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D.W.WEEKS LECTURE SERIES

2011-2012

Organizers: 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 26
11:00am
4-149

Olivia Caramello (University of Cambridge)
Toposes as 'Bridges' for Unifying Mathematics

The notion of topos, introduced by Alexandre Grothendieck in the early sixties in the context of Algebraic Geometry, has an intrinsically eclectic nature; indeed, a topos can be seen as a generalized space, as a mathematical universe but also as a theory. In this talk, I will give an introduction to this fascinating concept with the aim of illustrating its potential role in 'unifying Mathematics'; specifically, drawing from my
personal research experience, I will show that toposes can effectively act as 'bridges' for transferring ideas, information and results between distinct mathematical theories, by providing applications in various fields including Model Theory, Proof Theory, Algebra, Geometry and Topology.

Prerequisites: Some familiarity with the language of Category Theory would be very desirable but not essential.

Pizza after the talk in 2-290.

Oct 17
11:00am
4-149

Cathy O'Neil (Intent Media)
What's It Like to do Math in Business?

Cathy O'Neil has worked as an academic in math (M.I.T. Moore Instructor 1999, assistant professor Barnard College 2005), as a quant at a hedge fund (2007), as a researcher at a financial risk software company (2009), and more recently (2011) as a data scientist at a New York internet marketing startup. She wants young mathematicians to know what's out there so they can their compare options and can prepare themselves for a 'real world' job if it turns out to be a good fit. She will also explain how modeling is used outside of academics, for good and for evil, and how mathematicians should educate themselves about how mathematics is used by some people to authenticate otherwise questionable practices.

Pizza after the talk in 2-290.

Nov 07
12:00pm
2-135

Rita Meyer-Spasche (MPI fuer Plasmaphysik)
Oscar Buneman, Douglas Hartree, and the Development of Particle-Methods

Mathematical models for moving particles were developed first for studying the orbits of planets in a gravitational field. Later on the trajectories of charged particles in electric, magnetic and electromagnetic fields were studied. Today, numerical particle methods are well-established computational methods for various applications, including the generation of computer graphics on playstations.

This talk will focus on the development until 1966 which started in England ca 1920 at the universities of Cambridge and Manchester, in cooperation with MIT. It is an example of the successful application of mathematics to problems in physics and engineering. It was avant-garde w.r.t. the development and implementation of algorithms and the usage of computers (desk-top calculators, the analog computer `differential analyzer', ..., super computers).

In England, the leading persons were the mathematicians Douglas Hartree (*1897 in Cambridge; +1958 in Cambridge) and his student Oscar Buneman (*1913 in Milan, Italy; +1993 at Stanford, USA). Buneman emigrated with help of Emil Artin (1898 - 1962) from Hamburg to Manchester in 1935, after anti-Nazi activities and prison. Hartree's contacts at MIT were John C. Slater (1900 - 1976) at the Department of Physics (Quantum Theory, Microwave Electronics) and Vannevar Bush (1890-1974) at the Department of Electrical Engineering (Differential Analyzer).

Pizza after the talk.

Nov 14
11:00am
4-149

Monika Ludwig (Vienna University of Technology and NYU Poly)
Valuations on Convex Bodies: From Hilbert's Third Problem to Recent Results

Since Dehn's solution of Hilbert's Third Problem (concerning the elementary definition of volume) in 1902, valuations on convex bodies have played a prominent role in geometry. Here a real-valued function $\Phi$ defined on a family ${\mathcal C}$ of convex bodies (compact, convex sets) in ${\mathbb R}^n$ is called a valuation if
$$\Phi(K)+\Phi(L)= \Phi(K\cup L) +\Phi(K\cap L)$$
for all $K,L\in{\mathcal C}$ whenever $K\cup L, K\cap L\in{\mathcal C}$. The most celebrated result on valuations is Hadwiger's classification of continuous, rigid motion invariant valuations and characterization of volume and (Euclidean) surface area. In the talk, a short overview of results on valuations will be given. Recent result on SL$(n)$ invariant valuations and the characterization of affine surface areas will be presented.

