Seminars and Colloquia by Series

Spectral analysis in bipartite biregular graphs and community detection

Series
Stochastics Seminar
Time
Thursday, September 14, 2017 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gerandy Brito – Georgia Institute of Technology –
This talk concerns to spectral gap of random regular graphs. First, we prove that almost all bipartite biregular graphs are almost Ramanujan by providing a tight upper bound for the non trivial eigenvalues of its adjacency operator, proving Alon's Conjecture for this family of graphs. Also, we use a spectral algorithm to recover hidden communities in a random network model we call regular stochastic block model. Our proofs rely on a technique introduced recently by Massoullie, which we developed for random regular graphs.

Two-three linked graphs

Series
Graph Theory Seminar
Time
Thursday, September 14, 2017 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shijie Xie – Math, GT
Let G be a graph containing 5 different vertices a0, a1, a2, b1 and b2. We say that (G, a0, a1, a2, b1, b2) is feasible if G contains disjoint connected subgraphs G1, G2, such that {a0, a1, a2}⊆V(G1) and {b1, b2}⊆V(G2). In this talk, we will continue our discussion on the operations we use for characterizing feasible (G, a0, a1, a2, b1, b2). If time permits, we will also discuss useful structures for obtaining that characterization, such as frame, ideal frame, and framework. Joint work with Changong Li, Robin Thomas, and Xingxing Yu.

Some Recent Sparse Bounds

Series
Analysis Seminar
Time
Wednesday, September 13, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael Lacey – Georgia Tech
A sparse bound is a novel method to bound a bilinear form. Such a bound gives effortless weighted inequalities, which are also easy to quantify. The range of forms which admit a sparse bound is broad. This short survey of the subject will include the case of spherical averages, which has a remarkably easy proof.

Tight contact structures on the Weeks manifold

Series
Geometry Topology Student Seminar
Time
Wednesday, September 13, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hyun Ki Min – Georgia Tech
The Weeks manifold W is a closed orientable hyperbolic 3-manifold with the smallest volume. Understanding contact structures on hyperbolic 3-manifolds is one of problems in contact topology. Stipsicz previously showed that there are 4 non-isotopic tight contact structures on the Weeks manifold. In this talk, we will exhibit 7 non-isotopic tight contact structures on W with non-vanishing Ozsvath-Szabo invariants.

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.

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