July 2009
Mingchao Cai (Technical University of Dortmund, Germany)-Decoupled algorithms for the surface-subsurface flow interaction problems
Monday, 7/27/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Research works on the coupling of incompressible surface flow with subsurface porous media flow arouse increasing interest recently. The coupled problems are typical multi-domain problems with multi-physics. Correspondingly, heterogeneous partial differential equations for modeling these problems are coupled together at the interface between two domains. We propose several decoupled algorithms so that numerical computations can be realized in parallel. Specifically, we investigate decoupled preconditioning techniques and two grid algorithms. Numerical examples and mathematical analysis are given to show that our algorithms are effective and efficient.
For more information, e-mail ma-chair@wpi.edu.
August 2009
Patrick Dondl (University of Bonn)-Pinning of interfaces in random media
Friday, 8/28/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: We consider the evolution of an interface, modeled by a parabolic equation, in a random environment. The randomness is given by a distribution of smooth obstacles of random strength. To provide a barrier for the moving interface, we construct a positive, steady state supersolution. This construction depends on the existence, after rescaling, of a Lipschitz hypersurface separating the domain into a top and a bottom part, consisting of boxes that contain at least one obstacle of sufficient strength. We prove this percolation result.
Joint work with N. Dirr (Bath University) and M. Scheutzow (TU Berlin).
For more information, e-mail ma-chair@wpi.edu.
September 2009
Dara Entekhabi (MIT)-Math Awareness Month Talk: Mathematics and the Weather Forecast Problem
Friday, 9/18/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: The atmospheric and oceanic systems are chaotic in nature which, in the context of environmental forecasting, means that small initialization errors will lead to increasing large divergence of model forecasts with respect to true trajectory. That is why weather forecasting is a challenge and the reliability of weather forecasts goes down the farther out in time we look. To reduce model initialization errors the scientific and governmental communities have embarked on unprecedented efforts to increase observing networks, launch Earth-observing satellites, and openly share data in real-time and internationally. We have transitioned from a data-starved state to becoming overwhelmed with observations. How do we ingest the massive volume of observations into models? Both observations and models have errors. Can the two random variables be combined in a Bayesian probabilistic framework? Given the volume of data (millions counts per day) and model sizes (millions of state variables), is this computationally feasible? How do chaotic models respond to observations that d not lie on any possible model trajectory? Everyone complains about the weather, but no-one does anything about it (attributed to Mark Twain). When it comes to weather forecasts however, much has been done about it.
For more information, e-mail ma-chair@wpi.edu.
Lucian Beznea (Simion Stoilow Institute of Mathematics of the Romanian Academy)-Nonlinear PDE and Measure-Valued Branching Processes
Tuesday, 9/22/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: We intend to present relations between two classes of measure-valued Markov processes (superprocesses and processes with discrete branching) and nonlinear operators of the form Lu + Phi(u), where L is a second order elliptic differential operator and Phi is a "branching mechanism"; in particular we may take Phi(u)= u^2. We follow the pioneering works of M. Nagasawa, S. Watanabe, M.L. Silverstein, and the approaches of E.B. Dynkin and P. Fitzsimmons. We shall develop potential theoretical methods in the construction of the measure-valued branching processes.
For more information, e-mail ma-chair@wpi.edu.
Katharine Ott (University of Kentucky)-The Netflix Prize: How Mathematics Can Predict Movies You'll Love
Wednesday, 9/23/2009 4:00 PM-5:00 PM
Stratton Hall, 308
ABSTRACT: Recommendation engines are programs that use a set of ratings from a particular customer, along with ratings from the whole customer base, to predict new items that a consumer will like. Online stores such as Netflix, Amazon and iTunes employ recommendation systems to encourage users to make future purchases. In October 2006 Netflix offered $1,000,000 to anyone who can improve their current recommendation engine by 10%. Within the first month of the competition a mathematical technique from linear algebra called singular value decomposition (SVD) improved the recommendation engine by almost 4%. In this talk I will discuss how user data collected by Netflix is arranged into a matrix, how to factor a matrix into its singular value decomposition, and why the SVD can find connections between movies a particular user likes and dislikes. I'll also discuss why, despite early advances via singular value techniques, the Netflix prize remained unclaimed until July 2009.
Undergraduate students are welcome and encouraged to attend this talk.
For more information, e-mail ma-chair@wpi.edu.
