| 1 (Thursday) | Faculty Colloquium
Elliptic curves and stable homotopy theory
Paul Pearson. UR
12 pm - 1 pm, Hylan 1106A
In this talk we will discuss topological refinements of elliptic
curves and modular forms and their important role in stable homotopy
theory. Stable homotopy theory tries to determine the homotopy groups
of "stable" spaces called spectra. Central to the study of all
spectra is the sphere spectrum. Calculation of the homotopy groups of
the sphere spectrum relies extensively on algebraic approximation
(spectral sequences) arising from a cohomology theory called complex
cobordism. Such an algebraic approximation is often displayed as a
chart which appears to have large-scale repeating patterns that are
not immediately discernible. These patterns can be separated from
each other by means of the "chromatic filtration" developed by
Ravenel, et. al. Each layer of this filtration detects a family of
elements with the same kind of periodic pattern. We will discuss how
elliptic curves and modular forms give rise to elliptic spectra and
the spectrum of topological modular forms, and how these new spectra
have been used to detect the patterns in the first and second layers
of the chromatic filtration for the homotopy of the sphere spectrum.
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| 2 (Friday) | Honors Thesis Talk
Why do we approximate Pi by 22/7 and other Rational Approximations.
Michael Wijaya
3 pm - 4 pm, Hylan 1106B
We were taught in school that Pi is an irrational number, for
which 22/7 is a good approximation. Have you ever wondered why 22/7 is a good
approximation, when 3.141 is obviously closer to the actual value of Pi?
I will give three personal reasons why I liked 22/7 as a student in middle
school. Unfortunately for me, Pi was the only constant for which a rational
approximation was provided. Is that because there is no good rational
approximation to a random real number such as 0.123456789101112...? We will
see that the answer depends on what we mean by a ``good approximation".
Rather unexpectedly, this also has something to do with the fact that there
are only finitely many integer solutions to x^3 - 2y^3 = 11.
|
| 8 (Thursday) | Graduate Colloquium
Godel's Incompleteness Theorem
Matthew Wampler-Doty
12:30 pm - 1:30 pm, Hylan 1106A
|
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