Student Colloquia
Most Tuesday afternoons during the academic year, the Mathematics students host a math talk. The talks are directed to our mathematics majors but are usually accessible on a variety of levels. Refreshments are served before the talks.
2014-15 Schedule
Spring
4:40 in Physics 123 (unless marked otherwise).
| Jan 27 | Initial Meeting and Tea: Info, signups, and more Time: 4:00 PM |
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| Feb 3 | Infinite Games and Preposterously Large Sets Riley Thornton '16 Time: 4:00 PM Let’s play a game. First, we a fix a subset of the reals, A0. I name two disjoint open subsets of A0, you pick one, A1, I name two disjoint opens in A1, and we repeat. You win if ∩i∈NAn is nonempty, and I win otherwise. Who has a winning strategy? Does anyone? How does it depend on A0? It turns out the answer relates to such set theoretic bugbears as the Continuum Hypothesis, the Axiom of Choice, and the existence of large cardinals. In this talk we’ll discuss his and other games and their relation to logic, topology, and set theory. |
| Feb 10 | Why, how, and which functions admit Fourier series: an introduction to spectral decompositions Justin Katz Time: 4:00 PM |
| Feb 24 | Too Many Dimensions, and Other Reasons Not to Make a Wheel out of Straight Lines Nico Terry Time: 4:00 PM What is a wheel graph, and what is its dimension? Is there a simple formula or set of formulae that allow us to understand geometric representations of these structures? How can we generalize further, and do any interesting patterns emerge? All of these questions can be answered with some elementary geometric reasoning, and they give a convenient way to begin to think in more than three dimensions. The first paper published "On The Dimension of a Graph" was authored by Erdös, Harary, and Tutte, yet this question has received relatively little attention since their 1965 paper, perhaps because for graphs in general the problem is NP-hard! Studying this question on specific subclasses of graphs can generate results that increase the number of classes of graphs for which an answer is known, and thus each advancement leads naturally to several similar results and opens new questions to investigation. This talk will be 20 minutes long, which may include time for questions, so please arrive promptly if possible. |
| Mar 3 | The Kakeya Needle Problem Riley Thornton Time: 4:00 PM Suppose you want to move a needle of unit length continuously through space in such a way that it points in every direction? How large of an area do you need? A circle of diameter 1 will do the job with area π equilateral triangle with altitude 1 will do even better, with an area of √ Now suppose we drop the continuity condition. What is the smallest area of a set which contains a line segment at every angle? Such sets are called Besicovitch sets, and they are an active area of mathematical research. In the first half of this talk I will give a completely elementary solution to the needle problem. In the second half I will sketch how some beautiful machinery from fractal analysis and general topology show that almost every Besicovitch set has measure 0. |
| Mar 17 | Sensitivity study: Impact of reactor model uncertainty on the measurement of the amplitude of neutrino oscillation in the Double Chooz experiment Liz Grace '15 Time: 4:00 PM Neutrinos are small, nearly massless, weakly interacting particles. One property of neutrinos, termed the "flavor," determines which particle the neutrino interacts with. There are three different active flavors of neutrinos: electron, tau, and muon, and these three flavors will turn into one another in a process called neutrino oscillation. In order to measure this oscillation, neutrino detectors were set up near power reactors (which produce electron antineutrinos). The precision of the experiment was analyzed using a sensitivity study. In particular, the sensitivity study tested how the uncertainty in the reactor neutrino flux affected the uncertainty in the measurement of the amplitude of neutrino oscillation as a function of time for both the single and double detector cases. |
| Mar 31 | An Introduction to Topological Quantum Field Theory Andrew Erlanger Time: 4:00 PM |
| Apr 21 | Numbers: Who, What, Where, When, How, and Why They Were Invented Nico Terry Time: 4:10 PM A brief overview of the development of number systems, starting with the most mathematically basic systems and following the course of history and its occasional regressions. This lecture will trace the many stages in the development of the concepts behind numbers and the symbols used to represent them. After this introduction, we may spend some time playing with the more interesting systems! |
| Apr 28 | Geostatistics: The Variogram, Kriging, and Spatial Interpolation Philip Stallworth Time: 4:10 PM Suppose you have information on metal concentration near a river and want to create a predictive model for other locations near the river. One could proceed by just using a linear model and calling it a day. However, this ignores spatial correlation! We deal with this problem by using a tool called the variogram to incorporate spatial autocorrelation into our statistical model. This talk will take an application-based rather than theoretically-based approach to the problem. Consequently, it should be useful for anyone with some background in R and linear modeling.
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