Seminars and Colloquia by Series

Antibiotic Cycling: A Cautionary Tale

Series
Research Horizons Seminar
Time
Wednesday, September 13, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Howie Weiss – GA Tech
Antibiotics have greatly reduced morbidity and mortality from infectious diseases. Although antibiotic resistance is not a new problem, it breadth now constitutes asignificant threat to human health. One strategy to help combat resistance is to find novel ways of using obsolete antibiotics. For strains of E. coli and P. aeruginosa, pairs of antibiotics have been found where evolution of resistance to one increases, sometimes significantly, sensitivity to the other. These researchers have proposed cycling such pairs to treat infections. Similar strategies are being investigated to treat cancer. Using systems of ODEs, we model several possible treatment protocols using pairs and triples of such antibiotics, and investigate the speed of ascent of multiply resistant mutants. Rapid ascent would doom this strategy. This is joint work with Klas Udekwu (Stockholm University).

High degree vertices on recursive trees

Series
Combinatorics Seminar
Time
Friday, September 8, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Laura Eslava – Georgia Tech
Among the most studied tree growth processes there are recursive trees and linear preferential attachment trees. The study of these two models is motivated by the need of understanding the evolution of social networks. A key feature of social networks is the presence of vertices that serve as hubs, connecting large parts of the network. While such type of vertices had been widely studied for linear preferential attachment trees, analogous results for recursive trees were missing. In this talk, we will present joint laws for both the number and depth of vertices with near-maximal degrees and comment on the possibilities that our methods open for future research. This is joint work with Louigi Addario-Berry.

The travel time to infinity in percolation

Series
Stochastics Seminar
Time
Thursday, September 7, 2017 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael Damron – Georgia Institute of Technology –
On the two-dimensional square lattice, assign i.i.d. nonnegative weights to the edges with common distribution F. For which F is there an infinite self-avoiding path with finite total weight? This question arises in first-passage percolation, the study of the random metric space Z^2 with the induced random graph metric coming from the above edge-weights. It has long been known that there is no such infinite path when F(0)<1/2 (there are only finite paths of zero-weight edges), and there is one when F(0)>1/2 (there is an infinite path of zero-weight edges). The critical case, F(0)=1/2, is considerably more difficult due to the presence of finite paths of zero-weight edges on all scales. I will discuss work with W.-K. Lam and X. Wang in which we give necessary and sufficient conditions on F for the existence of an infinite finite-weight path. The methods involve comparing the model to another one, invasion percolation, and showing that geodesics in first-passage percolation have the same first order travel time as optimal paths in an embedded invasion cluster.

Two-three linked graphs

Series
Graph Theory Seminar
Time
Thursday, September 7, 2017 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shijie Xie – School of Mathematics, Georgia Tech
Let $G$ be a graph containing 5 different vertices $a_0, a_1, a_2, b_1$ and $b_2$. We say that $(G,a_0,a_1,a_2,b_1,b_2)$ is feasible if $G$ contains disjoint connected subgraphs $G_1, G_2$, such that $\{a_0, a_1, a_2\}\subseteq V(G_1)$ and $\{b_1, b_2\}\subseteq V(G_2)$. We give a characterization for $(G,a_0,a_1,a_2,b_1,b_2)$ to be feasible, answering a question of Robertson and Seymour. This is joint work with Changong Li, Robin Thomas, and Xingxing Yu.In this talk, we will discuss the operations we will use to reduce $(G,a_0,a_1,a_2,b_1,b_2)$ to $(G',a_0',a_1',a_2',b_1',b_2')$ with $|V(G)|+|E(G)|>|V(G')|+E(G')$, such that $(G,a_0,a_1,a_2,b_1,b_2)$ is feasible iff $(G',a_0',a_1',a_2'b_1',b_2')$ is feasible.

Swarming, Interaction Energies and PDEs

Series
School of Mathematics Colloquium
Time
Thursday, September 7, 2017 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
José Antonio Carrillo – Imperial College London
I will present a survey of the main results about first and second order models of swarming where repulsion and attraction are modeled through pairwise potentials. We will mainly focus on the stability of the fascinating patterns that you get by random particle simulations, flocks and mills, and their qualitative behavior. Qualitative properties of local minimizers of the interaction energies are crucial in order to understand these complex behaviors. Compactly supported global minimizers determine the flock patterns whose existence is related to the classical H-stability in statistical mechanics and the classical obstacle problem for differential operators.

Summer Program for Operations Research Technology (SPORT)

Series
Research Horizons Seminar
Time
Wednesday, September 6, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Virginia Ahalt – DoD
SPORT is a 12-week *PAID* summer internship offered by the National Security Agency (NSA) that provides 8 U.S. Citizen graduate students the opportunity to apply their technical skills to current, real-world operations research problems at the NSA. SPORT looks for strong students in operations research, applied math, computer science, data science, industrial and systems engineering, and other related fields. Program Highlights: -- Paid internship (12 weeks, late May to mid-August 2018) -- Applications accepted September 1 - October 31, 2017 -- Opportunity to apply operations research, mathematics, statistics, computer science, and/or engineering skills -- Real NSA mission problems -- Paid annual and sick leave, housing available, most travel costs covered -- Flexible work schedule -- Opportunity to network with other Intelligence Agencies

Finite dimension Balian-Low type theorems

Series
Analysis Seminar
Time
Wednesday, September 6, 2017 - 01:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shahaf Nitzan – Georgia Tech
The classical Balian-Low theorem states that if both a function and it's Fourier transform decay too fast then the Gabor system generated by this function (i.e. the system obtained from this function by taking integer translations and integer modulations) cannot be an orthonormal basis or a Riesz basis.Though it provides for an excellent `thumbs--rule' in time-frequency analysis, the Balian--Low theorem is not adaptable to many applications. This is due to the fact that in realistic situations information about a signal is given by a finite dimensional vector rather then by a function over the real line. In this work we obtain an analog of the Balian--Low theorem in the finite dimensional setting, as well as analogs to some of its extensions. Moreover, we will note that the classical Balian--Low theorem can be derived from these finite dimensional analogs.

Rogue Fixed Points of Tree Automata on Galton-Watson Trees

Series
Combinatorics Seminar
Time
Friday, September 1, 2017 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Moumanti Podder – Georgia Tech –
This talk will focus on tree automata, which are tools to analyze existential monadic second order properties of rooted trees. A tree automaton A consists of a finite set \Sigma of colours, and a map \Gamma: \mathbb{N}^\Sigma \rightarrow \Sigma. Given a rooted tree T and a colouring \omega: V(T) \rightarrow \Sigma, we call \omega compatible with automaton A if for every v \in V(T), we have \omega(v) = \Gamma(\vec{n}), where \vec{n} = (n_\sigma: \sigma \in \Sigma) and n_\sigma is the number of children of v with colour \sigma. Under the Galton-Watson branching process set-up, if p_\sigma denotes the probability that a node is coloured \sigma, then \vec{p} = (p_\sigma: \sigma \in \Sigma) is obtained as a fixed point of a system of equations. But this system need not have a unique fixed point. Our question attempts to answer whether a fixed point of such a system simply arises out of analytic reasons, or if it admits of a probabilistic interpretation. I shall formally defined interpretation, and provide a nearly complete description of necessary and sufficient conditions for a fixed point to not admit an interpretation, in which case it is called rogue.Joint work with Tobias Johnson and Fiona Skerman.

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