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Series: CDSNS Colloquium

We present a mean field model of electroencephalographic activity in the brain, which is composed of a system of coupled ODEs and PDEs. We show the existence and uniqueness of weak and strong solutions of this model and investigate the regularity of the solutions. We establish biophysically plausible semidynamical system frameworks and show that the semigroups of weak and strong solution operators possess bounded absorbing sets. We show that there exist parameter values for which the semidynamical systems do not possess a global attractor due to the lack of the compactness property. In this case, the internal dynamics of the ODE components of the solutions can create asymptotic spatial discontinuities in the solutions, regardless of the smoothness of the initial values and forcing terms.

Series: AMS Club Seminar

All of us have seen talks where the speaker uses slides. Some are great,
and some are awful. Come and learn how to make great slide decks and
how to avoid making awful ones. We will share a number of pieces of
software that are easy to use and that can help
you to improve your slide decks. We will also discuss best practices
and dissect several short slide decks together. Next week there will be a follow-up, hands-on workshop on using the software Inkscape to create mathematical
figures for talks, posters, and papers.

Series: Combinatorics Seminar

The search for the asymptotics of the Ramsey function R(3,k) has a long and fascinating history. It begins in the hill country surrounding Budapest and winding over the decades through Europe, America, Korea and Rio de Janiero. We explore it through a CS lens, giving algorithms that provide the various upper and lower bounds. The arguments are various more or less sophisticated uses of Erdos Magic and, indeed, many of the most important advances in the Probabilistic Method have come from these investigations.

Friday, November 3, 2017 - 15:00 ,
Location: Skiles 154 ,
Hassan Attarchi ,
Georgia Tech ,
Organizer:

This presentation is about the results of a paper by L. Bunimovich in
1974. One considers dynamical systems generated by billiards which are
perturbations of dispersing billiards. It was shown that such dynamical
systems are systems of A. N. Kolmogorov (K-systems), if the perturbation
satisfies certain conditions which have an intuitive geometric
interpretation.

Friday, November 3, 2017 - 13:55 ,
Location: Skiles 006 ,
John Etnyre ,
Georgia Tech ,
Organizer: John Etnyre

In this series of talks I will introduce branched coverings of manifolds and sketch proofs of most the known results in low dimensions (such as every 3 manifold is a 3-fold branched cover over a knot in the 3-sphere and the existence of universal knots). This week we sstart discussing branched covers of 3-manifolds.

Friday, November 3, 2017 - 10:00 ,
Location: Skiles 114 ,
Jaewoo Jung ,
GA Tech ,
Organizer: Timothy Duff

We continue our discussion of free resolutions and Stanley-Reisner ideals. We introduce Hochster's formula and state results on the behavior of Betti tables under clique-sums.

Series: Stochastics Seminar

The Sherrington-Kirkpatirck (SK) model is
a mean-field spin glass introduced by theoretical physicists in order
to explain the strange behavior of certain alloys, such as CuMn. Despite
of its seemingly simple formulation, it was conjectured to possess a
number of profound properties. This talk will be focused on the energy
landscapes of the SK model and the mixed p-spin model with both Ising
and spherical configuration spaces. We will present Parisi formule for
their maximal energies followed by descriptions of the energy landscapes
near the maximum energy. Based on joint works with A. Auffinger, M. Handschy, G. Lerman, and A. Sen.

Series: Graph Theory Seminar

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 introduce
ideal frames, slim connectors and fat connectors. We will first deal
with the ideal frames without fat connectors, by studying 3-edge and
5-edge configurations. Joint work with Changong Li, Robin Thomas, and
Xingxing Yu.

Series: School of Mathematics Colloquium

Traditional Erdos Magic (a.k.a. The Probabilistic Method) proves the existence of an object with certain properties
by showing that a random (appropriately defined) object will have those properties with positive probability. Modern Erdos Magic analyzes a random process, a random (CS take note!) algorithm. These, when successful, can find a "needle in an exponential haystack" in polynomial time.
We'll look at two particular examples, both involving a family of n-element sets under suitable side conditions. The Lovasz Local Lemma finds a coloring with no set monochromatic. A result of this speaker finds a coloring with low discrepency. In both cases the original proofs were not implementable but Modern Erdos Magic finds the colorings in polynomial times.
The methods are varied. Basic probability and combinatorics. Brownian Motion. Semigroups. Martingales. Recursions ... and Tetris!

Thursday, November 2, 2017 - 11:05 ,
Location: Skiles 006 ,
Joel Spencer ,
Courant Institute, New York University ,
Organizer: Lutz Warnke
Traditional Erdos Magic (a.k.a. The Probabilistic Method) proves the existence of an object with certain properties by showing that a random (appropriately defined) object will have those properties with positive probability. Modern Erdos Magic analyzes a random process, a random (CS take note!) algorithm. These, when successful, can find a "needle in an exponential haystack" in polynomial time. We'll look at two particular examples, both involving a family of n-element sets under suitable side conditions. The Lovasz Local Lemma finds a coloring with no set monochromatic. A result of this speaker finds a coloring with low discrepency. In both cases the original proofs were not implementable but Modern Erdos Magic finds the colorings in polynomial times. The methods are varied. Basic probability and combinatorics. Brownian Motion. Semigroups. Martingales. Recursions ... and Tetris!