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D.W.WEEKS LECTURE SERIES

2012-2013

Organizers: Shan-Yuan Ho, Gigliola Staffilani, Katrin Wehrheim

This lecture series presents:

The lecture series is named in honour of Dorothy W. Weeks, who was the first woman awarded a Ph.D. in Mathematics at MIT in 1930. She had a substantial career as a professor and head of physics at Wilson College (PA), and as a researcher in the spectroscopy lab at MIT. She died in Newton, MA in 1990.

This series is intended for a general audience and in particular advanced undergraduates or beginning graduate students. There will be pizza available after each talk.

Mathematicians of all levels, areas, and genders are welcome!

• The solicitation for applications and suggestions for lecture series speakers is here.
• For titles and abstracts from past lecture series, visit the archive.

 

Sep 17
5:30pm
Room 4-145

Elza Erkip (Polytechnic Institute of NYU)
Energy Efficient Wireless Communication: Impact of Energy Harvesting and Processing Energy

Energy efficiency in wireless devices, from smart phones to wireless sensors, is of paramount interest not only for ensuring continuous network operation despite battery limitations, but also for reducing the carbon footprint of communication systems. There are many demands on the power supply of a wireless device, including signal processing algorithms and the wireless modem. In particular, with the advance of complex multimedia tasks, and shorter communication distances (as in sensor or machine-to-machine communications), the energy cost of signal processing becomes comparable to transmit energy. Battery limitations can be partly alleviated by energy harvesting, which corresponds to collecting various forms of energy such as solar, kinetic from the environment and then converting into electrical energy.

This talk examines the impact of signal processing energy and energy harvesting on communication system design. Using simple and mathematically tractable models for energy costs of sensing, transmitter operation, and energy harvesting, we study total energy consumption and optimal system configuration for various wireless systems including fading channel, interference channel and parallel sensor network. Our results highlight the importance of joint energy allocation to sensing and communication as well as proper consideration of the energy harvesting process, and further point to the need of obtaining accurate mathematical models for energy consumption of wireless devices.

Pizza after the talk.

Oct 22
3:00pm
4-149

Sennur Ulukus (University of Maryland at College Park)
Information-Theoretic Physical-Layer Security

Abstract:
The last couple of decades have witnessed an amazing growth in wireless communications and networking applications. More and more subscribers are relying solely on their wireless communication and computing devices for communicating sensitive information. Ensuring secure transfer of information is thus essential. This important issue is currently dealt with at the higher layers of the protocol hierarchies using cryptographic algorithms, which provide useful protection against computationally-limited adversaries.

Our research explores providing security in the physical-layer using techniques from information theory, communication theory and signal processing. This approach is a fundamental departure from the currently available cryptographic solutions in that the security we provide is unbreakable, provable and quantifiable (in bits/sec). We use unique characteristics of the wireless medium, such as the inherent random fluctuations in the wireless channel, overheard information, multi-dimensional signalling through multiple antennas, and signal alignment, to secure wireless communications in the physical-layer. In this talk, we will provide a general introductory background on information-theoretic physical-layer security, and then present some of our latest results on secure degrees of freedom for one-hop wireless networks.

Pizza after the talk.

Oct 29
10:00am
4-349

Bin Yu (UC Berkeley)
Data and a Career in Statistics

***** This talk was cancelled due to Hurricane Sandy. It will be rescheduled. *****

In this interactive talk, I would like to advocate for statistics as being a wonderful and fulfilling career for mathematically skilled people, who seek to make a difference in real life.

In particular, I will demonstrate the diversity of problems in statistics through the many research projects going on in my group at UC Berkeley. They include theoretical machine learning, algorithm developments, and interdisciplinary research in neuroscience, remote sensing, bioinformatics and text summarization.

Biography: Bin Yu is Chancellor's Professor in the Departments of Statistics and of Electrical Engineering & Computer Science at UC Berkeley. She has published over 100
scientific papers in premier journals in Statistics, EECS, remote sensing and
neuroscience, in a wide range of research areas including empirical process theory, information theory (MDL), MCMC methods, signal processing, machine learning, high dimensional data inference (boosting and Lasso and sparse modeling in general),
and interdisciplinary data problems.

