UNIVERSITY OF NEVADA, RENO
MATHEMATICS & STATISTICS
COLLOQUIUM SCHEDULE
Spring 2008
Normal meeting time: Thursdays at 2:30
Thursday, 31 January at 2:30 in AB 206
Matt Hedden
Department of Mathematics
Massachusetts Institute of Technology
On Floer homology and knots admitting lens space surgeries
ABSTRACT:
There is a simple procedure called (Dehn) surgery which alters three
dimensional manifolds using knots. The simplest three-manifolds are called
lens spaces, and there is a conjecture regarding the knots on which one can
perform surgery to obtain these manifolds. In this talk, I'll review these
notions and discuss this conjecture, known as the Berge conjecture. I'll then
discuss a strategy, developed jointly with Ken Baker and Eli Grigsby by which
the knot Floer homology invariants of Ozsvath, Szabo, and Rasmussen could be
used to prove this conjecture.
Thursday, 7 February at 2:30 in AB 206
Prof. Alex Trindade
Department of Mathematics & Statistics
Texas Tech University
Modeling and Approximating the Distributions of Estimators of
Financial Risk Under Asymmetric Laplace Laws
ABSTRACT:
Explicit expressions are derived for parametric and nonparametric
estimators of two measures of financial risk, Value-at-Risk (VaR) and
Conditional Value-at-Risk (CVaR), under
random sampling from the Asymmetric Laplace (AL)
distribution. Asymptotic distributions are established under very
general conditions. Finite sample distributions are investigated by
means of saddlepoint approximations. The latter are highly
computationally intensive, requiring novel approaches to approximate
moments and special functions that arise in the evaluation of the
moment generating
functions. Plots of the resulting density functions shed new light on
the quality of the estimators. Calculations for CVaR reveal that the
nonparametric estimator enjoys greater asymptotic efficiency relative
to the parametric estimator than is the case for VaR. An application
of the methodology in modeling currency exchange rates suggests that
the AL distribution is successful in capturing the peakedness,
leptokurticity, and skewness, inherent in such data. We conclude with some
extensions of the methodology when the sampling is under the framework of a
stationary time series covariance structure. Preliminary results
suggest that, in certain types of financial data, an ARMA model driven
by IID AL noise provides a competitive fit to a classical ARMA driven by
GARCH noise.
Wednesday, 20 February at 4:00, AB 634 :
Prof. Semyon Tsynkov
Department of Mathematics
North Carolina State University
Nonlocal Far-Field Artificial Boundary Conditions for
3D Computational Aerodynamics
ABSTRACT:
Numerical solution of the problem originally formulated on an
unbounded domain typically requires that the domain be
truncated. Truncation, in turn, necessitates that the artificial
boundary conditions (ABCs) be set at the far-field computational
boundary. The issue of ABCs is critically important in many areas of
scientific computing, for example, in computational fluid dynamics
(CFD). In particular, the problems of external configuration analysis
(fluid flows around aerodynamic shapes) represent a wide class of key
practical applications in CFD, for which the proper treatment of
artificial boundaries has a profound impact on the overall quality and
performance of numerical algorithms, as well as on interpretation of
their results. In the talk, we will describe the nonlocal ABCs that we
have introduced for the computation of external compressible viscous
flows. We will also provide an overview of other conceptually similar
ABCs for various wave propagation problems. Our methodology combines
the advantages relevant to both local and global methods proposed
previously by other authors. It employs finite-difference counterparts
to Calderon's pseudodifferential boundary projection operators and
exploits the difference potentials method by Ryaben'kii. The resulting
ABCs are accurate and robust, and at the same time inexpensive,
geometrically universal, and easy to use. We will review the
implementation of these ABCs along with the NASA-developed production
multigrid flow solvers. We will show the results of configuration
analysis for both two and three space dimensions (subsonic and
transonic flows, turbulent flows with separation and reattachment,
flows with jet exhaust), and demonstrate a consistent superiority of
the proposed approach over the standard existing methods.
Friday, 22 February at 1:00, AB 201 :
Prof. Eun Heui Kim
Department of Mathematics
California State University Long Beach
Transonic problems in 2-dimensional conservation laws
ABSTRACT:
Many practical problems in science and engineering, for example in aerodynamics, multi-phase flow and hemodynamics, involve conserved quantities, and lead to partial differential equations in the form of conservation laws. Understanding the mathematical structure of these equations and their solutions is essential to obtain physical insight into such practical problems.
There are special difficulties associated (e.g. shock formation) with these equations that are not seen elsewhere and must be dealt with carefully.
Moreover, in multidimensional conservation laws, there is little theory at present. One approach, the study of self-similar solutions, leads to the study of
equations that change their type, namely, equations that are hyperbolic far from the origin and mixed near the origin. Some results have been obtained recently in this area, but there are still many open problems.
In this talk, we discuss transonic problems in multidimensional conservation
laws, present current results and ongoing research in this area.
