Seminars and Colloquia Schedule

Metastability for discontinuous dynamical systems under Lévy noise: Case study on Amazonian Vegetation

Series
CDSNS Colloquium
Time
Monday, September 25, 2017 - 11:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Larissa Serdukova – Georgia Institute of Technology
For the tipping elements in the Earth’s climate system, the most important issue to address is how stable is the desirable state against random perturbations. Extreme biotic and climatic events pose severe hazards to tropical rainforests. Their local effects are extremely stochastic and difficult to measure. Moreover, the direction and intensity of the response of forest trees to such perturbations are unknown, especially given the lack of efficient dynamical vegetation models to evaluate forest tree cover changes over time. In this study, we consider randomness in the mathematical modelling of forest trees by incorporating uncertainty through a stochastic differential equation. According to field-based evidence, the interactions between fires and droughts are a more direct mechanism that may describe sudden forest degradation in the south-eastern Amazon. In modeling the Amazonian vegetation system, we include symmetric α-stable Lévy perturbations. We report results of stability analysis of the metastable fertile forest state. We conclude that even a very slight threat to the forest state stability represents L´evy noise with large jumps of low intensity, that can be interpreted as a fire occurring in a non-drought year. During years of severe drought, high-intensity fires significantly accelerate the transition between a forest and savanna state.

Computational hemodynamics for Computer Aided Clinical Trials: looking at the theory, struggling with the practice

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 25, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Alessandro Veneziani – Emory Department of Mathematics and Computer Science
When we get to the point of including the huge and relevant experience of finite element fluid modeling collected in over 25 years of experience in the treatment of cardiovascular diseases, the risk of getting “lost in translation” is real. The most important issues are the reliability that we need to guarantee to provide a trustworthy decision support to clinicians; the efficiency we need to guarantee to fit into the demand coming from a large volume of patients in Computer Aided Clinical Trials as well as short timelines required by special circumstances (emergency) in Surgical Planning. In this talk, we will report on some recent activities taken at Emory to make this transition possible. Reliability requirements call for an appropriate integration of measurements and numerical models, as well as for uncertainty quantification. In particular, image and data processing are critical to feeding mathematical models. However, there are several challenges still open, e.g. in simulating blood flow in patient-specific arteries after stent deployment; or in assessing the correct boundary data set to be prescribed in complex vascular districts. The gap between theory, in this case, is apparent and good simulation and assimilation practices in finite elements for clinical hemodynamics need to be drawn. The talk will cover these topics. For computational efficiency, we will cover some numerical techniques currently in use for coronary blood flow, like the Hierarchical Model Reduction or efficient methods for coping with turbulence in aortic flows. As Clinical Trials are currently one of the most important sources of information for medical research and practice, we envision that the suitable achievement of reliability and efficiency requirements will make Computer Aided Clinical Trials (specifically with a strong Finite-Elements-in-Fluids component) an important source of information with a significant impact on the quality of healthcare. This is a joint work with the scholars and students of the Emory Center for Mathematics and Computing in Medicine (E(CM)2), the Emory Biomech Core Lab (Don Giddens and Habib Samady), the Beta-Lab at the University of Pavia (F. Auricchio ). This work is supported by the US National Science Foundation, Projects DMS 1419060, 1412963 1620406, Fondazione Cariplo, Abbott Vascular Inc., and the XSEDE Consortium.

On boundaries of relatively hyperbolic right-angled Coxeter groups

Series
Geometry Topology Seminar
Time
Monday, September 25, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hung Tran – Georgia
We give "visual descriptions" of cut points and non-parabolic cut pairs in the Bowditch boundary of a relatively hyperbolic right-angled Coxeter group. We also prove necessary and sufficient conditions for a relatively hyperbolic right-angled Coxeter group whose defining graph has a planar flag complex with minimal peripheral structure to have the Sierpinski carpet or the 2-sphere as its Bowditch boundary. We apply these results to the problem of quasi-isometry classification of right-angled Coxeter groups. Additionally, we study right-angled Coxeter groups with isolated flats whose $\CAT(0)$ boundaries are Menger curve. This is a joint work with Matthew Haulmark and Hoang Thanh Nguyen.

p-adic metric line bundles and integral points on curves

Series
Algebra Seminar
Time
Monday, September 25, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Amnon Besser – Georgia Tech –

postponed from September 18

In this talk I first wish to review my work with Balakrishnan and Muller, giving an algorithm for finding integral points on curves under certain (strong) assumptions. The main ingredients are the theory of p-adic height pairings and the theory of p-adic metrized line bundles. I will then explain a new proof of the main result using a p-adic version of Zhang's adelic metrics, and a third proof which only uses the metric at one prime p. At the same time I will attempt to explain why I think this last proof is interesting, being an indication that there may be new p-adic methods for finding integral points.

