Seminars, Colloquia, and Conferences
Colloquium
The colloquium meets on Fridays at 4:00pm in
BromfieldPearson 101, unless otherwise indicated.
Fall 2016
September 16, 2016
Metamathematical framework for a new music; inspired by Algebraic Geometry
Bangere P. Purnaprajna (University of Kansas)
Abstract:
It is wellknown that one can obtain deep insights about algebraic varieties defined
over a field K by working in a more general setting where varieties are defined over
rings containing K. In particular, the behavior of a variety as it moves in a family is
of deep interest, and plays a vital role in the theory of moduli spaces. This viewpoint
has yielded many interesting results, a few of which are proved by the speaker and his
collaborators. Inspired by these results and by Grothendieck's writing on nilpotents
in algebraic geometry, we develop a meta geometric framework for a new music that
integrates elements of Indian and western classical music, Jazz and the Blues. This
is part of an ongoing work with David Balakrishnan, director of the Turtle Island
String Quartet. This talk will feature some music as well.
September 23, 2016
Tempered representations: the stellar picture
Pierre Clare (Dartmouth University)
Abstract:
HarishChandra's Plancherel formula for semisimple Lie groups is a deep result of
harmonic analysis that can be seen as a generalization of the theory of Fourier series
in the context of unitary representations. The classes of representations that occur in
the Plancherel measure of a given group form a topological space called the tempered dual
of that group.
The purpose of this talk is to show how the use of C*algebras allows to study the
tempered dual of a Lie group as a noncommutative space and casts a new light on
representationtheoretic problems. The main concepts will be illustrated on 'small'
concrete examples.
September 30, 2016
The social role of mathematical proofs
Kenny Easwaran (Texas A&M University)
Abstract:
Much of mathematics proceeds by means of proof, but what makes proofs different from
other forms of verification or communication? What is the role of proofs in spreading
mathematical knowledge? Does the success of a proof depend on trusting the author?
What would it take to conclusively defeat a proof?
The talk is at 4pm in Eaton 206 and will be aimed at a level suitable to students
without much background assumed in math or philosophy.
October 7, 2016
Student Presentations from Directed Reading Program
Ruth MeadowMcLeod, Ryan Kohl, and Zach Munro
October 14, 2016
Inverse Problems in Adaptive Optics
Ronny Ramlau (Johannes Kepler University Linz)
Abstract:
Currently there is a new generation of large astronomical telescope under construction,
e.g. the European Extremely Large Telescope (EELT) of the European Southern Observatory
(ESO) with a mirror diameter of 39 meters or the Thirty Meter Telescope (TMT), build by
a consortium headed by Caltech. The operation of those huge telescopes require new
mathematical methods in particular for the
Adaptive Optics systems of the telescopes.
The image quality of ground based astronomical telescopes suffers from
turbulences in the atmosphere. Adaptive Optics (AO) systems use wavefront
sensor measurements of incoming light from guide stars to determine an optimal
shape of deformable mirrors (DM) such that the image of the scientific object
is corrected after reflection on the DM. The solution of this task involves
several inverse problems: First, the incoming wavefronts have to be reconstructed
from wavefront sensor measurements. The next step involves the solution of the
Atmospheric Tomography problem, i.e., the reconstruction of the turbulence profile
in the atmosphere. Finally, the optimal shape of the mirrors has to be determined.
As the atmosphere changes frequently, these computations have to be done in real time.
In the talk we introduce mathematical models for the elements of different Adaptive Optics
system such as Single Conjugate Adaptive Optics (SCAO) or Multi Conjugate Adaptive Optics
(MCAO) and present fast reconstruction algorithms as well as related numerical results for
each of the subtasks that achieve the accuracy and speed required for the operation of ELTs.
October 21, 2016
Reconfiguring Chains with Discrete Moves: Flips and Pops
Dr. Perouz Taslakian [Université libre de Bruxelles (Brussels, Belgium) and ROI Research on Investment Corp. (Montreal, Canada)]
Abstract:
Understanding motion has long been a central theme in both the theoretical and
applied sciences. But even as our expanding knowledge of the mechanism in which
objects move has led to developments in an array of applications, many basic
questions remain unresolved.
In this talk, we will look into the mechanics of motion for polygonal chains
and explore the question of whether it is possible to move between two different
configurations of a given polygon using a predefined move. We frame our question
as a problem in discrete geometry, whereby the moves we consider are a discrete
sequence of steps. We will see that even when considering restricted moves applied
to simple objects such as polygons, reconfiguration questions remain challenging.
In particular, we will talk about Erdős flips, and a more restricted version of
such flips called pops. Given a polygonal chain that lies in the 2dimensional plane,
a pop reflects a vertex of this chain across the line through its two neighbouring
vertices such that the resulting polygon lies in the same plane. We will see that
using techniques from dynamical systems theory, we can show that for certain classes
of polygons, the neighbourhood of any configuration that can be reached by smooth
motion can also be reached by pops.
November 4, 2016
Economic inequality from statistical physics point of view
Victor Yakovenko (University of Maryland, Physics Dept.)
Abstract:
By analogy with the probability distribution of energy in statistical physics,
the probability distribution of money among the agents in a closed economic system
is expected to follow the exponential BoltzmannGibbs law, as a consequence of entropy
maximization. Analysis of empirical data shows that income distributions in the USA,
European Union, and other countries exhibit a welldefined twoclass structure.
The majority of the population (about 97%) belongs to the lower class characterized
by the exponential ("thermal") distribution. The upper class (about 3% of the population)
is characterized by the Pareto powerlaw ("superthermal") distribution, and its share of
the total income expands and contracts dramatically during booms and busts in financial
markets. Globally, data analysis of energy consumption per capita around the world shows
decreasing inequality in the last 30 years and convergence toward the exponential probability
distribution, in agreement with the maximal entropy principle. Similar results are found
for the global probability distribution of CO2 emissions per capita.
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Spring 2017
February 24, 2017
Title TBA
David ZureickBrown (Emory College)