Monday, 25 February at 4:00, AB 202 :
Prof. Miklós Bóna
Department of Mathematics
University of Florida.
Real Zeros, Unimodality, Log-concavity, Normality, and All That
Analysis Helping Combinatorics and Probability
ABSTRACT:
If a combinatorially defined polynomial has only real roots, then that
analytical property has a plethora of interesting combinatorial and
probabilistic consequences. We will give a survey of some of these
facts located on the borderline of various lines of research, such
as enumerative combinatorics, extremal combinatorics, and probability.
The talk is meant to be accessible for a general mathematics audience.
Tuesday, 26 February at 2:30, WRB 2007 :
Prof. Aaron Yip
Department of Mathematics
Purdue University
Motion by Mean Curvature in Heterogeneous Medium
ABSTRACT:
The talk will discuss some mathematical questions motivated by the
motion of materials phase boundaries in heterogeneous medium.
The ultimate goal is to derive effective, homogenized equation and
study the property of the solution in large space-time regime. Motion
by mean curvature is used as a simple but illustrative example. It
already involves interesting mathematical analysis due to the nonlinear
interaction between the curvature and the background heterogeneity.
In this talk, we will concentrate on periodic background environment.
For some linearized version of motion by mean curvature flow, we derive
the scaling behavior for the averaged velocity in some pinning and
de-pinning transition regime. For the fully nonlinear version, we
prove the existence, uniqueness and stability of pulsating waves
(above the pinning threshold) for any normal direction. Furthermore,
the effective speed of propagation is a Lipschitz continuous function
of the normal. Connection with homogenization will be discussed.
(This talk is based on joint works with Nicolas Dirr and Georgia
Karali.)
Thursday, 28 February at 2:30, MSS 216 :
Prof. Pavel Solin
Department of Mathematics
University of Texas at El Paso &
Academy of Sciences of the Czech Republic
High-Fidelity Computer Methods for Large-Scale Multi-Physics Engineering Problems
ABSTRACT:
Nowadays, the computer simulation of natural and industrial processes described by (systems of) partial
differential and/or integral equations plays an essential role in engineering, science, biology, medicine,
and many other fields. In contrast to ten years ago, results computed today need to be accompanied by information
about their accuracy and the role of aleatory/epistemic uncertainty in input data. Such information cannot be
provided without efficient self-adaptive computational methods equipped with reliable error control
and uncertainty estimation mechanisms. From this point of view, the most difficult cases are multi-physics
problems where phenomena spanning vastly different spatial and/or temporal scales interact in nonlinear
ways. As examples of such processes let us mention microwave heating, induction heating, electromagnetic
stirring of reactive liquids, magnetorheological fluids, magnetohydrodynamics, turbulent flows, fluid-structure
interaction problems, thermoelasticity, or moisture and heat transfer
in drying concrete. For many such problems, reliable computational
methods equipped with error control are missing.
Thursday, 1 May at 2:30 in WRB 2007.
Prof. Gastão de Almeida Braga
Departamento de Matematica
Universidade Federal de Minas Gerais
Belo Horizonte - MG, Brazil
Asymptotics of the connectivity function for percolation and spin systems
ABSTRACT:
The outline of the presentation is as follows: We show several large-scale problems rooted in electrical,
civil, mechanical and chemical engineering, and explain standard difficulties that practitioners face in their
solution. We will explain what was done in this field so far and what are the limitations of standard methods.
The advantages of modern higher-order methods will be discussed and main difficulties encountered in
multi-physics problems will be described. In the second part of the talk, we will present our leading
project aimed at universal self-adaptive higher-order computational methods applicable to a wide range
of single- as well as multi-physics problems. Several practitioners have already adopted the new method
and we hope that more will follow.
Thursday, 8 May at 2:30,
Prof. Frederic Schoenberg
Dept. of Statistics
UCLA
Forecasting the occurrences of wildfires and earthquakes using point
processes with directional covariates
ABSTRACT:
Tremendous progress has been made in recent years in the development
of methods for the description of directional data. However, one area
that has remained largely unexplored is the inclusion of directional
variables into point process models. This is an important subject,
since such covariates appear to be very promising predictors in a
variety of applications. For instance, forecasts of wildfire hazard
could be improved by taking wind direction into account, and
forecasts of earthquake hazard could benefit by using estimates of
focal mechanisms of previous earthquakes as predictors. This talk
explores methods for incorporating such information into the current
best-fitting point process models for wildfires and earthquakes, in
order to provide improved forecasts of wildfire and earthquake hazard
for Southern California. Particular attention will be placed on
extending separable models for wildfire hazard and branching point
process models for earthquakes, such as the Epidemic-Type Aftershock
Sequence (ETAS) models that are now commonly used in studies of
seismic hazard, to include these important types of predictors.
Last fall's colloquium schedule.
The
Department of Mathematics & Statistics
is located on the 6th floor of the
Ansari Business Bldg.