Pizza after the talk in 2-290.

Dec 01
5:45pm
2-136

Carla Cederbaum (Duke University)
The Newtonian Limit of General Relativity

Einstein's General Relativity is a geometric theory of space, time, and gravitation. In some sense, it is the successor of Newton's famous theory of gravitation -- the theory Newton is said to have come up with when an apple fell onto his head. But although Einstein's theory is much better at predicting gravitational effects in our universe, Newton's theory is not at all outdated or even obsolete. In fact, many astrophysical measurements and simulations still heavily rely on Newtonian intuitions, calculations, and concepts. In the talk, I will explain how and to what extent this usage of Newtonian theory in astrophysics and related fields is motivated and mathematically justified. This will lead us to the notion of Newtonian limit. We will also see some examples for the behavior of relativistic quantities like mass and center of mass under this Newtonian limit.

Pizza after the talk.

Dec 05
5:30pm
2-139

Sarah Spence Adams (Franklin W. Olin College of Engineering)
Complex Orthogonal Designs and their Associated Space-Time Block Codes

Complex orthogonal designs were first introduced in the 1970's, and the conditions for their existence are based on number theoretic results from the early 1900's. The application of these designs as space-time block codes in multiple-antenna wireless communications systems has led to a renewed interest in orthogonal design theory over the past decade. Space-time block codes resulting from complex orthogonal designs perform well and enjoy a simple decoding algorithm. In this talk, we'll review some recent results in generalized complex orthogonal design theory, and we’ll explain the application of these results in the context of wireless communications systems.

Pre-requisites: I am intentionally making this talk accessible to all undergraduates, though some familiarity with matrices (for example, through a linear algebra class) will be helpful. In fact, most of the results that will be discussed were achieved in collaboration with dedicated undergraduate students.

Pizza after the talk.

Jan 09
1:00pm
35-255

TWO SPECIAL LECTURES: Tara Holm (Cornell University) and Janet Mertz (University of Wisconsin-Madison) ()

Speaker: Tara Holm (Cornell University)
Time: 1:00PM-2:30PM in 35-225
Title: 'Dance of the Astonished Topologist (...or how I left Squares and Hexes for Math)'
Abstract: I will give a friendly introduction to some key ideas and tools in topology, including covering spaces and monodromy. The main example will come from square dancing, a hobby I picked up whilst a graduate student at MIT. Tech Squares will provide live demonstrations. No prior experience with topology or square dancing will be assumed.

Tea: 2:30-3:30PM in 2-290

Speaker: Janet Mertz (University of Wisconsin-Madison)
Time: 3:30-5:00PM in 35-225
Title: Debunking Myths about Gender, Culture, and Math Performance
Abstract: Are boys really better at mathematics than girls? They sometimes outperform girls on mathematics tests. Also, boys' mathematics scores usually exhibit greater variance than girls' scores. But, are these observed differences due to innate biological differences between the sexes or to a variety of country-specific sociocultural factors? To answer these questions, we analyzed data on mathematics performance of students from 86 countries throughout the world obtained from recent Trends in International Mathematics and Science Studies (TIMSS), Programme in International Student Assessments (PISA), and International Mathematical Olympiads (IMOs). We found that gender gap and variance ratio are unrelated to a country's wealth, major religion, or co-educational schooling. Rather, mathematics performance of both boys and girls at the low, mean, high, and very high levels strongly correlates with some measures of gender equity, especially participation rate and salary of women in the paid labor force relative to men. Thus, sociocultural factors appear to be primary determinants of mathematics performance at all levels for both girls and boys, not intrinsic biological differences between the sexes.

Mar 05
5:00pm
2-132

Julie Mitchell (University of Wisconsin - Madison)
The Geometry of Molecules

Abstract: Enzymes and antibodies are two types of molecules that are essential to survival. These molecules are proteins, which are formed as a linear sequence of amino acids. Folded proteins have unique geometric structures, much like pieces of a
jigsaw puzzle. It is the structure and other properties of a protein that allow it to identify its binding parter and perform its job. The talk will introduce students to the
properties of molecules and explain how mathematics can be used to model their behavior. Although high-level mathematics is frequently used, the basic principles of molecular modeling can readily be understood by those with a basic math and science
background.

