Seminars and Colloquia by Series

The weak Pinsker property

Series
School of Mathematics Colloquium
Time
Thursday, April 19, 2018 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tim Austin – UCLA Mathematics Department
This talk is about the structure theory of measure-preserving systems: transformations of a finite measure space that preserve the measure. Many important examples arise from stationary processes in probability, and simplest among these are the i.i.d. processes. In ergodic theory, i.i.d. processes are called Bernoulli shifts. Some of the main results of ergodic theory concern an invariant of systems called their entropy, which turns out to be intimately related to the existence of `structure preserving' maps from a general system to Bernoulli shifts. I will give an overview of this area and its history, ending with a recent advance in this direction. A measure-preserving system has the weak Pinsker property if it can be split, in a natural sense, into a direct product of a Bernoulli shift and a system of arbitrarily low entropy. The recent result is that all ergodic measure-preserving systems have this property. This talk will assume graduate-level real analysis and measure theory, and familiarity with the basic language of random variables. Past exposure to entropy, measure-theoretic probability or ergodic theory will be helpful, but not essential.

The Dehn-Nielsen-Baer Theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, April 18, 2018 - 14:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sarah Davis – GaTech
The theorem of Dehn-Nielsen-Baer says the extended mapping class group is isomorphic to the outer automorphism group of the fundamental group of a surface. This theorem is a beautiful example of the interconnection between purely topological and purely algebraic concepts. This talk will discuss the background of the theorem and give a sketch of the proof.

On the probability that a stationary Gaussian process with spectral gap remains non-negative on a long interval

Series
Analysis Seminar
Time
Wednesday, April 18, 2018 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Benjamin Jaye – Clemson University –
We discuss the probability that a continuous stationary Gaussian process on whose spectral measure vanishes in a neighborhood of the origin stays non-negative on an interval of long interval. Joint work with Naomi Feldheim, Ohad Feldheim, Fedor Nazarov, and Shahaf Nitzan

Dynamics of a degenerate PDE model of epitaxial crystal growth

Series
PDE Seminar
Time
Tuesday, April 17, 2018 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jian-Guo Liu – Duke University –
Epitaxial growth is an important physical process for forming solid films or other nano-structures. It occurs as atoms, deposited from above, adsorb and diffuse on a crystal surface. Modeling the rates that atoms hop and break bonds leads in the continuum limit to degenerate 4th-order PDE that involve exponential nonlinearity and the p-Laplacian with p=1, for example. We discuss a number of analytical results for such models, some of which involve subgradient dynamics for Radon measure solutions.

Joint GT-UGA Seminar at GT - Augmentations and immersed exact Lagrangian fillings by Yu Pan

Series
Geometry Topology Seminar
Time
Monday, April 16, 2018 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yu Pan – MIT
Augmentations and exact Lagrangian fillings are closely related. However, not all the augmentations of a Legendrian knot come from embedded exact Lagrangian fillings. In this talk, we show that all the augmentations come from possibly immersed exact Lagrangian fillings. In particular, let ∑ be an immersed exact Lagrangian filling of a Legendrian knot in $J^1(M)$ and suppose it can be lifted to an embedded Legendrian L in J^1(R \times M). For any augmentation of L, we associate an induced augmentation of the Legendrian knot, whose homotopy class only depends on the compactly supported Legendrian isotopy type of L and the homotopy class of its augmentation of L. This is a joint work with Dan Rutherford.

Joint GT-UGA Seminar at GT - Asymmetric L-space Knots by Ken Baker

Series
Geometry Topology Seminar
Time
Monday, April 16, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ken Baker – University of Miami
Based on the known examples, it had been conjectured that all L-space knots in S3 are strongly invertible. We show this conjecture is false by constructing large families of asymmetric hyperbolic knots in S3 that admit a non-trivial surgery to the double branched cover of an alternating link. The construction easily adapts to produce such knots in any lens space, including S1xS2. This is joint work with John Luecke.

Convolutional Neural Network with Structured Filters

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 16, 2018 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Xiuyuan Cheng – Duke University –
Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. The properties of convolutional filters in a trained network directly affect the quality of the data representation being produced. In this talk, we introduce a framework for decomposing convolutional filters over a truncated expansion under pre-fixed bases, where the expansion coefficients are learned from data. Such a structure not only reduces the number of trainable parameters and computation load but also explicitly imposes filter regularity by bases truncation. Apart from maintaining prediction accuracy across image classification datasets, the decomposed-filter CNN also produces a stable representation with respect to input variations, which is proved under generic assumptions on the basis expansion. Joint work with Qiang Qiu, Robert Calderbank, and Guillermo Sapiro.

Chaotic Transition States on the Monkey Saddle

Series
CDSNS Colloquium
Time
Monday, April 16, 2018 - 11:15 for 1 hour (actually 50 minutes)
Location
skiles 005
Speaker
Thomas Bartsch – Loughborough University

Please Note: Transition State Theory describes how a reactive system crosses an energy barrier that is marked by a saddle point of the potential energy. The transition from the reactant to the product side of the barrier is regulated by a system of invariant manifolds that separate trajectories with qualitatively different behaviour. The situation becomes more complex if there are more than two reaction channels, or possible outcomes of the reaction. Indeed, the monkey saddle potential, with three channels, is known to exhibit chaotic dynamics at any energy. We investigate the boundaries between initial conditions with different outcomes in an attempt to obtain a qualitative and quantitative description of the relevant invariant structures.

TBA

Trace Test

Series
Student Algebraic Geometry Seminar
Time
Friday, April 13, 2018 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tim Duff – Georgia Tech
The fundamental data structures for numerical methods in algebraic geometry are called "witness sets." The term "trace test" refers to certain numerical methods which verify the completeness of such witness sets. It is natural to ask questions about the complexity of such a test and in what sense its output may be regarded as "proof." I will give a basic exposition of the trace test(s) with a view towards these questions

Pages