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Series: Other Talks

Hosted by Roman Grigoriev, School of Physics

We have studied large, heterogeneous populations of discrete
chemical oscillators (~100,000) to characterize two different types of
density-dependent transitions to synchronized behavior, a gradual Kuramoto
synchronization and a sudden quorum sensing synchronization. We also
describe the formation of phase clusters, where each cluster has the same
frequency but is phase shifted with respect to other clusters, giving rise
to a global signal that is more complex than that of the individual
oscillators. Finally, we describe experimental and modeling studies of
chimera states and their relation to other synchronization states in
populations of coupled chemical oscillators.

Series: Other Talks

We will discuss an extension of the entropy power inequality
in terms of the Renyi entropy to sums of independent random vectors
(with densities). Joint work with G. Chistyakov.

Series: Other Talks

Second featured lecture in the Atlanta Lecture Series in Combinatorics and Graph Theory mini-conference

The study of graphs with high girth and high chromatic number
had a profound influence on the history of Combinatrics and Graph Theory,
and led to the development of sophisticated methods involving tools
from probability, topology, number theory, algebra and combinatorics. I
will discuss the topic focusing on a recent new explicit construction
of graphs (and hypergraphs) of high girth and high chromatic number,
in joint work with Kostochka, Reiniger, West and Zhu.

Series: Other Talks

First featured lecture in the Atlanta Lecture Series in Combinatorics and Graph Theory mini-conference

I will describe several old and new applications of topological
and algebraic methods in the derivation of combinatorial results. In all
of them the proofs provide no efficient solutions for the corresponding
algorithmic problems.

Series: Other Talks

We propose a term structure power price model that, in contrast
to widely accepted no-arbitrage based approaches, accounts for the
non-storable nature of power. It belongs to a class of equilibrium game
theoretic models with players divided into producers and consumers. The
consumers' goal is to maximize a mean-variance utility function subject to
satisfying an inelastic demand of their own clients (e.g households,
businesses etc.) to whom they sell the power. The producers, who own a
portfolio of power plants each defined by a running fuel (e.g. gas, coal,
oil...) and physical characteristics (e.g. efficiency, capacity, ramp
up/down times...), similarly, seek to maximize a mean-variance utility
function consisting of power, fuel, and emission prices subject to
production constraints. Our goal is to determine the term structure of the
power price at which production matches consumption. We show that in such a
setting the equilibrium price exists and discuss the conditions for its
uniqueness. The model is then extended to account for transaction costs and
liquidity considerations in actual trading. Our numerical simulations
examine the properties of the term structure and its dependence on various
model parameters. We then further extend the model to account for the
startup costs of power plants. In contrast to other approaches presented in
the literature, we incorporate the startup costs in a mathematically
rigorous manner without relying on ad hoc heuristics. Through numerical
simulations applied to the entire UK power grid, we demonstrate that the
inclusion of startup costs is necessary for the modeling of electricity
prices in realistic power systems. Numerical results show that startup
costs make electricity prices very spiky. In a final refinement of the
model, we include a grid operator responsible for managing the grid.
Numerical simulations demonstrate that robust decision making of the grid
operator can significantly decrease the number and severity of spikes in
the electricity price and improve the reliability of the power grid.

Series: Other Talks

The workshop will be held from Monday October 26 - Wednesday October 28, 2015.
The purpose of this workshop is to promote communication among the many mathematical and engineering communities currently researching polytopal discretization methods for the numerical approximation of solutions of partial differential equations. A variety of distinct polytopal element methods (POEMs) have been designed to solve the same types of problems, but a workshop-type environment is required to foster a community-wide understanding of the comparative advantages of each technique and to develop a set of ‘best practices’ in regards to implementation. Registration is required.

Series: Other Talks

Friday October 23 through Sunday October 25 Emory will host the
Georgia Algebraic Geometry symposium
featuring the following invited speakers:
Valery Alexeev (University of Georgia);
Brian Conrad (Stanford University);
Brian Lehman (Boston College);
Max Lieblich (University of Washington);
Alexander Merkurjev (UCLA);
Alena Pirutka (Ecole Polytechnique);
Aaron Pixton (Harvard University);
Tony Varilly-Alvarado (Rice University);
Olivier Wittenberg (CNRS - Ecole Normale Superieure).

Series: Other Talks

This is the fourth meeting in a series of a reading seminars. In this lecture we will analyze the distribution of the eigenvalues of GUE ensembles. We will use Hermite polynomials to get very concrete computations. This way we will recover the semicircular law and we will also discuss a little bit the top eigenvalue.

Series: Other Talks

Light refreshments at 6:30pm

Theoretical models of disordered materials yield precise
predictions about the efficiency of communication codes
and the typical complexity of certain combinatorial
optimization problems. The underlying common structure
is that of many discrete variables, whose interaction is
represented by a random 'tree like' sparse graph.
We review recent progress in proving such predictions
and the related algorithmic insights gained from it.
This talk is based on joint works with Andrea Montanari,
Allan Sly and Nike Sun.

Series: Other Talks

All students interested in graduate studies in the School of Math are invited to attend the "prospective student day."
This event will offer the opportunity to hear about our graduate degree options, requirements for admission, as well as meet our Faculty and current graduate students. Prospective students from underrepresented groups in the Mathematical Sciences and students from the Atlanta area are particularly encouraged to attend.
If you plan to attend, please send your name, the year you plan to graduate, and the college you are attending to dgs@math.gatech.edu. See the schedule for more details.