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• #### Speaker: Mark Skandera (Lehigh University) - http://www.lehigh.edu/~mas906/

When: Mon, May 1, 2017 - 2:00pm
Where: Kirwan Hall 1311

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Abstract: The (type A) Hecke algebra $H_n(q)$ is a certain module over $\mathbb Z[q^{1/2},q^{-1/2}]$ which is a deformation
of the group algebra of the symmetric group. The $\mathbb Z[q^{1/2},q^{-1/2}]$-module of its trace functions
has rank equal to the number of integer partitions of $n$, and has bases which are natural deformations of
those of the symmetric group algebra trace module. While no known formulas give the evaluation of these traces at
the natural basis elements of $H_n(q)$, there are some nice combinatorial formulas for the evaulation of certain traces at certain Kazhdan-Lusztig basis elements. We will also discuss the open problem of evaluating these traces at other basis elements.
• #### Speaker: Martin Molina (University of Maryland) -

When: Mon, May 1, 2017 - 3:00pm
Where: Kirwan Hall 1311

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Abstract: http://www.terpconnect.umd.edu/~lvrmr/2016-2017-S/Classes/RIT.shtml
• #### Speaker: Grace Work (Vanderbilt University) -

When: Mon, May 1, 2017 - 3:15pm
Where: Kirwan Hall 1313

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Abstract: Computing the distribution of the gaps between slopes of saddle connections is a question that was studied first by Athreya and Cheung in the case of the torus, motivated by the connection with Farey fractions, and then in the case of the golden L by Athreya, Chaika, and Lelievre. Their strategy involved translating the question of gaps between slopes of saddle connections into return times under horocycle flow on the space of translation surfaces to a specific transversal. We show how to use this strategy to explicitly compute the distribution in the case of the octagon, how to generalize the construction of the transversal to the general Veech case (both joint work with Caglar Uyanik), and how to parametrize the transversal in the case of a generic genus 2 translation surface.
• #### Speaker: Andreas Stathopolous (College of William and Mary) - http://www.cs.wm.edu/~andreas/

When: Tue, May 2, 2017 - 3:30pm
Where: 3258 AV Williams

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Abstract: The computation of the trace of the inverse of a large matrix, A, appears
in many statistics, machine learning, and quantum mechanics applications.
Our driving application comes from Lattice Quantum Chromodynamics (LQCD).
When the size of A does not allow the use of direct methods, most
applications rely on the Hutchinson method, a Monte Carlo variant that
requires the solution of a linear system with A per step.
The variance of the estimator determines the accuracy and therefore the
computational cost of the method. For Hutchinson, the variance equals the
squared Frobenious norm of the matrix inverse, excluding its diagonal.

In this talk, we present some variance reduction techniques we developed
over the last few years that speed up the Hutchinson method. The goal is
to approximate the off-diagonal elements of the inverse of A based either
on structural or on spectral information.

For LQCD, where the discretization space is a 4D regular lattice torus,
our Hierarchical Probing method produces a sequence of Hadamard vectors
that, if used in the Hutchinson method, hierarchically annihilate elements
of the inverse of A whose vertices in the lattice are increasingly farther
from each other. Based on the decay of Green's function, this approach
has yielded significant variance reduction.

Our second approach is to deflate A from its smallest singular triplets.
The hope is that the variance of the deflated A is (much) smaller. Contrary
to low rank matrix approximations, the above deflation may actually
increase variance. We provide an analysis based on standard random unitary
matrices, and derive criteria on when to expect improvement.

Finally, we touch upon the daunting computational task of computing
the smallest singular triplets of A, and the recent progress our group
has made in this direction which are included in the software PRIMME.

• #### Speaker: Tsao-Hsien Chen (University of Chicago) - https://sites.google.com/site/tsaohsienchen/

When: Wed, May 3, 2017 - 2:00pm
Where: Kirwan Hall 1311

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Abstract: TBA
• #### Speaker: Miguel SanjuÃ¡n ( Physics, Universidad Rey Juan Carlos) -

When: Thu, May 4, 2017 - 12:30pm
Where: ERF 1207
• #### Speaker: Leonid Koralov (UMD) - https://www.math.umd.edu/~koralov/

When: Thu, May 4, 2017 - 2:00pm
Where: Kirwan Hall 1311

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Abstract: TBA