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WEEKLY CALENDAR |
| Monday 25 |
3:10 pm, room 1431. Graph Theory and Combinatorics Seminar. Adam Weaver, Vanderbilt University.
Constructing all minimum genus embeddings of K_{3,n}. Ringel determined the minimum orientable and non-orientable genus for
all
complete bipartite graphs. For K_{3,n} the orientable genus is [(n-2)/4]
and the nonorientable genus is [(n-2)/2]. Euler's formula implies that
almost all of the faces in such an embedding must be 4-cycles. We
discovered that these embeddings can be represented by certain edge
colorings of n-vertex cubic graphs. Using this correspondence and
results
of Kotzig, we show that every minimum genus embedding of K_{3,n} can be
constructed using simple operations that involve adding one crosscap or
one handle at a time.
4:10-5:30 pm, room 1432. Subfactor Seminar. Paramita Das, Vanderbilt University. A new construction of subfactors from random matrix theory IV. |
| Tuesday 26 |
4:10-5:00 pm, room 1310.
Computational
Analysis Seminar. Qiang Wu, Duke University. Dimension Reduction in Supervised Learning. Dimension reduction in supervised setting aims at inferring the data structure that are most relevant to the prediction of the labels. It can be motivated from either predictive models or descriptive models.
Starting from a predictive model, we showed the gradient outer product matrix contains the information of relevant features and predictive dimensions. Several well known feature selection and dimension reduction methods follow this criterion either implicitly or explicitly. We designed an algorithm of learning gradients specifically for the small sample size setting using kernel regularization. The asymptotic analysis shows the convergence depends only on the intrinsic dimension of the data and can be fast if the underlying data concentrate on a low dimensional manifold. The gradient estimate was successfully applied to feature selection, dimension reduction, estimation of conditional dependency and task similarity in high dimensional data analysis. Sliced inverse regression (SIR) is a well known and widely used dimension reduction methods in statistics community. It is motivated from a descriptive model. We studied the relation between the gradient out product matrix and covariance matrix of the inverse regression function and found they are locally equivalent in certain sense. This observation not only helps clarify the theoretical comparison between these two methods but also motivates a new algorithm. We developed localized sliced inverse regression (LSIR) for dimension reduction which overcomes the degeneracy problem of original SIR and has the advantage of finding clustering structure in classification problems.
4:10-5:15 pm, room 1432. Noncommutative Geometry Seminar. Erik Guentner, University of Hawaii at Manoa. Approximation in group C*-algebras (part 3). 4:10-5:30 pm, room 1432. Universal Algebra and Logic Seminar. Yuri Bahturin, Memorial University of Newfoundland. Functional Identities and Graded Algebras. Functional identities are the identical relations for arbitrary functions on algebras. This is a comparatively new piece of techniques which was recently successfully used in the study of Lie, Jordan and other types of maps on associative algebras to prove famous Herstein conjectures. This is summarized in a recent monograph "Functional Identities" by M. Bresar, M. Chebotar and W. Martindale. It was recently discovered that using elementary techniques of Hopf algebras these results can be applied to the study of graded algebras. |
| Wednesday 27 | |
| Thursday 28 | 4:10-5 pm, room 5211. Colloquium. Ian Agol, University of California, Berkeley. Finiteness of arithmetic reflection groups. We show that there are only finitely many maximal reflection groups in hyperbolic spaces. This talk will define the terms in this theorem, and explain some of the ingredients of the proof. Tea at 3:30 pm in SC 1425. |
| Friday 29 | 4:10-5:00 pm, room 1307. Partial Differential Equations Seminar. John Graef, University of Tennessee at Chattanooga. Nonlinear Boundary Value Problem for a Wing in an Air Flow or Why Engineers Should Use Nonlinear Analysis. We consider the problem of modeling the torsion of a wing in an air flow. An approximate equation for the torsion is derived. Along with the boundary conditions, this forms a non-linear Sturm-Liouville problem with the Mach number as the spectral parameter. Conditions under which a unique solution of the problem exists are presented and a characterization of the corresponding (smallest) Mach number is given. This smallest eigenvalue, which leads to the failure of the wing, is estimated by using a cubic approximation. The techniques used here also allow the calculation of the exact value for dry air. For some values of the parameters, these are both found to be significantly smaller than the value obtained using standard linear approximation techniques. (This is joint work with B. P. Belinskiy and R. E. Melnik of the University of Tennessee at Chattanooga.) |