Department of

Mathematics


Seminar Calendar
for events the day of Friday, May 1, 2015.

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Friday, May 1, 2015

10:00 am in Digital Computer Lab (DCL) room L440,Friday, May 1, 2015

Introduction to Sage

Sean Shahkarami (UIUC Math )

Abstract: Introduction to Sage, 10:00–noon (2 hours) SageMath is a highly-regarded open-source mathematics package. We will introduce the basics of using Sage and exploring mathematical structures in this hands-on workshop. Highly recommended for graduate students and other researchers in Mathematics. The Digital Computer Lab building is at Springfield and Mathews, just north of Grainger Library. Room L440 is located in the basement level at the east end of the building - enter through room L426.

4:00 pm in 147 Altgeld Hall,Friday, May 1, 2015

The maximum likelihood degree for rank 2 matrices via Euler characteristics

Jose Israel Rodriguez   [email] (University of Notre Dame )

Abstract: The maximum likelihood degree (ML degree) measures the algebraic complexity of a fundamental computational problem in statistics: maximum likelihood estimation on a statistical model. Work by June Huh, relates the ML degree of an algebraic variety (statistical model) to an Euler characteristic in the smooth case. More recent work by Nero Budur and Botong Wang relate a weighted sum of ML degrees to an Euler characteristic in the singular case. The new work presented here proves a closed form expression for the ML degree of 3 × n rank at most 2 matrices (this variety corresponds to a mixture of 2 independence models in statistics). This expression solves a conjecture by Hauenstein, [], and Sturmfels based on computations performed by the numerical algebraic geometry software Bertini. The talk will have a running example based on “DiaNA’s dice” to bridge statistics, Euler characteristics, and applied algebraic geometry. Joint work with Botong Wang.

4:00 pm in 241 Altgeld Hall,Friday, May 1, 2015

Directed paths in partially ordered spaces

Ben Fulan (UIUC Math)

Abstract: In topology, it is common to study the set of paths in a space $X$ (with some restrictions) as a space in its own right; one such example is the loop space $\Omega X$. If $X$ is equipped with a partial order, we can consider the space of directed paths in $X$, which are paths that are monotone increasing with respect to the partial order on $X$. Such spaces arise in computer science, particularly in the study of parallel computing. We will discuss properties of these spaces and investigate a few examples that are particularly useful in applications.

4:00 pm in 345 Altgeld Hall,Friday, May 1, 2015

Operator spaces with "few" subspaces

Timur Oikhberg (UIUC)

Abstract: It is known that, on the set of subspaces of a given separable Banach space (equipped with its Effros-Borel structure), the relation of isomorphism is analytic. Moreover, on the set of subspaces of $C[0,1]$, this relation is complete analytic - in a sense, $C[0,1]$ is the "most complicated" separable Banach space. On the opposite end of the scale, the Hilbert space is the "simplest" one - all of its infinite dimensional subspaces are isomorphic to each other. For other Banach spaces, very little is known about the complexity of the isomorphism relation between subspaces. In this joint work with C.Rosendal, we asked the same question about the relation of complete isomorphism between operator spaces. We constructed a separable operator space where this relation is $K_\sigma$. Do "simpler" operator spaces exist? A possible candidate will be mentioned. The talk does not require extensive knowledge of operator spaces. This if a joint work with C. Rosendal.