| Date: September 24 |
| Speaker: Janos Csirik, D E Shaw |
| Title: My experiences with mathematics outside academia |
| Abstract: The speaker attended the Berkeley Math PhD program from 1995 to 1999, completing his magnum opus "The kernel of the Eisenstein ideal" in algebraic number theory under the direction of Ken Ribet. He is currently a quantitative analyst at D. E. Shaw & Co, one of the largest hedge funds in the world. |
| In this very informal seminar he will aim to provide some information that he would have found interesting and/or useful back when he was a graduate student. He will comment on his various experiences including an internship in cryptography with Arjen Lenstra at Citibank, being a researcher at two major industrial research labs (HP and AT&T), and being a quant at D. E. Shaw & Co. |
| The speaker will be available for Q&A after the seminar. |
| There will be a recruiting presentation by D. E. Shaw & Co. at 6:30pm on the same day at the Nassau Inn, which the speaker whole-heartedly recommends to all who are interested in finding out about a career in finance. |
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| Date: October 1 |
| Speaker: Panos Papadopoulos, Mechanical Engineering, University of California, Berkeley |
| Title: A Critical Look at Mesh-Tying and Contact Algorithms in Computational Mechanics |
| Abstract: The solution of boundary-value problems in solid and fluid mechanics often involves interfaces between similar or dissimilar domains. On such interfaces, the underlying physics dictates that certain conditions be enforced. The enforcement of such conditions, in turn, poses numerical challenges arising from the choice of approximation spaces, as well as from the geometry and discrete character of the associated computational grids. In this talk, a mathematical framework for the analysis of a class of such interface problems involving contact between deformable solids will be reviewed and certain convergent dual algorithms will be discussed within the context of the finite element method. |
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| Date: October 8 |
| Speaker: Carlos Brody, Molecular Biology, Princeton University |
| Title: Modeling complex brain dynamics |
| Abstract: It is thought that the neural activity in specific, specialized structures of the brain is responsible for what we experience as "cognition." I will describe recordings from the brains of awake primates, performing a cognitive task, that show that the relevant neural activity has a very complex and heterogeneous dynamical pattern. In these recordings, only a few neurons (less than 10) are recorded from at a time, and only a few hundreds of neurons are recorded from in the course of an entire experiment. Yet the number of neurons in the relevant brain areas is in the tens of millions. We aim to build dynamical systems models that describe the mechanisms responsible for the observed patterns in the data. How can we build models that are faithful to the complexity of the data, and faithful to the very large number of neurons involved, yet simple enough that we can understand their principles of operation? |
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| Date: October 22 |
| Speaker: Lai-Sang Young, Courant Institute, New York University |
| Title: Shear-induced Mixing |
| Abstract: I will discuss the phenomenon of shear-induced mixing in driven dynamical systems. The unforced system is assumed to have certain simple underlying structures, such as attracting periodic solutions or equilibria undergoing Hopf bifurcations. Specifics of the defining equations are unimportant. A geometric mechanism for producing chaos - or equivalently promoting mixing - is proposed. In the case of periodic kicks followed by long periods of relaxation, rigorous results establishing the presence of strange attractors with SRB measures are presented. These attractors belong in a class of chaotic systems that can be modeled (roughly) by countable-state Markov chains. From this I deduce information on their statistical properties. In the last part of this talk, I will explore numerically the range of validity of the geometric ideas discussed. Examples including stochastically forced coupled oscillators will be presented. |
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| Date: November 5 |
| Speaker: John Lafferty, Computer Science, Carnegie Mellon University |
| Title: Functional Sparsity |
| Abstract: Substantial progress has recently been made on understanding the behavior of sparse linear models in the high dimensional setting, where the number the variables can greatly exceed the number of samples. This problem has attracted the interest of multiple communities, including applied mathematics, signal processing, statistics, and machine learning. But linear models often rely on unrealistically strong assumptions, made more by convenience than conviction. Can we understand the properties of high dimensional nonlinear functions that enable them to be estimated accurately from sparse data? In this talk we present some progress on this problem, showing that many of the recent results for sparse linear models can be extended to the infinite dimensional setting of nonparametric function estimation. In particular, we present some theory for estimating sparse additive models, together with algorithms that are scalable to high dimensions. We illustrate these ideas with an application to functional sparse coding of natural images. This is joint work with Han Liu, Pradeep Ravikumar, and Larry Wasserman. |
