Seminars and Colloquiums
for the week of October 5, 2009
Speaker:
Associate Professor Hongqiu Chen, University of Memphis, Monday
Professor Danuta Kolodziejczyk, Warsaw University of Technology, Monday
Dr. Erol Akcay, NIMBioS Post Doc, Tuesday
Professor Danuta Kolodziejczyk, Warsaw University of Technology, Wednesday
Mr. Keith Penrod, Wednesday
Professor Stefan Richter, Wednesday
Associate Professor Alex Freire, Wednesday
Assistant Professor Fernando Schwartz, Thursday
Assistant Professor Remus Nicoara, Friday
Monday, October 5
MATHEMATICS COLLOQUIUM
TIME: 3:35 -4:35 p.m.
ROOM: Haslam Business Building, 102
SPEAKER: Associate Professor Hongqiu Chen, University of Memphis
TITLE: Solitary-wave Solutions of Systems of Nonlinear Dispersive Wave Equations
ABSTRACT: Evolution equations that feature both nonlinear and dispersive effects
often possess solitary-wave solutions. Theory for such waves has been developed
for
classes of equations of Korteweg-de Vries type, Schrodinger-type and regularized
long-wave-type, for example. Much less common has been an analysis of solitary-wave
solutions for systems of equations. This talk is concerned with solitary-wave
solutions of systems of nonlinear, dispersive wave equations arising in fluid
mechanics. While the general approach is guided by the methods that apply to
single
equations, the details of the theory are considerably more involved. After a
sketch
of the ideas that are used, we indicate how the theory works for various systems
arising in the physical description of waves. We illustrate this first for
a system
derived by Gear and Grimshaw (1984) for modelling the interaction of internal
waves. Parameters for the model are determined by the details of the stratification
upon which the waves subsist. As time permits, we will also discuss Boussinesq
systems that arise in describing the two-way propagation of long-crested surface
water waves and the systems recently derived by Bona, Cohen, and Wang.
TOPOLOGY SEMINAR
TIME: 11:15 -12:05 p.m.
ROOM: Jesse Harris Building, 12
SPEAKER: Professor Danuta Kolodziejczyk, Warsaw University of Technology
TITLE: Polyhedra for which every homotopy domination over itself is a homotopy
equivalence.
ABSTRACT: We consider a natural but open question, if there exists a finite
polyhedron $P$ and a homotopy domination of $P$ over $P$ that is not a homotopy
equivalence. (By a polyhedron we understand here a finite one.) The answer is
known
to be negative for orientable manifolds (Bernstein and Ganea, 1959). The same
can be
obtained for polyhedra with virtually-polycyclic fundamental groups (see DK,
2005),
by using some "regular" properties of such groups (as Hopficity),
and for
$1$-dimensional polyhedra (an easy exercise). We suspect that for $2$-dimensional
polyhedra and for polyhedra with soluble fundamental groups such an example
may
exist.
Tuesday, October 6
MATH ECOLOGY SEMINAR
TIME: 9:00 -9:50 a.m.
ROOM: NIMBioS small conference room
SPEAKER: Dr. Erol Akcay, NIMBioS Post Doc
TITLE: Habitat Placement for the Black-footed Ferret
Wednesday, October 7
TOPOLOGY SEMINAR
TIME: 11:15 -12:05
ROOM: Haslam Business Building, 112
SPEAKER: Professor Danuta Kolodziejczyk, Warsaw University of Technology
TITLE: "Homotopy dominations of polyhedra"
ABSTRACT: In this talk we consider natural, easy formulated, sometimes old but
unsolved, problems on homotopy dominations of polyhedra (by a polyhedron we
mean
here a finite one). We concentrate mainly on questions about the cardinality
of the
class of homotopy types dominated by a given polyhedron and about a quasi-order
in
this class determined by the relation of domination. The point of start to our
considerations was a problem of Karol Borsuk (in 1968): Does every polyhedron
homotopy dominate only finitely many different homotopy types? Unexpectedly,
the
answer is negative. On the other hand, for example, polyhedra with finite
fundamental group homotopy dominate only finitely many different homotopy types.
We
study also, among others, a similar question concerning homotopy decompositions
of
polyhedra into cartesian products (K. Borsuk, 1971): Does there exist a polyhedron
with infinitely many cartesian factors of different homotopy types? We present
some
results (including my new results) and some collection of still open questions
(including closely related, unsolved problems from algebra, i.e., finitely presented
groups theory).
ALGEBRA SEMINAR
TIME: 2:30- 3:20 p.m.
ROOM: Math Tutorial Center, 1st Floor, Temple Court
SPEAKER: Mr. Keith Penrod
TITLE: Big Free Groups
ANALYSIS SEMINAR
TIME: 3:35-4:30 p.m.
ROOM: Aconda Court 113
SPEAKER: Professor Stefan Richter
TITLE: Two-isometric operators and operator tuples on Hilbert spaces. I will
give an overview of some results concerning two-isometric operators. In a later
talk I plan to prove some results about two-isometric commutative operator tuples.
GEOMETRIC ANALYSIS SEMINAR (Optimal Transportation)
TIME: 4:30 -5:30 p.m.
ROOM: Haslam Business Building, 102
SPEAKER: Associate Professor Alex Freire
TITLE: Fluid mechanics and gradconvex rearrangements of maps
(Chapter 3 of Villani's 2003 textbook)
Thursday, October 8
JUNIOR COLLOQUIUM
TIME: 3:35 -4:35 p.m.
ROOM: Haslam Business Building, 102
SPEAKER: Assistant Professor Fernando Schwartz
TITLE: A taste of differential geometry: The Gauss-Bonnet theorem
ABSTRACT: Will give a proof of one of the most beautiful theorems in differential
geometry. Vector calculus is the only prerequisite for this talk.
***Free pizza will be available at 3:15 in AC113***
Friday, October 9
MATHEMATICS COLLOQUIUM
TIME: 3:35 -4:35 p.m.
ROOM: Haslam Business Building, 102
SPEAKER: Assistant Professor Remus Nicoara
TITLE: Subfactors and Quantum Symmetries
ABSTRACT: The theory of subfactors was initiated by V. Jones in the eighties
as a
Galois theory for inclusions of von Neumann algebras. Subfactors can be used
to
capture symmetries of various mathematical and physical objects. Part of this
structure can be uncovered by computing the standard invariant of the subfactor.
This is a group-like object naturally associated to the subfactor, consisting
in
commuting squares of inclusions of finite dimensional matrix algebras. We present
some recent finiteness results for commuting squares and standard invariants.
Applications to groups, Hopf algebras and Hadamard matrices are also discussed.
If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.
If you have questions, or a date you would like to confirm, please contact Dr. Steve Wise.
Week of:
Past notices:
Seminars from 2008-2009 academic year
Seminars from 2007-2008 academic year
Seminars from 2006-2007 academic year