; Georgia Institute of Technology. School of Mathematics ; New York University. Courant Institute of Mathematical SciencesA function of many variables, when chosen at random, is typically very complex. It has an exponentially large number of local minima or maxima, or critical points. It defines a very complex landscape, the topology of its level lines (for instance their Euler characteristic) is surprisingly complex. This complex picture is valid even in very simple cases, for random homogeneous polynomials of degree p larger than 2. This has important consequences. For instance trying to find the minimum value of such a function may thus be very difficult. The mathematical tool suited to understand this complexity is the spectral theory of large random matrices. The classification of the different types of complexity has been understood for a few decades in the statistical physics of disordered media, and in particular spinglasses, where the random functions may define the energy landscapes. It is also relevant in many other fields, including computer science and Machine learning. I will review recent work with collaborators in mathematics (A. Auffinger, J. Cerny) , statistical physics (C. Cammarota, G. Biroli, Y. Fyodorov, B. Khoruzenko), and computer science (Y. LeCun and his team at Facebook, A. Choromanska, L. Sagun among others), as well as recent work of E. Subag and E.Subag and O.Zeitouni.

ItemRole of Mathematics Across Science and Beyond(Georgia Institute of Technology, 20101122) Glimm, James ; Georgia Institute of Technology. School of Mathematics ; Stony Brook University. Dept. of Applied Mathematics and StatisticsThe changing status of knowledge from descriptive to analytic, from empirical to theoretical and from intuitive to mathematical has to be one of the most striking adventures of the human spirit. The changes often occur in small steps and can be lost from view. In this lecture we will review vignettes drawn from the speaker's personal knowledge that illustrate this transformation in thinking. Examples include not only the traditional areas of physics and engineering, but also newer topics, as in biology and medicine, in the social sciences, in commerce, and in the arts. We also review some of the forces driving these changes, which ultimately have a profound effect on the organization of human life.