Departmental Colloquium 2009-2010
Thursdays, 4:15 PM, JWB 335
October 8: No Colloquium -- Special Lecture sponsored by the Center for Science and Mathematics Education
NOTE: Different Room and time: Aline Skaggs Auditorium, 5:00 p.m.
Speaker:
Deborah Ball,
University of Michigan
Title: Improving Outcomes in Mathematics and Science: Making Change Work
Abstract:
Deborah Ball has been involved in mathematics education at many levels, from elementary school teacher,
through teacher educator, to Dean of a School of Education. She is among the very few who deserve and
enjoy genuine and deep respect from both research communities, in mathematics and education.
Her research focuses on the nature of mathematical knowledge, and the development of measures
that make possible the relationship among mathematical knowledge, quality of teaching and student performance.
She has long been involved in the study of interventions designed to improve quality and effectiveness of mathematical
instruction. Dr. Ball has served on many international commissions, and is at present on the National Mathematics Advisory Panel.
In this talk, Dr. Ball will discuss what we know about interventions that work, why they work, and ways in which serious
change can be effected.
October 29:
Speaker:
Oscar Garcia Prada,
Consejo Superior de Investigaciones Cientificas
Title:
Geometry of surface group representations
Abstract:
Given a compact real surface S and a semisimple
Lie group G, we consider the moduli space R(S,G) of representations
of the fundamental group of S in G (sometimes called the character
variety). This moduli space plays a central role in many problems
in geometry, topology and physics. By considering a complex
structure on the surface S (thus making it a Riemann surface),
the moduli space of representations is in bijection with a moduli
space of holomorphic objects, known as Higgs bundles. We explain
this correspondence and show how to use it to study the topology
of R(S,G). We give special attention to the case where G is the
isometry group of a non-compact Hermitian symmetric space.
In this situation the moduli space has special components that
can be regarded in some sense as generalizations of the
Teichmueller space of S (which can be identified with
a component of the character variety when G=PSL(2,R)).
November 5: SPECIAL COLLOQUIUM
Speaker:
Sam Payne,
Stanford University
Title:
Nonarchimedean geometry
Abstract:
The usual archimedean norm on the complex numbers and its associated
analytic geometry (holomorphic functions and differential forms) have
been fundamental tools for understanding the geometry and topology of
complex algebraic varieties, for instance through Hodge theory and
Lefschetz hyperplane theorems, since the beginnings of the subject.
Nonarchimedean norms, such as the p-adic norm on the rational numbers,
also have an associated analytic geometry which is well-known to
number theorists, but this theory is just beginning to be applied in
other areas of mathematics, such as algebraic geometry and dynamical
systems. This talk will be an introduction to nonarchimedean
geometry, through the basic notions of tropicalization and
analytification.
November 12:
Speaker:
Anthony Henderson,
University of Sydney
Title:
Enhancing the Jordan canonical form
Abstract:
In undergraduate linear algebra, we learned the Jordan canonical form theorem:
that every n x n complex matrix A is similar to an essentially unique matrix B
which is block-diagonal with each block having a very simple form (a single eigenvalue repeated down the diagonal,
ones on the super-diagonal, and zeroes elsewhere). This is of course very
useful for matrix calculations.
From the Lie-theoretic viewpoint, this theorem is about classifying the orbits of
the general linear group GL_n(C) in its adjoint representation. This suggests natural
follow-up questions about the closures of the orbits. It also raises the hope of finding
analogous orbit classifications for other representations of algebraic groups. After explaining
some of the general context, I will focus on a case which, despite its close proximity to the
Jordan canonical form theorem, has only recently been worked out: the direct
sum of the vector and adjoint representations of GL_n(C). This is joint work with Pramod Achar (Louisiana State University).
November 19:
Speaker:
George Papanicolaou,
Stanford University
Title:
Imaging with noise
Abstract:
It is somewhat surprising at first that it
is possible to locate a network of sensors from
cross correlations of noise signals that they
record. This is assuming that the speed of
propagation in the ambient environment is known and that the
noise sources are sufficiently diverse. If the
sensor locations are known and the propagation
speed is not known then it can be estimated from
cross correlation information. Although a basic
understanding of these possibilities had been
available for some time, it is the success of recent
applications in seismology that have revealed the
great potential of correlation methods, passive sensors
and the constructive use of ambient noise in imaging. I will
introduce these ideas in an interdisciplinary, mathematical
way and show that a great deal can be done with them.
Things become more complicated, and a mathematically
more interesting, when the ambient medium is also
strongly scattering. I will end with a review of what is
known so far in this case, and what might be expected.
December 3: SPECIAL COLLOQUIUM
Speaker:
Florian Herzig,
Northwestern University
Title: TBA
Abstract: TBA
January 14: SPECIAL COLLOQUIUM
Speaker:
Christel Hohenegger,
Courant Institute of Mathematical Science
Title: TBA
Abstract: TBA
March 4:
Speaker:
Liliana Borcea,
Rice University
Title: TBA
Abstract: TBA
March 11:
Speaker:
Gunther Uhlmann,
University of Washington
Title: TBA
Abstract: TBA
March 18:
Speaker:
Anne Thomas,
University of Oxford
Title: TBA
Abstract: TBA