UNIVERSITY OF NEVADA, RENO
MATHEMATICS & STATISTICS
COLLOQUIUM SCHEDULE
Fall Semester 2007
Normal meeting time: Thursdays at 2:30 in
AB 635.
The Undergraduate Seminar Series may meet in other rooms.
Thursday, 9 August at 2:30
Prof. Ryan Derby-Talbot
Department of Mathematics
American University in Cairo
Heegaard splittings and amalgamations
ABSTRACT:
As one of the oldest constructions used for studying 3-manifolds,
Heegaard splittings can be related to interesting aspects of the topology of their
underlying manifolds. For example, a series of results starting with Casson and
Gordon in 1987 implies that the presence of an incompressible surface in a
3-manifold is equivalent to the manifold admitting a kind of Heegaard splitting
called an amalgamation. We will discuss some basic notions of such Heegaard
splittings, address the question of how to determine if a given Heegaard splitting
is an amalgamation, and then use our findings to examine some questions about
Heegaard splittings and their relationship to the topology of 3-manifolds.
Thursday, 16 August at 2:30 in AB 209
Prof. Hong Wang
Department of Mathematics
University of South Carolina
Columbia, South Carolina
An Eulerian-Lagrangian Formulation for Porous Medium Flow
ABSTRACT:
The mathematical models used to describe these fluid flow processes are
coupled systems of nonlinear advection-diffusion equations, which are
advection-diffusiontype with advection being the dominant process, and
constraining equations. Due to the nonlinearity and couplings of these
equations, the moving steep fronts and complicated structures present in
the solutions to these systems, the singularities of the solutions at
sources and sinks, the numerical treatment of these systems often
encounters severe difficulties.
Thursday, September 13 & 20 at 2:30 in AB 635
Ladies and Gentlemen...
Introducing the Department of Mathematics & Statistics!
In these special colloquia the Department will "introduce" itself,
specifically to current and prospective graduate students. After some
introductory comments, each of the departments' research "groups" will make
a short presentation, in which they will describe (in very general terms)
the research that their constituent members do. Graduate students
will introduce themselves, and tell about the research areas in which
they are interested.
We enthusiastically invite any graduate student, prospective graduate
student, or anyone else interested in finding out more about the
math/stat department here at UNR.
Thursday, September 27 at 2:30 in AB 635
Lloyd Douglas
Office of the VP for Research
University of Nevada, Reno
Funding Opportunities in the Mathematical Sciences at the
National Science Foundation
ABSTRACT:
Lloyd E. Douglas has been Assistant to the Vice President for Research
at UNR since April. Before coming here he spent 23 years at the
National Science Foundation, most recently as a program officer in NSF's
Division of Mathematical Sciences. In this talk, Lloyd will give some
background information and talk about selected programs at NSF, focusing
on those in the mathematical sciences but also including some NSF-wide
programs for all disciplines that may be of interest to mathematical
scientists. He will discuss common pitfalls in proposal writing that
can be applied to proposal writing in general. There will be ample
time to ask specific questions that you may have about NSF.
Monday, 8 October at 4:00 in AB 213
(note unusual time).
Prof. Oliver Dragicevic
Department of Mathematics and Physics
University of Ljubljana
Bilinear embedding for the harmonic oscillator
ABSTRACT:
We prove a dimension-free bilinear embedding theorem for the
Hermite operator on R^n. As a consequence we obtain dimension-free
estimates for the associated Riesz transforms and their iterates.
The method we utilize -the Bellman functions- allows the possibility
of generalizing these results to several other settings. This is
joint work with Alexander Volberg.
Tuesday, 9 October at 2:30 in AB 635
Prof. Alexander Matros
Department of Economics
University of Pittsburgh
Contests with a Stochastic Number of Players
ABSTRACT:
We study Tullock~Rs n-player contests where each player has an independent
probability 0 < p <= 1 to participate. A unique symmetric equilibrium is
found and its properties are analyzed. In particular, we show that the
individual equilibrium spending is single-peaked in the probability p for
a given number of players and satisfies a single-crossing property; but
the total equilibrium spending is monotonically increasing in the
participation probability, p, and in the number of potential players, n.