Small scale creation in ideal fluid

Series
PDE Seminar
Time
Tuesday, September 26, 2017 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexander Kiselev – Duke University –
I will review recent results on small scale creation in solutions of the Euler equation. A numerical simulation due to Hou and Luo suggests a new scenario for finite time blow up in three dimensions. A similar geometry in two dimensions leads to examples with very fast, double exponential in time growth in the gradient of vorticity. Such growth is know to be sharp due to upper bounds going back to 1930s. If I have time, I will also discuss several models that have been proposed to help understand the three-dimensional case.

How to stretch taffy most efficiently?

Series
Research Horizons Seminar
Time
Wednesday, September 27, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Balazs Strenner – GA Tech
Taffy pullers are machines designed to stretch taffy. They can modeled by surface homeomorphisms, therefore they can be studied by geometry and topology. I will talk about how efficiency of taffy pullers can be defined mathematically and what some of the open questions are. I will also talk about Macaw, a computer program I am working on, which does related computations and which will hopefully help answer some of the open questions.

How to stretch taffy most efficiently?

Series
Research Horizons Seminar
Time
Wednesday, September 27, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Balasz Strenner – Georgia Tech
Taffy pullers are machines designed to stretch taffy. They can modeled by surface homeomorphisms, therefore they can be studied by geometry and topology. I will talk about how efficiency of taffy pullers can be defined mathematically and what some of the open questions are. I will also talk about Macaw, a computer program I am working on, which does related computations and which will hopefully help answer some of the open questions.

Quolloquium: Spectral geometry of quantum waveguides

Series
Other Talks
Time
Wednesday, September 27, 2017 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
David Krejcirik – Czech Technical University –

CORRECTED DATE. NOTE: This is the first in a forthcoming series of colloquia in quantum mathematical physics that will take place this semester. The series is a spin-off of last year's QMath conference, and is intended to be of broad interest to people wanting to know the state of the art of current topics in mathematical physics.

We shall make an overview of the interplay between the geometry of tubular neighbourhoods of Riemannian manifold and the spectrum of the associated Dirichlet Laplacian. An emphasis will be put on the existence of curvature-induced eigenvalues in bent tubes and Hardy-type inequalities in twisted tubes of non-circular cross-section. Consequences of the results for physical systems modelled by the Schroedinger or heat equations will be discussed.

Null-Homotopic Embedded Spheres of Codimenion One

Series
Geometry Topology Student Seminar
Time
Wednesday, September 27, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anubhav Mukherjee – Georgia Tech
Let S be an (n-1)-sphere smoothly embedded in a closed, orientable, smooth n-manifold M, and let the embedding be null-homotopic. We'll prove in the talk that, if S does not bound a ball, then M is a rational homology sphere, the fundamental group of both components of M\S are finite, and at least one of them is trivial. This talk is based on a paper of Daniel Ruberman.

Bounded Fourier multipliers with applications to Balian-Low type theorems

Series
Analysis Seminar
Time
Wednesday, September 27, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael Northington – Georgia Tech
The Gabor system of a function is the set of all of its integer translations and modulations. The Balian-Low Theorem states that the Gabor system of a function which is well localized in both time and frequency cannot form an Riesz basis for $L^2(\mathbb{R})$. An important tool in the proof is a characterization of the Riesz basis property in terms of the boundedness of the Zak transform of the function. In this talk, we will discuss results showing that weaker basis-type properties also correspond to boundedness of the Zak transform, but in the sense of Fourier multipliers. We will also discuss using these results to prove generalizations of the Balian-Low theorem for Gabor systems with weaker basis properties, as well as for shift-invariant spaces with multiple generators and in higher dimensions.

Curvature and Isoperimetry in Graphs

Series
Dissertation Defense
Time
Thursday, September 28, 2017 - 09:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Peter Ralli – School of Mathematics, Georgia Tech –
This dissertation concerns isoperimetric and functional inequalities in discrete spaces. The majority of the work concerns discrete notions of curvature. There isalso discussion of volume growth in graphs and of expansion in hypergraphs. [The dissertation committee consists of Profs. J. Romberg (ECE), P. Tetali (chair of the committee), W.T. Trotter, X. Yu and H. Zhou.]

