Seminar Schedule
April 10 – 14, 2006
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY April 10, 2006
Algebra
2:30pm, Room 410
Speaker: Sarah Mason, UPenn and UGA
Title of talk: Some properties of nonsymmetric Schur functions,
part I.
Abstract: The first talk will introduce the nonsymmetric Schur
functions and the combinatorial object (skyline augmented fillings) used to
define them. The main result is a bijection which provides a decomposition of
the ordinary Schur functions.
The second talk will describe a combinatorial application and an application
to Schubert polynomials. Specifically, we introduce an analgoue of the Robinson-Schensted-Knuth
algorithm in the nonsymmetric setting and a method for computing the standard
basis associated to a given partition and permutation.
Topology/Geometry
2:30pm, Room 222
Speaker: Igor Belegradek, Georgia Tech
Title of talk: Towards negatively curved manifolds from
another universe.
Abstract: How many finite volume negatively curved manifolds
are out there? In dimensions >3 known examples typically involve ``surgery''
on arithmetic lattices. This procedure does not affect cusps, and in each known
example the cusps are inherited from the corresponding arithmetic hyperbolic
manifold. Is there another way? I shall survey some recent work (partially joint
with Vitali Kapovitch) on topology of cusps, and then exhibit a huge class of
manifolds that, in many ways, look like negatively curved ones.
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
VIGRE-Algebraic Geometry
3:30pm, Room 304
TUESDAY, April 11, 2006
*Please note, VIGRE groups that normally meet on THURSDAY are meeting on TUESDAY for this week only. Please also be aware that some of the rooms have changed.
VIGRE – Feynman Diagrams
2:00pm, Room 326
VIGRE – Cardiac Physiology
2:00pm, Room 640
VIGRE- Zeta Functions
2:15pm, Room 410
VIGRE-Algebraic Geometry
2:00pm, Room 304
WEDNESDAY, April 12, 2006
Geometry in the Curriculum Seminar
1:25pm, Aderhold, Room 111
Speaker: TBA
Title of talk: TBA
Algebraic Geometry
2:30pm, Room 410
Speaker: Valery Alexeev, University of Georgia
Title of talk: Rational cubic hypersurfaces in all dimensions
> 6 (after Mella)
Abstract: Questions about rationality of cubic hypersurfaces
are some of the most classical in algebraic geometry. The 1972 proof by Clemens-Griffiths
of nonrationality of all smooth cubic 3-folds was a major advance. The problem
whether a general cubic 4-fold is rational has been outstanding for over a century.
Numerous examples of higher-dimensional rational cubics were constructed, including
a series of examples of 4-folds by Hassett, but they all concerned even-dimensional
cubics. I will report on new major advance on rationality of cubics made by
Massimiliano Mella.
VIGRE- Algebra
2:30pm, Room 303
Speaker: Students
Title of talk: Cohomology in degree p+r
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Arithmetic Geometry/Number Theory
3:30pm, Room 304
No Meeting this week
Colloquium
3:30pm, Room 304
Speaker: Frank Zeilfelder (Mannheim, Germany)
Title of talk: Recent Developements in Multivariate Spline
Theory and Its Applications
Abstract: We report on some recent developements in the field
of multivariate splines and its applications, where the usage of these models
turns out to be advantageous. Multivariate splines are natural generalizations
of splines in one variable, where the piecewise polynomials satisfying smoothness
conditions are associated with partitions (such as triangulations and tetrahedral
partitions) of a given n-dimensional domain. Having certain applications in
mind, by definition these spaces provide the necessary flexiblity, but on the
other hand, the vast literature shows that these are very complex mathematical
objects. We investigate basic questions such as local interpolation by the spline
spaces, and discuss some related approximation methods, such as quasi-interpolation.
A common feature of the associated operators is the locality and stability of
the spline constructions, so that we are able to show that the splines (and
its piecewise derivatives) yield optimal (and nearly-optimal) approximation
order. The algorithmic complexity of the interpolation and approx-imation methods
is linear, and therefore the splines can be efficiently computed, evaluated,
and visualized on standard PCs. For these purposes, we take advantage of the
piecewise Bernstein-Bezier form of the splines that allows to apply standard
techniques well-known from CAGD (Computer Aided Geometric Design). We illustrate
the effectivity and efficiency of the new spline methods by showing some applications
involving the (re)construction of terrains and surfaces of arbitrary topology
type, as well as the high quality, interactive visualization of volume data,
which plays a key role in medical imaging, industrial quality control and other
areas.
THURSDAY, April 13, 2006
*Please note, VIGRE groups that normally meet on THURSDAY are meeting on
TUESDAY for this week only. Please also be aware that some of the rooms have
changed.
VIGRE-Graduate
Student Seminar
2:00p.m., Room 304
Speaker: Tara
Brendle, Louisiana State University
Title of talk: Mapping class groups and complexes of curves
Abstract: We will give a brief introduction to some elementary
combinatorial structures which arise naturally when studying curves on a surface.
Examples include the "curve complex", the "pants complex",
and the "cut-system complex". These simplicial complexes have recently
become important in topology, since, although simple to define, they in fact
encode a great deal of algebraic information, including the entire algebraic
structure of the mapping class group of a surface.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea
Special Topology Seminar
3:30pm, Room 304
Speaker: Tara
Brendle, Louisiana State University
Title of talk: Wicket subgroups of braid groups
Abstract: If we consider the standard embedding of a surface
in S3 bounding a handlebody on either side, then the Heegaard subgroup of the
mapping class group of the surface consists of those maps of the surface which
extend to both handlebodies. Hilden studied a particular subgroup of the Heegaard
group which also embeds as a subgroup of the braid group and hence arises naturally
in certain knot theoretic contexts and gave a finite set of generators for this
group. In this talk, we will consider Hilden's group as a group of motions of
"wickets" in upper-half space, and give a finite presentation for
it. We will also use the "wicket" viewpoint to relate Hilden's group
to the so-called "string group", or the group of motions of circles
in 3-space. This is joint work with Allen Hatcher.
FRIDAY, April 14, 2006
Probability Theory
2:30-3:30pm, Room 303
Speaker: Dong Hoon Shin, University of Georgia
Title of talk: Filtering of Markov Chains