We also show that over-dissipation is a natural feature of the equilibrium
in our model. Our model has another interpretation: n-player private-value
contests where each player has two possible values 0 and V . Each player
can have value V with probability 0 < p <= 1.
Keywords: Contests, Stochastic number of players, Over-dissipation,
Imperfect Information.
JEL classification: C72, D72, D82.
The paper can be found
here (pdf).
Thursday, 18 October at 2:30 in AB 635
Prof. Elisenda Grigsby
Department of Mathematics
Columbia University
Applications of grid diagrams to questions in
low dimensional topolog
ABSTRACT:
Roughly speaking, low dimensional topology is the study of $3$-dimensional
manifolds and cobordisms between them. Several years ago, Ozsv{\'a}th and Szab{\'o}
introduced a collection of invariants, particularly well-adapted to this perspective, that
have had remarkable success in addressing numerous topological questions. However, until
recently, computation of these invariants was difficult, since their definition relied on
counts of $J$-holomorphic curves in a symplectic manifold.
Recent work of Manolescu, Ozsv{\'a}th, Sarkar, Szab{\'o}, Thurston, and Wang (in various
combinations) have placed a subset of these invariants on a firmly combinatorial footing.
In particular, the most robust of the Floer homology invariants, associated to a knot in
the three-sphere, can be combinatorially defined using so-called grid diagrams,
simple combinatorial objects obtained from a particular type of knot projection.
I will describe joint work with Baker and Hedden which generalizes this construction.
This generalization has already, in joint work with Ruberman and Strle, provided new
information about the smooth concordance group (which I will define), and we hope that it
will have applications to certain long-standing surgery questions.
Friday, 19 October at 2:00 in AB 635
(note unusual time).
Prof. Alexander Zevin
National Academy of Ukraine
SOME AMAZING PHENOMENA IN NONLINEAR DYNAMICS
ABSTRACT:
In this presentation we discuss some rigorously proved unexpected
qualitative properties of oscillations and stability of nonlinear
systems.
The first group of the results relates to periods and amplitudes of
periodic solutions of autonomous and nonautonomous systems. It is shown
that an ordinary harmonic oscillator possesses the smallest period and
largest forced oscillations amplitudes in the wide range of
nonconservative nonlinear systems. Analogous extreme properties are
found for multidegree of freedom systems.
Some of the results are associated with periodic oscillations of systems
with non-monotonic elastic characteristics. It is shown that in a system
with a softening characteristic (e.g., in a pendulum) forced and
parametric oscillations become unstable as the amplitudes increase. On
contrary, forced oscillations of a system with non-monotonic repulsive
characteristic (e.g., of an overturned pendulum) are unstable for small
and stable for large amplitudes. The above features are missed when
perturbation approaches are used.
Stability of systems consisting of a linear part and nonlinear bounded
uncertain terms when the last contain arbitrary time-varying delays is
considered. It appears that in a wide class of systems the "worst"
destabilizing terms are linear. Another surprising feature is that in
such systems the critical values of the uncertain terms are independent
upon the delay functions. Moreover, in some systems with uncertain
time-varying delay the most destabilizing nonlinear terms and delay
function can be simultaneously found while in the absence of the delay
the problem remains unsolved.
It is also shown that known mathematical models for some famous physical
processes are erroneous. In particular, modeling of a swing by a
pendulum with a periodic length is incorrect.
Monday, 22 October at 1:00 in AB 634
(note unusual time).
Undergraduate Seminar Series
Prof. Michael J. Adams
Department of Mathematics
Truman State University
Graphs, Linear Algebra, and Ecology
ABSTRACT:
The connections between graph theory and linear algebra,
and between linear algebra and ecology, are well-established. There
is also a small but growing body of literature built around
applications of graph theory to ecology: one such application is a
technique known as demographic loop analysis. In this talk I will
describe recent work in loop analysis in which graph theory, linear
algebra, and ecology come together in a beautiful and surprising way.
This talk should be accessible to anyone with a basic undergraduate
background in calculus and linear algebra.