She was a 2006 Guggenheim Fellow and the 2012 Tukey Memorial Lecturer of the Bernoulli Society (selected every four years). She is President-Elect of IMS (Institute of Mathematical Statistics).

Pizza after the talk.

Nov 05
5:30pm
4-145

Alice Guionnet (MIT)
The Spectrum of Non-Normal Random Matrices

In this talk, we will give an introduction to spectral properties of non-normal matrices; that is matrices which do not commute with their adjoint. We shall see that the spectrum of such matrices is in general not stable under small perturbation of the entries, but that it can be “stabilized” by adding a small random matrix. We will also review classical ensembles of random non-normal matrices and the behavior of their spectrum as the dimension goes to infinity. No previous experience with random matrices is needed to follow this talk.

Pizza after the talk.

Nov 14
5:30pm
4-145

Margaret Readdy (University of Kentucky)
The Characteristic Polynomial

Given a subspace arrangement, the characteristic polynomial is a polynomial in the variable t which weights each k-dimensional intersection X by the Mobius function of X times t^k. I will describe many interpretations of the characteristic polynomial, including counting lattice points due to Blass and Sagan, Athanasiadis' modulo q interpretation, and the valuation approach of Ehrenborg and Readdy. We will also review Zaslavsky's work on specializing the characteristic polynomial at certain integer values of t, as well as Stanley's result on the number of acyclic orientations of a graph. Surprisingly all but one of these authors have some connection to MIT.

Pizza after the talk.

Nov 26
5:30pm
4-145

Muriel Médard (MIT)
To PHY or not to PHY - on the Capacity of Wireless Networks at Different Levels of SNR

The intersection of network coding and wireless communications leads to potentially rich
interactions among layers. In this talk, we examine whether coding in ways that blend network coding and PHY layer coding is beneficial. In the high SNR regime, we argue that analog network coding, in effect amplify and forward, is optimal, thus requiring only PHY-layer ISI coding. In the low SNR regime, we argue that network coding and PHY coding can be separated. A secondary effect of such separation is that network planning may lend itself to elegant design. In intermediate regimes, equivalence theory provides bounds that point to the frequent desirability of separating network coding and PHY coding, but no asymptotic optimality.

Pizza after the talk.

Dec 03
5:30pm
4-145

Carla D. Savage ( North Carolina State University)
Lecture Hall Partitions

Lecture hall partitions are finite sequences of nonnegative integers, constrained by a certain condition on the ratio of consecutive parts. They were introduced in 1996 by Bousquet-Melou and Eriksson, who discovered their remarkably simple generating function. Lecture hall partitions have been found to have surprising connections in combinatorics, algebra, geometry, and number theory.

In this talk, we will describe several interesting properties of lecture hall partitions (some never before revealed). No special background is required.

Pizza after the talk.

Dec 10
5:30pm
4-145

Agnes H. Chan (Northeastern University)
Cloud Security

In this talk, I will provide an overview of the security issues associated with cloud computing, in particular, I will discuss privacy-preserving information retrieval schemes. Much work has been done on Private Information Retrieval (PIR) that allows retrieval of information from a database without letting the server know about the user’s access patterns. Most of these schemes incur enormous computation and communication overhead that outweigh any cost saving advantages of cloud computing. We present a practical, highly efficient protocol for PIR using MapReduce. The talk will end with an open discussion on the joy and obstacles of being a woman and an academician.

Pizza after the talk.

Jan 07
12:00pm
2-135

Shan-Yuan Ho (MIT)
Horse Racing, Information Theory, and the Optimal Portfolio

If the sequence of outcomes in horse racing and stock market investments can be modeled as a stationary stochastic process, then information theory provides insight to optimal betting schemes on the horse race and optimal allocations for the portfolio. Specifically, the growth rate of an investment in a 'win bet' horse race is related to the entropy rate of that race. We discuss some simple portfolio strategies including constant rebalancing and show its optimality in a variety of situations. In particular, the exponential growth rate of wealth of the best strategy has at most a vanishing probability of growing at a greater rate than that of the constant balanced portfolio. This talk highlights some of Cover's seminal contributions to portfolio theory with a different representation. No previous knowledge is assumed.

Pizza after the talk.

