Seminars and Colloquia by Series

All finite groups are involved in the mapping class group

Series
Geometry Topology Seminar
Time
Friday, November 8, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
G. Masbaum – Institut de Mathématiques de Jussieu
Let g be a positive integer and let Gamma_g be the mapping class group of the genus g closed orientable surface. We show that every finite group is involved in Gamma_g. (Here a group G is said to be involved in a group Gamma if G is isomorphic to a quotient of a subgroup of Gamma of finite index.) This answers a question asked by U. Hamenstadt. The proof uses quantum representations of mapping class groups. (Joint work with A. Reid.)

Forbidden Vertices

Series
ACO Student Seminar
Time
Friday, November 8, 2013 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Gustavo Angulo – ISyE, Georgia Tech
In this talk, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of linear optimization over the subset of vertices of P that are not contained in X. This problem is closely related to finding the k-best basic solutions to a linear problem. We show that the complexity of the problem changes significantly depending on how both P and X are described, that is, on the encoding of the input data. For example, we analyze the case where the complete linear formulation of P is provided, as opposed to the case where P is given by an implicit description (to be defined in the talk). When P has binary vertices only, we provide additional tractability results and linear formulations of polynomial size. Some applications and extensions to integral polytopes will be discussed. Joint work with Shabbir Ahmed, Santanu S. Dey, and Volker Kaibel.

The 2-core of a Random Inhomogeneous Hypergraph

Series
Stochastics Seminar
Time
Thursday, November 7, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Omar Abuzzahab – Georgia Tech
The 2-core of a hypergraph is the unique subgraph where all vertices have degree at least 2 and which is the maximal induced subgraph with this property. This talk will be about the investigation of the 2-core for a particular random hypergraph model --- a model which differs from the usual random uniform hypergraph in that the vertex degrees are not identically distributed. For this model the main result proved is that as the size of the vertex set, n, tends to infinity then the number of hyperedges in the 2-core obeys a limit law, and this limit exhibits a threshold where the number of hyperedges in the 2-core transitions from o(n) to Theta(n). We will discuss aspects of the ideas involved and discuss the background motivation for the hypergraph model: factoring random integers into primes.

On Higher-Dimensional Oscillation in Ergodic Theory

Series
Analysis Seminar
Time
Wednesday, November 6, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ben Krause – UCLA
We will discuss the fine notion of the pointwise convergence of ergodic averages in setting where one the ergodic transformation is a Z^d action, and the averages are over more exotic sets than just cubes. In this setting, pointwise convergence does not follow from the usual ergodicity arguments. Bourgain, in his study of the polynomial ergodic averages invented the variational technique, which we extend to our more exotic averages.

A general learning framework in vector-valued Reproducing Kernel Hilbert Spaces

Series
Applied and Computational Mathematics Seminar
Time
Tuesday, November 5, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ha Quang, Minh – Istituto Italiano di Technologia (IIT), Genova, Italy –
Reproducing kernel Hilbert spaces (RKHS) have recently emerged as a powerful mathematical framework for many problems in machine learning, statistics, and their applications. In this talk, we will present a formulation in vector-valued RKHS that provides a unified treatment of several important machine learning approaches. Among these, one is Manifold Regularization, which seeks to exploit the geometry of the input data via unlabeled examples, and one is Multi-view Learning, which attempts to integrate different features and modalities in the input data. Numerical results on several challenging multi-class classification problems demonstrate the competitive practical performance of our approach.

Tropical schemes, tropical cycles, and valuated matroids

Series
Algebra Seminar
Time
Monday, November 4, 2013 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Diane Maclagan – University of Warwick
The tropical cycle associated to a subvariety of a torus is the support of a weighted polyhedral complex that that records information about the original variety and its compactifications. In a recent preprint Jeff and Noah Giansiracusa introduced a notion of scheme structure for tropical varieties, and showed that the tropical variety as a set is determined by this tropical scheme structure. I will outline how to also recover the tropical cycle from this information. This involves defining a variant of Grobner theory for congruences on the semiring of tropical Laurent polynomials. The lurking combinatorics is that of valuated matroids. This is joint work with Felipe Rincon.

A history of psd and sos polynomials (before the work of the speaker and his host)

Series
Algebra Seminar
Time
Monday, November 4, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bruce Reznick – University of Illinois, Urbana-Champaign
A real polynomial is called psd if it only takes non-negative values. It is called sos if it is a sum of squares of polynomials. Every sos polynomial is psd, and every psd polynomial with either a small number of variables or a small degree is sos. In 1888, D. Hilbert proved that there exist psd polynomials which are not sos, but his construction did not give any specific examples. His 17th problem was to show that every psd polynomial is a sum of squares of rational functions. This was resolved by E. Artin, but without an algorithm. It wasn't until the late 1960s that T. Motzkin and (independently) R.Robinson gave examples, both much simpler than Hilbert's. Several interesting foundational papers in the 70s were written by M. D. Choi and T. Y. Lam. The talk is intended to be accessible to first year graduate students and non-algebraists.

Nonlocal models for insect swarms

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 4, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Chad Higdon-Topaz – Macalester College
From bird flocks to ungulate herds to fish schools, nature abounds with examples of biological aggregations that arise from social interactions. These interactions take place over finite (rather than infinitesimal) distances, giving rise to nonlocal models. In this modeling-based talk, I will discuss two projects on insect swarms in which nonlocal social interactions play a key role. The first project examines desert locusts. The model is a system of nonlinear partial integrodifferential equations of advection-reaction type. I find conditions for the formation of an aggregation, demonstrate transiently traveling pulses of insects, and find hysteresis in the aggregation's existence. The second project examines the pea aphid. Based on experiments that motion track aphids walking in a circular arena, I extract a discrete, stochastic model for the group. Each aphid transitions randomly between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid’s nearest neighbor. For large nearest neighbor distances, when an aphid is isolated, its motion is ballistic and it is less likely to stop. In contrast, for short nearest neighbor distances, aphids move diffusively and are more likely to become stationary; this behavior constitutes an aggregation mechanism.

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