Seminars and Colloquia by Series

Torus actions and faithful tropicalisations

Series
Algebra Seminar
Time
Friday, April 11, 2014 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jan Draisma – TU Eindhoven
Given a closed subvariety X of affine space A^n, there is a surjective map from the analytification of X to its tropicalisation. The natural question arises, whether this map has a continuous section. Recent work by Baker, Payne, and Rabinoff treats the case of curves, and even more recent work by Cueto, Haebich, and Werner treats Grassmannians of 2-spaces. I will sketch how one can often construct such sections when X is obtained from a linear space smeared around by a coordinate torus action. In particular, this gives a new, more geometric proof for the Grassmannian of 2-spaces; and it also applies to some determinantal varieties. (Joint work with Elisa Postinghel)

The Gaussian Radon transform for Banach spaces and machine learning

Series
Stochastics Seminar
Time
Thursday, April 10, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Irina Holmes – Louisiana State University
In this talk we investigate possible applications of the infinitedimensional Gaussian Radon transform for Banach spaces to machine learning. Specifically, we show that the Gaussian Radon transform offers a valid stochastic interpretation to the ridge regression problem in the case when the reproducing kernel Hilbert space in question is infinite-dimensional. The main idea is to work with stochastic processes defined not on the Hilbert space itself, but on the abstract Wiener space obtained by completing the Hilbert space with respect to a measurable norm.

The algebra of symmetric high-dimensional data

Series
School of Mathematics Colloquium
Time
Thursday, April 10, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jan Draisma – Eindhoven University of Technology
In this age of high-dimensional data, many challenging questions take the following shape: can you check whether the data has a certain desired property by checking that property for many, but low-dimensional data fragments? In recent years, such questions have inspired new, exciting research in algebra, especially relevant when the property is highly symmetric and expressible through systems of polynomial equations. I will discuss three concrete questions of this kind that we have settled in the affirmative: Gaussian factor analysis from an algebraic perspective, high-dimensional tensors of bounded rank, and higher secant varieties of Grassmannians. The theory developed for these examples deals with group actions on infinite-dimensional algebraic varieties, and applies to problems from many areas. In particular, I will sketch its (potential) relation to the fantastic Matroid Minor Theorem.

Hardy Space Theory on Product Spaces of Homogeneous Type Via Orthonormal Wavelet Bases

Series
Analysis Seminar
Time
Thursday, April 10, 2014 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ji Li – Macquarie University, Sydney, Australia
We study Hardy spaces on spaces X which are the n-fold product of homogeneous spaces. An important tool is the remarkable orthonormal wavelet basis constructed Hytonen. The main tool we develop is the Littlewood-Paley theory on X, which in turn is a consequence of a corresponding theory on each factor space. We make no additional assumptions on the quasi-metric or the doubling measure for each factor space, and thus we extend to the full generality of product spaces of homogeneous type the aspects of both one-parameter and multiparameter theory involving Littlewood-Paley theory and function spaces. Moreover, our methods would be expected to be a powerful tool for developing function spaces and the boundedness of singular integrals on spaces of homogeneous type. This is joint work with Yongsheng Han and Lesley Ward.

KP hierarchy for the cyclic quiver

Series
Analysis Seminar
Time
Wednesday, April 9, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Oleg Chalykh – University of Leeds
I will discuss a generalization of the KP hierarchy, which is intimately related to the cyclic quiver and the Calogero-Moser problem for the wreath-product $S_n\wr\mathbb Z/m\mathbb Z$.

Interpolating Sequences, Complex Analysis and Linear Algebra

Series
Research Horizons Seminar
Time
Wednesday, April 9, 2014 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Wick – School of Math
An important question in modern complex analysis is to obtain a characterization of the sequence of points in the disc {z_j} that interpolates any given target sequence {a_j} with an element of a space of analytic functions. In this talk we will discuss this question and reformulate it as a problem in linear algebra and then show how this can be solved with relatively straightforward tools. Connections to open questions will also be given.

Derivatives Pricing on Integrated Diffusion Processes: A General Perturbation Approach

Series
Mathematical Finance/Financial Engineering Seminar
Time
Tuesday, April 8, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Minqiang Li – Bloomberg
Many derivatives products are directly or indirectly associated with integrated diffusion processes. We develop a general perturbation method to price those derivatives. We show that for any positive diffusion process, the hitting time of its integrated process is approximately normally distributed when the diffusion coefficient is small. This result of approximate normality enables us to reduce many derivative pricing problems to simple expectations. We illustrate the generality and accuracy of this probabilistic approach with several examples, with emphasis on timer options. Major advantages of the proposed technique include extremely fast computational speed, ease of implementation, and analytic tractability.

Bergman Spaces, Toeplitz Operators and the Berezin Transform

Series
AMS Club Seminar
Time
Tuesday, April 8, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Robert Rahm – School of Math
This is the first meeting of the newly formed AMS chapter at Georgia Tech. There will be refreshments provided by the AMS club. Robert will discuss Bergman spaces , Toeplitz operators and the Berezin transform and how they are related.

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