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Sessions
Morning Concurrent Sessions - 10:15-10:55 a.m. An Introduction to Topology
Topology is the study of geometric properties of an object which do not change when we squeeze or stretch it, without tearing or sticking pieces together (think of the object as made of play-dough). So, topologists do not care about distances and angles, but instead ask questions like "is it connected?" or "how many holes has it got?" For example, a topologist cannot tell the difference between a donut and a coffee cup. We will study some key ideas from topology and see how they are applied in mathematics and elsewhere.
Images of Hyperbolic Geometry
Attempts to describe hyperbolic geometry often lead to references to Alice in Wonderland. The non-Euclidean world can seem like a strange one at times. Size and scale are not what we are used to. Our understanding is aided by a number of models that describe the distortion in various ways. Each model brings a different aspect into view. The basics of hyperbolic geometry will be introduced, and we will peer through the looking glass at a few representations of the hyperbolic plane.
Symmetries, Tessellations, and Escher's Prints
Among Escher's fascinating and puzzling collection of drawings, there is a special series of "symmetry" prints consisting of 136 pieces. Yet, from a mathematician's point of view, there are only 17 essentially different wallpaper patterns, corresponding to 17 crystallographic groups. We shall explore how wallpaper patterns (or tessellations) are created by applying symmetries to a given object. We'll also play a "wallpaper game", distinguishing Escher's prints which have truly different patterns from those which only differ because of the crawling, flying, or running creature that's being reflected around the print.
Mapping the Sky: How to Unravel Dark Energy in a 100 Billion Easy Steps
Understanding dark energy is one of the fundamental challenges facing astronomy. The signatures it imprints on the properties and distributions of galaxies are, however, very subtle (often parts in a million). In this talk we will show how, by building telescopes to map much of the visible universe, we can begin to measure its effects and unravel its mysteries.
Morning Concurrent Sessions - 11:15-11:55 a.m. Neutrinos and Mass
Neutrinos are ghostly subatomic particles that travel through matter almost as though matter were transparent. This talk will describe some spectacular sources of neutrinos - the Big Bang, big crunches (like the collapse of a massive star to form a neutron star or black hole), and the sun - and we'll count the number of neutrinos they might produce. About a billion billion neutrinos pass through us every day, and we will calculate why these neutrinos don't harm us. We will also figure out how close a starship could approach a supernova explosion without worrying about the neutrinos, talk about "dark matter," and estimate how much of the universe's mass is in neutrinos compared to the amount of mass in all of the visible stars.
Tricky Mathematics and Mathematical Tricks
Do you have to be a “math geek” to enjoy it? Did you ever wonder
why your grandmother spends hours solving Sudoku puzzles?
Mathematics is the study of numbers, shapes, and patterns. As such,
even elementary mathematics provides many opportunities to create
fun puzzles, develop “tricks” and entertain everyone. Come join us
for some exploration of puzzles, games, and math based card tricks.
Warped Spaces
What would the world look like if you lived in a strange place where
the sum of the angles in a triangle is not 180 degrees, and it’s not true
that a line has a unique parallel through a given point? The familiar
set of rules for lines and angles on a plane is just one possibility
for the geometry of a space. We’ll take a look at alternative, non-
Euclidean geometries, and the resulting “curved” spaces. Some
Escher prints show beautiful models of such worlds. In fact, modern
physics suggests that our own universe is non-Euclidean, despite our
intuition to the contrary.
Afternoon Concurrent Sessions - 1:20-2 p.m.
Robots that Run, Climb, Flap, and Swim
Science fiction has posited pervasive robots for years--as pets, personal servants, or even full-blown companions. Meanwhile, most robots today work on assembly lines building cars and household goods, and few robots ever enter our homes. One big obstacle to creating ubiquitous robots is that it seems difficult to build machines that are adept at moving around the world. This limitation is striking since animals of all shapes and sizes have mastered the art of rapid locomotion in complicated and adversarial environments. We'll discuss the state-of-the-art technology in mobile and autonomous robotics and explore some promising avenues for the development of biologically-inspired locomoting robots.
Mathematical Genetics: an Art of Thinking Backwards
Modern technology allows us to measure genetic variation between and within species. For example, we can take a sample from a human population and uncover chromosomal locations where we observe a difference in genetic material among sampled individuals. Such data collection techniques enable us to tackle problems of medical importance, such as "What genes contribute to the risk of being affected by a certain disease?" and more general evolutionary biology questions, such as "What genetic changes made us human?" I will present several examples that demonstrate the role of mathematical modeling and statistical inference in genetic and evolutionary research.
How are Weather Forecasts Made?
This talk will describe the basis of modern weather forecasting - numerical weather prediction using fast supercomputers to integrate the equations describing atmospheric motions and physics.
Math Day 2009 is presented by the UW Department of Mathematics in conjunction with the Departments of Aeronautics and Astronautics, Applied Math, Astronomy, Atmospheric Sciences, Civil and Environmental Engineering, Earth and Space Sciences, Genetics, Molecular Biotechnology, Oceanography, Physics, Statistics, Zoology, the UW Medical Center, Center for Digital Arts and Experimental Media and the Center for Advanced Research Technology in the Arts and Humanities. |
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