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| Date: November 12 |
| Speaker: Patrick Cheridito, Operations Res & Financial Eng, Princeton University |
| Title: Coherent and convex risk measures: representation results and dynamic consistency conditions |
| Abstract: Coherent and convex risk measures were introduced to address drawbacks of traditional risk measures such as variance, value-at-risk or default probability. After a short introduction I will give representation results for static risk measures. Then I will discuss dynamic risk measures and conditions for time-consistency. |
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| Date: November 19 |
| Speaker: Dargan Frierson, Atmospheric Sciences, University of Washington |
| Title: A Hierarchy of Mathematical Models for Studying the Earth's Climate |
| Abstract: The Earth's climate is a remarkably complex physical system; constructing models to study it is a difficult task which requires parameterization of a multitude of physical processes. Not surprisingly, such models quickly become difficult to understand due to the vast number of nonlinear processes that are active in them. |
| Therefore, an important line of work in atmospheric science involves the development and use of intelligently chosen idealized models, designed to better understand the results of comprehensive climate models as well as the fundamental dynamics of atmospheric circulations. These models are simpler to interpret than the full climate models, but hopefully can still provide insight into the dynamics of their more complex cousins. |
| In this talk, we give a summary of some topical problems in climate dynamics, and the hierarchical modeling approach we have used to study them. We will discuss physical problems such as the predicted poleward shift of the midlatitude jet stream with global warming, and changes in energy fluxes and temperature gradients in the atmosphere. Focusing on the effect of moist convection on these issues, we present a variety of idealized models that we have used to study these problems. These range from models of 3-D fluid motion on a rotating sphere in the presence of condensation, to highly idealized 1-D PDE models of diffusive energy transport. |
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| Date: December 3 |
| Speaker: Marsha Berger, Courant Institute, New York University |
| Title: Cartesian Cut Cell Methods: Where Do Things Stand? |
| Abstract: We discuss some of the steps involved in preparing for and carrying out a fluid flow simulation in complicated geometry. Our goal is to automate this process as much as possible to enable high quality inviscid flow calculations. We use multilevel Cartesian meshes with irregular cells only in the region intersecting a solid object. We present some of the technical issues involved in this approach, including the special discretizations needed to avoid loss of accuracy and stability at irregular boundary cells, as well as how we obtain highly scalable parallel performance. This method is in routine use for aerodynamic calculations in several organizations, including NASA Ames Research Center. Many open problems are discussed. |
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| Date: December 10 |
| Speaker: Iain Couzin, Ecology & Evolutionary Biology, Princeton University |
| Title: Collective motion and decision-making in animal groups |
| Abstract: Animal groups such as bird flocks, insect swarms and fish schools are spectacular, ecologically important and sometimes devastating features of the biology of various species. Outbreaks of the desert locust, for example, can invade approximately one fifth of the Earth's land surface and are estimated to affect the livelihood of one in ten people on the planet. |
| Using a combined theoretical and experimental approach involving insect and vertebrate groups I will address how, and why, individuals move in unison and investigate the principals of information transfer in these groups, particularly focusing on leadership and collective consensus decision-making. |
| For very large animal groups, despite huge differences in the size and cognitive abilities of group members, recent models from theoretical physics ('self-propelled particle', SPP, models) have suggested that general principles underlie collective motion. Such models demonstrate that some group-level properties may be largely independent of the types of animals involved. I shall present recent experimental work on locusts that validates some of the predictions of simple mechanistic models including a density-dependent "phase transition" from disordered to ordered motion. |
| Details of the mechanism by which individuals interact, however, also provide important biological insights into swarm behaviour. Using laboratory studies involving nerve manipulation and field experiments we demonstrate that some swarming insects are in effect on a "forced march" driven by cannibalism. |
| These results will be discussed in the context of the evolution of functional complexity and pattern formation in biological systems. |
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