Friday, August 30, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rani Hod – School of Mathematics, Georgia Tech
We study the Maker-Breaker component game, played on the edge set of a
regular graph.
Given a graph G, the s-component (1:b) game is defined as follows: in
every round Maker claims one free edge of G and Breaker claims b free
edges.
Maker wins this game if her graph contains a connected component of
size at least s; otherwise, Breaker wins the game.
For all values of Breaker's bias b, we determine whether Breaker wins
(on any d-regular graph) or Maker wins (on almost every d-regular
graph) and provide explicit winning strategies for both players.
To this end, we prove an extension of a theorem by
Gallai-Hasse-Roy-Vitaver about graph orientations without long
directed simple paths.
Joint work with Alon Naor.
Wednesday, August 28, 2013 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Matthew Clark – Northrop Grumman
Have you heard the urban legend that an experienced college
recruiter can make an initial decision on whether or not to read your
resume in less than six seconds? Would you like to see if your current resume can survive the six-second glance?Would you like to improve your chances of surviving the initial cut? Do you know what happens to your resume once you hand it to the recruiter? How do you craft a resume that competes with 100,000 other resumes? Dr. Matthew Clark has supported college recruiting efforts for a
variety of large corporations and is a master at sorting resumes in six
seconds or under. Join us August 28th, 2013 in Skiles 005 at noon for a discussion of how most industry companies handle resumes,
what types of follow up activities are worth-while, and, how to improve
your chances of having your resume pass the "six second glance".
Wednesday, August 28, 2013 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles Bld Room 005
Speaker
Mason Porter – Oxford, UK
I discuss "simple" dynamical systems on networks and examine how
network structure affects dynamics of processes running on top of
networks. I consider results based on "locally tree-like" and/or
mean-field and pair approximations and examine when they seem to work
well, what can cause them to fail, and when they seem to produce accurate
results even though their hypotheses are violated fantastically. I'll
also present a new model for multi-stage complex contagions--in which
fanatics produce greater influence than mere followers--and examine
dynamics on networks with hetergeneous correlations. (This talk discusses
joint work with Davide Cellai, James Gleeson, Sergey Melnik, Peter Mucha, J-P Onnela, Felix Reed-Tsochas, and Jonathan Ward.)
Monday, August 26, 2013 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Adam M. Fox – Department of Mathematics, Georgia Institute of Technology
Volume preserving maps naturally arise in the study of many natural phenomena including incompressible fluid-flows, magnetic field-line flows, granular mixing, and celestial mechanics. Codimension one invariant tori play a fundamental role in
the dynamics of these maps as they form boundaries to transport; orbits that begin on one side cannot cross to the other. In this talk I will present a Fourier-based, quasi-Newton scheme to compute
the invariant tori of three-dimensional volume-preserving maps. I will
further show how this method can be used to predict the perturbation
threshold for their destruction and study the mechanics of their breakup.
Chip-firing on graphs is a simple process with suprising connections to various areas of mathematics. In recent years it has been recognized as a combinatorial language for describing linear equivalence of divisors on graphs and tropical curves. There are two distinct chip-firing games: the unconstrained chip-firing game of Baker and Norine and the Abelian sandpile model of Bak, Tang, and Weisenfled, which are related by a duality very close to Riemann-Roch theory. In this talk we introduce generalized chip-firing dynamics via open covers which provide a fine interpolation between these two previously studied models.
Monday, August 26, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
John Etnyre – Georgia Tech
We will discuss how to define two invariants of knots using sutured Heegaard Floer homology, contact structures and limiting processes. These invariants turn out to be a reformulation of the plus and minus versions of knot Heegaard Floer homology and thus give a``sutured interpretation'' of these invariants and point to a deep connection between Heegaard Floer theory and contact geometry. If time permits we will also discuss the possibility of defining invariants of non-compact manifolds and of contact structures on such manifolds.
Thursday, August 22, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jordi-Lluis Figueras – Uppsala Univ.
Abstract: We develop techniques for the verication of the Chebyshev property of Abelian
integrals. These techniques are a combination of theoretical results, analysis of asymptotic
behavior of Wronskians, and rigorous computations based on interval arithmetic. We apply
this approach to tackle a conjecture formulated by Dumortier and Roussarie in [Birth of
canard cycles, Discrete Contin. Dyn. Syst. 2 (2009), 723781], which we are able to prove
for q <= 2.
Wednesday, August 21, 2013 - 16:30 for 1 hour (actually 50 minutes)
Location
Klaus 1116W
Speaker
Vijay V. Vazirani – School of Computer Science, Georgia Tech
Please Note: Hosted by School of Computer Science.
Equilibrium computation is among the most significant
additions to the theory of algorithms and computational complexity in
the last decade - it has its own character, quite distinct from the
computability of optimization problems.
Our contribution to this evolving theory can be summarized in the
following sentence: Natural equilibrium computation problems tend to
exhibit striking dichotomies. The dichotomy for Nash equilibrium,
showing a qualitative difference between 2-Nash and k- Nash for k > 2,
has been known for some time. We establish a dichotomy for market
equilibrium.
For this purpose. we need to define the notion of Leontief-free
functions which help capture the joint utility of a bundle of goods that
are substitutes, e.g., bread and bagels. We note that when goods are
complements, e.g., bread and butter, the classical Leontief function
does a splendid job. Surprisingly enough, for the former case, utility
functions had been defined only for special cases in economics, e.g.,
CES utility function.
We were led to our notion from the high vantage point provided by an
algorithmic approach to market equilibria.
Note: Joint work with Jugal Garg and Ruta Mehta.
Wednesday, August 21, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jose Rodriguez – UC Berkeley
Maximum likelihood estimation is a fundamental computational task in
statistics and it also involves some beautiful mathematics. The MLE
problem can be formulated as a system of polynomial equations whose
number of solutions depends on data and the statistical model. For
generic choices of data, the number of solutions is the ML-degree of the
statistical model. But for data with zeros, the number of solutions can
be different. In this talk we will introduce the MLE problem, give
examples, and show how our work has applications with ML-duality.This is a current research project with Elizabeth Gross.