Seminars and Colloquia by Series

Some Properties of Effective Hamiltonians

Series
PDE Seminar
Time
Tuesday, October 18, 2016 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Yifeng Yu – Universtiy of California, Irvine –
A major open problem in periodic homogenization of Hamilton-Jacobi equations is to understand deep properties of the effective Hamiltonian. In this talk, I will present some related works in both convex and non-convex situations. If time permits, relevant problems from applications in turbulent combustion and traffic flow will also be discussed.

Constrained exact optimization in Phylogenetics

Series
Mathematical Biology Seminar
Time
Tuesday, October 18, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tandy Warnow – The University of Illinois at Urbana-Champaign
The estimation of phylogenetic trees from molecular sequences (e.g., DNA, RNA, or amino acid sequences) is a major step in many biological research studies, and is typically approached using heuristics for NP-hard optimization problems. In this talk, I will describe a new approach for computing large trees: constrained exact optimization. In a constrained exact optimization, we implicitly constrain the search space by providing a set X of allowed bipartitions on the species set, and then use dynamic programming to find a globally optimal solution within that constrained space. For many optimization problems, the dynamic programming algorithms can complete in polynomial time in the input size. Simulation studies show that constrained exact optimization also provides highly accurate estimates of the true species tree, and analyses of both biological and simulated datasets shows that constrained exact optimization provides improved solutions to the optimization criteria efficiently. We end with some discussion of future research in this topic. (Refreshments will be served before the talk at 10:30.)

Genome-scale estimation of the Tree of Life

Series
IMPACT Distinguished Lecture
Time
Monday, October 17, 2016 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tandy Warnow – The University of Illinois at Urbana-Champaign
Estimating the Tree of Life is one of the grand computational challenges in Science, and has applications to many areas of science and biomedical research. Despite intensive research over the last several decades, many problems remain inadequately solved. In this talk I will discuss species tree estimation from genome-scale datasets. I will describe the current state of the art for these problems, what is understood about these problems from a mathematical perspective, and identify some of the open problems in this area where mathematical research, drawing from graph theory, combinatorial optimization, and probability and statistics, is needed. This talk will be accessible to mathematicians, computer scientists, probabilists and statisticians, and does not require any knowledge of biology. (Refreshments will be served after the talk.)

Backward SDE method for nonlinear filtering problems

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 17, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Yanzhao Cao – Auburn University Mathematics
A nonlinear filtering problem can be classified as a stochastic Bayesian optimization problem of identifying the state of a stochastic dynamical system based on noisy observations of the system. Well known numerical simulation methods include unscented Kalman filters and particle filters. In this talk, we consider a class of efficient numerical methods based on forward backward stochastic differential equations. The backward SDEs for nonlinear filtering problems are similar to the Fokker-Planck equations for SDEs. We will describe the process of deriving such backward SDEs as well as high order numerical algorithms to solve them, which in turn solve nonlinear filtering problems.

Pairings between periodic orbits in hyperbolic coupled map lattices.

Series
CDSNS Colloquium
Time
Monday, October 17, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Boris Gutkin – Georgia Tech (School of Physics)
Upon quantization, hyperbolic Hamiltonian systems generically exhibit universal spectral properties effectively described by Random Matrix Theory. Semiclassically this remarkable phenomenon can be attributed to the existence of pairs of classical periodic orbits with small action differences. So far, however, the scope of this theory has, by and large, been restricted to single-particle systems. I will discuss an extension of this program to hyperbolic coupled map lattices with a large number of sites (i.e., particles). The crucial ingredient is a two-dimensional symbolic dynamics which allows an effective representation of periodic orbits and their pairings. I will illustrate the theory with a specific model of coupled cat maps, where such a symbolic dynamics can be constructed explicitly.

Numerical calculation of domains of analyticity for Lindstedt expansions of KAM Tori.

Series
Dynamical Systems Working Seminar
Time
Friday, October 14, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 170
Speaker
Adrián P. Bustamante – Georgia Tech
In the first part of the talk(s) we are going to present a way to study numerically the complex domains of invariant Tori for the standar map. The numerical method is based on Padé approximants. For this part we are going to follow the work of C. Falcolini and R. de la LLave.In the second part we are going to present how the numerical method, developed earlier, can be used to study the complex domains of analyticity of invariant KAM Tori for the dissipative standar map. This part is work in progress jointly with R. Calleja.

Notions of knot concordance II

Series
Geometry Topology Working Seminar
Time
Friday, October 14, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jennifer Hom – Georgia Tech
The knot concordance group consists of knots in the three-sphere modulo the equivalence relation of smooth concordance. We will discuss two concordance invariants coming from knot Floer homology: tau and epsilon.

Approximately Sampling Elements with Fixed Rank in Graded Posets

Series
ACO Student Seminar
Time
Friday, October 14, 2016 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Matthew Fahrbach – College of Computing, Georgia Tech
Graded posets are partially ordered sets equipped with a unique rank function that respects the partial order and such that neighboring elements in the Hasse diagram have ranks that differ by one. We frequently find them throughout combinatorics, including the canonical partial order on Young diagrams and plane partitions, where their respective rank functions are the area and volume under the configuration. We ask when it is possible to efficiently sample elements with a fixed rank in a graded poset. We show that for certain classes of posets, a biased Markov chain that connects elements in the Hasse diagram allows us to approximately generate samples from any fixed rank in expected polynomial time. While varying a bias parameter to increase the likelihood of a sample of a desired size is common in statistical physics, one typically needs properties such as log-concavity in the number of elements of each size to generate desired samples with sufficiently high probability. Here we do not even require unimodality in order to guarantee that the algorithm succeeds in generating samples of the desired rank efficiently. This joint work with Prateek Bhakta, Ben Cousins, and Dana Randall will appear at SODA 2017.

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