Randomized Controlled Trials for Combinatorial Construction

Series
Joint School of Mathematics and ACO Colloquium
Time
Thursday, September 28, 2017 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tom Bohman – Carnegie Mellon University
The probabilistic method for constructing combinatorial objects has had a profound impact on the field since the pioneering work of Erdos in the first half of the twentieth century. Some recent applications of the probabilistic method build objects of interest by making a series of random choices that are guided by a simple rule and depend on previous choices. We give two examples of randomized algorithms of this type: random triangle removal and the triangle-free process. These algorithms address the classical questions of counting Steiner triple systems and determining the minimum independence number of a triangle-free graph on n vertices, respectively. Pseudo-random heuristics and concentration of measure phenomena play a central role in analyzing these processes.

Stability results in graphs of given circumference

Series
Graph Theory Seminar
Time
Thursday, September 28, 2017 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jie Ma – University of Science and Technology of China
In this talk we will discuss some Tur\'an-type results on graphs with a given circumference. Let $W_{n,k,c}$ be the graph obtained from a clique $K_{c-k+1}$ by adding $n-(c-k+1)$ isolated vertices each joined to the same $k$ vertices of the clique, and let $f(n,k,c)=e(W_{n,k,c})$. Kopylov proved in 1977 that for $c a recent result of Li et al. and independently, of F\"{u}redi et al. on non-Hamiltonian graphs. Moreover, we prove a stability result on a classical theorem of Bondy on the circumference. We use a novel approach, which combines several proof ideas including a closure operation and an edge-switching technique.

Packing nearly optimal Ramsey R(3,t) Graphs

Series
ACO Student Seminar
Time
Friday, September 29, 2017 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
He Guo – School of Mathematics, Georgia Tech –
In 1995 Kim famously proved the Ramsey bound $R(3,t) \ge c t^2/\log t$ by constructing an $n$-vertex graph that is triangle-free and has independence number at most $C \sqrt{n \log n}$. We extend this celebrated result, which is best possible up to the value of the constants, by approximately decomposing the complete graph $K_n$ into a packing of such nearly optimal Ramsey $R(3,t)$ graphs. More precisely, for any $\epsilon>0$ we find an edge-disjoint collection $(G_i)_i$ of $n$-vertex graphs $G_i \subseteq K_n$ such that (a) each $G_i$ is triangle-free and has independence number at most $C_\epsilon \sqrt{n \log n}$, and (b) the union of all the $G_i$ contains at least $(1-\epsilon)\binom{n}{2}$ edges. Our algorithmic proof proceeds by sequentially choosing the graphs $G_i$ via a semi-random (i.e., Rödl nibble type) variation of the triangle-free process. As an application, we prove a conjecture in Ramsey theory by Fox, Grinshpun, Liebenau, Person, and Szabó (concerning a Ramsey-type parameter introduced by Burr, Erdös, Lovász in 1976). Namely, denoting by $s_r(H)$ the smallest minimum degree of $r$-Ramsey minimal graphs for $H$, we close the existing logarithmic gap for $H=K_3$ and establish that $s_r(K_3) = \Theta(r^2 \log r)$. Based on joint work with Lutz Warnke.

No seminar: ACO Student Seminar + ACO Colloquium + Atlanta Lecture Series (on Thursday + Friday + Weekend)

Series
Combinatorics Seminar
Time
Friday, September 29, 2017 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
none – Georgia Tech
No Combinatorics Seminar, but many others of interest: (a) on Friday [September 29th, 1pm-2pm in Skiles 005] He Guo, will give an ACO Student Seminar on "Packing nearly optimal Ramsey R(3,t) Graphs" (b) on Thursday [September 28th, 11am-12am in Skiles 006] Tom Bohman will give an ACO colloquim talk on "Randomized Controlled Trials for Combinatorial Construction" (c) on Saturday and Sunday [September 30th and October 1st] Atlanta Lecture Series in Combinatorics and Graph Theory XX takes place at Georgia Tech, with featured speaker Paul Seymour

An infinite dimensional hamiltonian dynamical system from MFG theory

Series
Dynamical Systems Working Seminar
Time
Friday, September 29, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 154
Speaker
Sergio Mayorga – Georgia Tech
We will look at a system of hamiltonian equations on the torus, with an initial condition in momentum and a terminal condition in position, that arises in mean field game theory. Existence of and uniqueness of solutions will be shown, and a few remarks will be made in regard to its connection to the minimization problem of a cost functional.