The Colloquia of the Department of Mathematics are normally held on Thursdays at 4:30pm in EA 160, preceded by Tea at 3:30pm in the Math Tower Top Floor Lounge (MW724), and followed by a dinner.
Our Colloquium is intended to be a vehicle for invited speakers to communicate to the entire department significant new developments in their fields of research, in a manner accessible to a broad mathematical audience. Graduate students and visitors are particularly welcome.
For information on a particular lecture, click the relevant "Abstract".
List of speakers and Abstracts will be updated as soon as relevant information becomes available.
A faculty member wishing to propose a speaker should click here
Colloquium
Time:
May 29 2008 - 4:30pm - 5:30 pm
Location: MA240
Speaker: Leonid Friedlander
Abstract:
Back in the 1930's, Pauling came up with an idea of approximating
electron wave functions in complicated molecules by functions on a graph:
the atoms are vertexes of this graph, and bonds are the edges. A wave
function is an eigenfunction
on the Schroedinger operator on the graph, which is a one-dimensional
variety, rather than
a combinatorial graph. Such a structure got a name of a quantum graph.
Recent advances in nano-technology drew attention to the study of
systems in narrow tubes,
and such system can also be approximated by quantum graphs.
In the talk, I will discuss both the approximation problems and the
Colloquium
Time:
May 22 2008 - 4:30pm - 5:30 pm
Location: MA240
Speaker: David Marker
Abstract:
In the 90s model theoretic methods were used by Wilkie to show
that sets defined in the real field with exponentiation have many of the
good geometric and topological properties of real algebraic varieties. For
example, any such set has only finitely many connected components. Complex
exponentiation has a very different flavor. The definability of the
integers leads to pathologies, but there is still some hope for a reasonable
theory of definable sets. In this lecture I will review some of the older
work on the real field and discuss Zilber's program for understanding
complex exponentiation.
Colloquium
Time:
May 15 2008 - 4:30pm - 5:30 pm
Location: MA 240
Speaker: Vladimir Turaev
Abstract:
Abstract. A study of Topological Quantum Field Theory in dimension 2 leads
to an interesting algebra (group-graded Frobenius algebras) and to
interesting topology (counting sections of fiber bundles over surfaces). I
will discuss these and related developments. No particular background is
required.
Colloquium
Time:
Apr 10 2008 - 4:30pm - 5:30 pm
Location: MA240
Speaker: Gunnar Carlsson
Abstract:
Abstract: The science and engineering disciplines are producing
enormous volumes of data from many different experimental sources. The
data comes in many forms, and developing methods for usefully analyzing
it is of great importance. In this talk, we will discuss some methods
arising out of topology for extracting qualitative information from
these data sets. We will discuss persistent homology, topological
methods for providing "roadmaps" to the data, and homotopy theoretic
methods for analyzing the stability of the road methods.
Colloquium
Time:
Mar 31 2008 - 4:30pm - 5:30 pm
Location: MA240
Speaker: Richard Schoen
Abstract:
We will discuss the geometric problem of classification of
compact Riemannian manifolds of positive sectional curvature. In
particular, we will describe our recent classification of pointwise
1/4-pinched manifolds. The work is joint with Simon Brendle and employs
the Ricci flow.
Colloquium
Time:
Mar 6 2008 - 4:30pm - 5:30 pm
Location: MA 240
Speaker: Einsiedler, Manfred
Abstract:
The dynamics on homogeneous spaces has many interesting connections to
number theory. One of the main problems here is to understand the
distribution of closed orbits for subgroups H of the ambient Lie group
G. In joint work with G.Margulis and A.Venkatesh we prove
an error rate in the equidistribution for semisimple subgroups H
acting on congruence quotients of G. This makes use of spectral gap in
the form of property (tau). However, the proof of our theorem can also
be used to prove all cases of property (tau) except for groups of type
A_1.
We will discuss the relationship between spectral gap, effective
Colloquium
Time:
Feb 21 2008 - 4:30pm - 5:30 pm
Location: MA 240
Speaker: Prof. Vitali Milman
Abstract:
The Asymptotic Geometric Analysis studies the asymptotic behavior of
finite- (but very high-)dimensional normed spaces and convex bodies when
dimension tends to infinity.
Contrary to common intuition, which anticipates enormous diversity
and chaotic behavior, we observe a uniform behavior for the whole family
of finite- (but high-)dimensional spaces. In the Introduction to our talk
we will demonstrate a couple of different and unexpected phenomena
accompanying high dimension.
In the second, the main part of the talk we will explain how the geometric
theory of convexity is extended to a larger category of log-concave
Colloquium
Time:
Feb 14 2008 - 4:30pm - 5:30 pm
Location: MA 240
Speaker: Prof.Karsten Grove
Abstract:
The simplest topologically non-trivial and also most symmetric
manifold is the euclidean n-sphere.
It is also characterized by having constant positive curvature (and
being simply connected).
This suggests two ways of approaching positive curvature: (1) Attempt
to understand manifolds with
so-called pinched positive curvature, i.e., bounded say between k and
1 with 0
Colloquium
Time:
Feb 28 2008 - 4:30pm - 5:30 pm
Location: MA 240
Speaker: Carl de Boor
Abstract:
While univariate polynomial interpolation has been a basic tool of scientific
computing for hundreds of years, multivariate polynomial interpolation is
much less understood. Already the question from which polynomial space to
choose an interpolant to given data has no obvious answer.
The talk presents, in some detail, one answer to this basic question, namely
the ``least interpolant'' of Amos Ron and the speaker which, among other nice
properties, is degree-reducing, then seeks some remedy for the resulting
discontinuity of the interpolant as a function of the interpolation sites,
then addresses the problem of a suitable representation of the interpolation
Colloquium
Time:
Jan 31 2008 - 4:30pm - 5:30 pm
Location: MA 240
Speaker: Anatole Katok
Abstract:
I will survey different methods of establishing that two
dynamical systems and, more generally, groups actions on compact
manifolds, are differentiably conjugate.
Those include among others regularity of the structural stability
conjugacy, KAM and combinatorics of invariant foliations. In the last
few years significant progress has been achieved in all
these directions.
In particular, I will consider situations when locally in the space
of systems smooth conjugacy can be determined by moduli.
One of attractive feature of the subject is that methods and
techniques from vastly different areas are used, including classical
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