Pizza after the talk.

Apr 09
5:30pm
2-132

Emina Soljanin (Bell Labs, Alcatel-Lucent)
Urns & Balls and Communications

Urns and balls models refer to basic probabilistic experiments in which balls are thrown randomly into urns, and we are interested in various patterns of urn occupancy (e.g, the number of empty urns). These models are central in many disciplines such as combinatorics, statistics, analysis of algorithms, and statistical physics. After covering the fundamentals, we will show how some modern network and traffic communications scenarios give rise to problems that are related to the classical urns and balls questions. We will also describe some new models and problems that emerge in content delivery because information packets can be processed (e.g., by using finite field arithmetic) in a way their physical counterparts, urns and balls, cannot.


Pizza after the talk.

Apr 23
5:30pm
2-132

Laura Miller (University of North Carolina Chapel Hill)
Excitable Tissues in Fluids

Abstract: A wide range of numerical, analytical, and experimental work in recent years has focused on understanding the interaction between fluids and elastic structures in the context of cardiovascular flows, animal swimming and flying, cellular flows, and other biological problems. While great progress has been made in understanding such systems, less is known about how these excitable tissues modulate their mechanical properties in response to fluid forces and other environmental cues. The broad goal of this work is to develop a framework to integrate the conduction of action potentials with the contraction of muscles, to the movement of organs and organisms, to the motion of the fluid, and back to the nervous system through environmental cues. Such coupled models can then be used to understand how small changes in tissue physics can result in large changes in performance at the organ and organism level. Two examples will be discussed in this presentation. The first example considers how active contractions generated by the cardiac conduction system can enhance flows in tubular hearts, particularly at low Reynolds numbers. The second example considers how the interactions between pacemakers in the upside down jellyfish can alter feeding currents generated by the bell pulsations. In both cases, the ultimate goal is to simulate the electropotentials in the nervous system that trigger mechanical changes in 1D fibers representing the muscular bands. The muscular contractions then apply forces to the boundaries that interacts with the fluid modeled by the Navier-Stokes equations. The computational framework used to solve these problems is the immersed boundary method originally developed by Charles Peskin.

Pizza after the talk.

Apr 25
12:00pm
2-132

Joel Brewster Lewis (MIT)
Math and Origami (but mostly origami)

We'll discuss two of the many connections between origami and mathematics. First, we'll discuss origami as a constructive system of plane geometry, akin to the classical rules of compass and straightedge. Second, we'll apply some lovely results from graph theory to the problem of making attractive polyhedra from modular origami. Most of the talk will be devoted to folding paper, including angle trisection and the Sonobe unit.

Pizza after the talk.

Apr 30
5:30pm
2-132

Youngmi Hur (Johns Hopkins University )
Searching for New Alternatives to Tensor Product in Wavelet Construction

In the last few decades, wavelets have been proved to be a powerful tool for mathematical analysis and signal processing. Tensor product has been a predominant method in constructing multivariate wavelets. In this talk, I will first provide a brief overview of wavelets and the use of tensor product in constructing multivariate wavelets. Then, I will introduce a new alternative to tensor product, to which we refer as Coset Sum, and discuss the similarities and differences between the two methods. In particular, we will see that some of the known limitations of tensor product can be overcome, in a limited sense, by Coset Sum.

Pizza after the talk.

May 09
12:00pm
2-132

Maria Gorelik (The Weizmann Institute of Science)
Queer Lie Superalgebras

The Lie superalgebras are generalizations of Lie algebras. The matrix Lie algebras have two close relatives in the 'super-world': the matrix Lie superalgebras and the queer Lie superalgebras. In my talk, we will get acquainted with these algebras.

Pizza after the talk.