Jan 28
12:00pm
2-135

Nancy Reid (University of Toronto)
Statistics in Research

Statistical methods are an important part of research in nearly every field of study. Statistical theory provides the backbone on which these methods are developed. I will describe aspects of statistical theory close to my own research on likelihood-based inference, and present some examples of problems in science, social science and humanities where statistical methods have been crucial to key advances. No special background is required.

Pizza after the talk.

Feb 25
5:30pm
4-149

Tamar Friedmann (University of Rochester)
From Representation Theory to Classification of Hadrons

How much can elementary representation theory of groups like SU(n) tell us about the properties of particles? As it turns out, far more than one might expect. It is quite remarkable that particles can be viewed as basis vectors for the representations of a Lie algebra, where a corresponding Lie group describes some symmetry of the system. In this talk, we will elaborate on this statement and explain how the representation theory of Lie groups and Lie algebras lies at the root of the classification of certain particles known as hadrons.

Previous knowledge of Lie groups/algebras and representations is not needed - this talk just works with nxn matrices.

Pizza after the talk.

Mar 11
5:30pm
4-149

Silvia Sabatini (EPFL)
The Geography of (some) Manifolds with Symmetries

In mathematics, the problem of classifying manifolds (i.e. the higher dimensional analogues of curves or surfaces) is very hard and has many open problems. However the problem becomes much easier when the manifold admits a certain symmetry, i.e. there is a Lie group acting on it. In this talk I will introduce a special class of manifolds, namely symplectic manifolds, with a special type of actions, namely Hamiltonian actions, which also naturally arise in physics. I will explain that, if the group acting is 'big enough', these manifolds are completely characterized by a polytope with some special properties: this is the remarkable Delzant's theorem. I will illustrate 'how to reconstruct the manifold from the polytope': for example, how to obtain a 2-dimensional sphere from a segment, and a complex projective space of complex dimension 2 from a triangle.

Previous knowledge of basic differential geometry is preferred but not essential.

Pizza after the talk.

Mar 18
5:30pm
4-149

Dana Randall (Georgia Institute of Technology )
Domino Tilings of the Chessboard: An Introduction to Sampling and Counting

How many ways are there to tile an n x n chessboard with unmarked dominoes? This question dates back to the early 20th century, when physicists used domino tilings as a statistical mechanical model of diatomic molecules. For some regions (that are natural like the chessboard), we can exactly count the number of tilings with simple formulae, while for other regions we can count using efficient algorithms. We will introduce some of these methods and will show algorithms for generating random domino tilings approximately. As we shall see, random tilings reveal a rich underlying structure that has led to deep and beautiful mathematical discoveries. We will conclude with recent extensions in the biased setting where we favor certain tilings over others.

Mar 20
5:30pm
4-149

Rongsong Liu (University of Wyoming)
Interaction Between Plant Toxicity and Herbivores can Shape Landscapes

In some areas of Alaska, it was found that after floods or forest fires willows became a dominant plant species. After about a duration of 10 years, willows were observed to become almost extinct, while alders became the dominant plant species. The reasons for the succession of willows and alders remain a puzzle in ecology. Some biologists suggest that a simple competitive advantage of alders is the cause of succession; however other biologists suggest that the interaction between the herbivores (snow hares and moose) and the plants is at play. In order to solve this puzzle, biologist J. P. Bryant conducted the ''hare-moose exclusion' experiment from 1985 to 2000 and proposed that herbivore browsing and plant toxicity could lead to the elimination of willows from the ecosystem. In this talk, we show how mathematical models can be applied to rationalize the data above and describe the subtle willow-alder-herbivore system. The dynamics will be discussed to gain insight into the role of plant toxicity in the cycle of succession of plant species.

Pizza after the talk.

Apr 22
5:30pm
4-149

Fu Liu (University of California, Davis)
Introduction to Ehrhart Polynomials

Given an integral convex polytope P, for any positive integer m, we define its mth dilation to be mP = { m x | x in P}. We then denote by i(P,m) the number of lattice points inside mP. Eugene Ehrhart discovered in 1960s that the function i(P, m) is actually a polynomial in m of degree dim(P). So we often call i(P, m) the Ehrhart polynomial of P.

In this talk, I will first survey some well-known results related to Ehrhart polynomials, and then discuss some of my own results on this subject. No previous knowledge on this topic is required.

Apr 29
5:30pm
4-149

Lynn Stein (Olin College)
TBA

TBA