Thursday, 1 November at 2:30 in AB 635
Josh Greene
Department of Mathematics
Princeton University
Milnor's freshman theorem
ABSTRACT:
When John Milnor was a freshman at Princeton, he proved that the total curvature
of a non-trivial knot in 3-space is more than 4*pi. I will present a recent "proof from
the book" of this result due to Ari Turner, which he also discovered as an undergraduate.
The proof involves a surprising application of the Buffon needle problem in probability,
and is completely elementary.
Thursday, 15 November at 2:30 in AB 635
Jongil Park
Department of Mathematical Sciences
Seoul National University, Korea
(& Math Dept, UC Berkeley)
ABSTRACT:
One of the fundamental problems in the classification of 4-manifolds is to find
a new family of simply connected smooth (symplectic, complex) 4-manifolds. Though
many interesting 4-manifolds have been constructed using techniques such as fiber
sum, rational blow-down, knot surgery and so on, it is still very hard to find a new
family of 4-manifolds with small Euler characteristic.
Since I discovered a new simply connected symplectic 4-manifold with b^+ = 1 and
K^2 = 2 in 2004 by using a rational blow-down surgery, many new simply connected
4-manifolds with small Euler characteristic have been constructed and now it is
one of most active research areas in 4-manifolds to find a new family of smooth
(symplectic, complex) 4-manifolds with b^+ = 1.
The aim of this talk is to review recent development in this area. In particular,
I'd like to survey the existence and the uniqueness problems of simply connected
4-manifolds with b^+= 1 in three levels - smooth category, symplectic category and
complex category.
Monday, 19 November at 5:30 in AB 638
(note unusual time).
Undergraduate Seminar Series
Prof. Paul Kirk
Department of Mathematics
Indiana University
Some comments on the Poincaré Conjecture
ABSTRACT:
Perelman recently settled the famous Poincaré conjecture and the
geometrization conjecture. I'll explain what the conjecture says, give a little
history, some examples, and the briefest outline of how Perelman approached and
solved the problem.
Tuesday, 2:30 in AB 635
Undergraduate Seminar Series
Postponed to the Spring semester; time and date to be determined.
Prof. Don Pfaff
Department of Mathematics & Statistics
University of Nevada, Reno
If circles were sqaure...
ABSTRACT: Since a circle is defined solely in terms of distance, if we changed
our definition of distance, the figure known as a circle would look different, as
would other figures such as ellipses, parabolas and hyperbolas. We will define
a reasonable distance so that circles are squares. What will ellipses look like?
Will the obvious answer, rectangles, be correct? Or will the answer be, like
all obvious answers to Pfaff's questions, wrong? Be sure to come and see the
exciting answer to this and, as time permits, other questions.
Thursday, 6 December at 2:30 in AB 635
Greggory Stefanelli
Server Systems Manager
University of Nevada, Reno Libraries
DataWorks server system and programs available, including Maple, SAS, Minitab, etc.
ABSTRACT:
The DataWorks citrix servers provide access to visualization tools and
mathematics oriented software packages on and off campus, accessible through the
Library website (see http://www2.library.unr.edu/dataworks/ for more information).
Various programs and services will be discussed, including data management
services, software development, system and software integration. I will also
discuss the DataWorks Analysis and Visualization Lab, located on Level 1 in the
Getchell Library.
Tuesday, 11 December at 2:30 in AB 635
Prof. Vladimir D. Shalfeev
Nizhny Novgorod University
Dynamic Chaos in Phase Systems: Generation, Synchronization and
Application to Chaos Communication
ABSTRACT:
In the last two decades the application of dynamic chaos to secure
wireless communication has attracted a flood of publications that
revealed the advantages and some pitfall of this approach as, for
example, weak noise resistance. In this presentation we describe a
promising solution to this problem which is based on exploiting the
properties of collective dynamics of ensembles of coupled self-excited
oscillators with phase control. This includes novel techniques for
generating and synchronizing of chaotic oscillators. In addition we will
illustrate the application of developed collective dynamics approach to
phasing antenna arrays.
Last spring's colloquium schedule.
Last fall's colloquium schedule.
The
Department of Mathematics & Statistics
is located on the 6th floor of the
Ansari Business Bldg.
