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WEEKLY CALENDAR |
| Monday 18 |
3:10 pm, room 1431. Graph Theory and Combinatorics Seminar. Arthur Finbow, St. Mary's University. Total Well-Dominated Trees. Abstract available at http://www.math.vanderbilt.edu/~calendar/Finbow.pdf
4:10-5:30 pm, room 1432. Subfactor Seminar. Paramita Das, Vanderbilt University. A new construction of subfactors from random matrix theory III. |
| Tuesday 19 |
4:10-5:00 pm, room 1310.
Computational
Analysis Seminar. Abey Lopez, Vanderbilt University. Asymptotic behavior of Greedy Energy configurations. In this talk we will discuss some results about the asymptotic behavior of
certain point configurations called Greedy Energy (GE) points. These
points form a sequence which is generated by means of a greedy algorithm,
which is an energy minimizing construction. The notion of energy that we
consider comes from the Riesz potentials V=1/r^{s} in R^{p}, where s>0 and
r denotes the Euclidian distance. It turns out that for certain values of
the parameter s, these configurations behave asymptotically like Minimal
Energy (ME) configurations. This property will also be discussed in more
abstract contexts like locally compact Hausdorff spaces. For other values
of s, GE and ME configurations exhibit different asymptotic properties,
for example for s>1 on the unit circle. We will discuss other questions
like second order asymptotics on the unit circle and weighted Riesz
potentials on unit spheres.
7-8 pm, room 1206. Undergraduate Seminar in Mathematics. Tara Davis, Vanderbilt University. Sudoku! Let's play Sudoku! Sudoku is a number puzzle that has recently become popular in America. It is a generalized version of a centuries old mathematical puzzle called Latin squares. In this talk we will discuss some history of and strategies for playing Sudoku. We will also look closer at how to engineer Sudoku puzzles, and focus on how to ensure a unique solution. Finally, we will explore the some of the symmetry and mathematics of Sudoku squares. Free pizza. |
| Wednesday 20 | 4:10 pm, room 1310. Topology & Group Theory Seminar. John Ratcliffe, Vanderbilt University. Fibered Orbifolds and Crystallographic Groups (Joint work with Steven Tschantz). It will be discussed how a normal subgroup N of an $n$-dimensional crystallographic group $\Gamma$ determines a natural fibered orbifold structure on the orbifold $E^n/\Gamma$, and conversely every natural fibered orbifold structure on $E^n/\Gamma$ is determined by a normal subgroup N of $\Gamma$, which is maximal in its commensurability class of normal subgroups of $\Gamma$. In particular, we prove that $E^n/\Gamma$ is a fiber bundle, with totally geodesic fibers, over a $\beta_1$-dimensional torus, where $\beta_1$ is the first Betti number of $\Gamma$. Let N be a normal subgroup of $\Gamma$ which is maximal in its commensurability class. We study the relationship between the exact sequence $1\to N \to \Gamma \to \Gamma/N \to 1$ splitting and the corresponding fibration projection having an affine section. If N is torsion-free, we prove that the exact sequence splits if and only if the fibration projection has an affine section. If the generic fiber $F = {\rm Span}({\rm N})/{\rm N}$ has an ordinary point that is fixed by every isometry of $F$, we prove that the exact sequence always splits. |
| Thursday 21 | 4:10-5 pm, room 5211. Colloquium. Denis Osin, CUNY. Group theoretic Dehn surgery and its applications. In my talk I will introduce a group theoretic version of Dehn surgery in 3-manifolds. It turns out that many basic facts about ordinary Dehn surgery can be translated to algebraic language. The main result in this direction is a group theoretic analogue of the Thurston Hyperbolic Dehn Surgery Theorem. Although this result is strongly motivated by geometry, it also has some unexpected algebraic applications. For example, most results obtained by means of small cancellation theory over hyperbolic and relatively hyperbolic groups can be recovered using Dehn surgery of a very special type. Tea at 3:30 pm in SC 1425. |
| Friday 22 |
4:10-5 pm, room 1310.
NCGOA
Research Training Group Seminar. Yi-Jun Yao, Vanderbilt University. TBA.
4:10-5:00 pm, room 1307. Partial Differential Equations Seminar. Gisele Goldstein, University of Memphis. The Fredholm alternative and semilinear elliptic equations. Abstract is available at http://sitemason.vanderbilt.edu/files/gfvANW/RomeAbs.pdf 5:10-6:00 pm, room 1307. Partial Differential Equations Seminar. Jerome Goldstein, University of Memphis. Instantaneous blow up and its outgrowths. Often the most important solutions of parabolic partial differential equations are positive. But if the equation contains a term that is too singular, positive solutions may fail to exist. We explain this, including the mechanism that causes "instantaneous blow up". The classical linear results are in Euclidean space and on the Heisenberg group, with a singular potential with special scaling properties. In nonlinear versions the Laplacian may be replaced by the p-Laplacian or the porous medium operator, and there is now the beginning of a theory on Carnot groups. The lecture should be accessible to those interested in analysis who do not know many of the above terms. |