Katharine Ott (University of Kentucky) - The mixed boundary value problem for the Laplacian in Lipschitz domains
Friday, 9/25/2009 11:00 AM-12:00 PM
Stratton Hall, 203
TITLE: The mixed boundary value problem for the Laplacian in Lipschitz domains
ABSTRACT: Two classical boundary value problems for the Laplacian are the Dirichlet and Neumann problems. A third type of boundary value problem is the mixed problem, or Zaremba's problem, where we specify Dirichlet data on a portion of the boundary and Neumann data on the remaining portion. In this talk I will discuss existence, uniqueness, and regularity of solutions to the mixed boundary value problem for the Laplacian in Lipschitz domains.
For more information, e-mail ma-chair@wpi.edu.
Mike Hill (Harvard University, University of Virgina)-Ruler, Compass, and Origami Constructions: Trisecting and Angle and Doubling a Cube
Wednesday, 9/30/2009 4:00 PM-5:00 PM
Stratton Hall, 308
ABSTRACT: We'll see in this talk how techniques in origami can be used to do the impossible: trisect and arbitrary angle and double a cube. Along the way, we'll play with the mathematical side of paper folding and try our hand at understanding the basic axiomatic approach.
Undergraduate students are welcome and encouraged to attend this talk.
For more information, e-mail ma-chair@wpi.edu.
October 2009
Irina Mitrea (WPI) - On the global regularity of conformal maps
Friday, 10/9/2009 11:00 AM-12:00 PM
Stratton Hall, 203
TITLE: On the global regularity of conformal maps
ABSTRACT: The Riemann mapping theorem, one of the most celebrated results in complex analysis, states that any bounded, connected and simply connected domain $D$ in ${\Bbb R}^2$ can be conformally mapped onto the unit disk. It has long been understood that there are subtle connections between the smoothness of the conformal transformation $\Phi$ near the boundary of the domain and the degree of regularity of $D$. In this talk we address the issue of global regularity of $\Phi$ on Sobolev-Besov scales, in the case when the domain $D$ is allowed to have a Lipschitz graph-like boundary. The approach employed relies on powerful tools from Harmonic Analysis and PDE's, in particular on boundary layer potentials and sharp estimates for the solution of the Dirichlet Laplacian with Besov data in Lipschitz domains.
For more information, e-mail ma-chair@wpi.edu.
November 2009
Abdelmalek Abdesselam (University of Virginia)-Introduction to the Renormalization Group
Friday, 11/6/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Ever since its introduction by Kenneth G. Wilson in the seventies, the renormalization group has been the main conceptual tool used by physicists in order to make meaningful calculations with functional integrals. The latter are, largely conjectural, infinite-dimensional probability measures over spaces of functions which one can try to construct rigorously using a scaling limit of similar measures where the continuum is discretized by finer and finer grids.
The renormalization group is a dynamical system corresponding to averaging over the short distance fluctuations of the random function and zooming out by a fixed scale ratio. Fixed points of this dynamical system correspond to the possible scaling limits one can achieve. The renormalization group provides a far reaching generalization of the familiar central limit theorem, in a situation where the random variables are dependent, in a way which is subordinated to the geometry of the space labeling these variables. In this nontechnical presentation, we will provide an introduction to the basic ideas of the renormalization group on the example of the usual central limit theorem, and the next simplest example: the so-called hierarchical model.
For more information, e-mail ma-chair@wpi.edu.
Johnny Guzman (Brown University) - Mixed methods for linear elasticity
Friday, 11/13/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Mixed methods are a class of finite element methods. Applied to elasticity problems, mixed methods approximate both the stress and displacement variables and the resulting approximation to the stress variable converges faster than displacement-based finite element methods. This is important since in many applications the stress variable is the quantity of interest. Mixed methods also have the advantage that they perform better than displacement-based finite element methods for nearly incompressible materials.
In this talk I will discuss a class of mixed methods for linear elasticity. The methods we consider are known as weakly imposed symmetry methods since the approximation to the stress variable will in general not be symmetric. This allows one to borrow stable mixed finite element spaces for the Poisson problem, which are well known, and modify them in order to obtain stable spaces for the elasticity problem.
For more information, e-mail ma-chair@wpi.edu.
Hasanjan Sayit (WPI) - On the Existence of Consistent Price Systems
Friday, 11/20/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: In a recent paper by Guasoni, Rasonyi, and Schachermayer, the conditional full support (CFS) condition was introduced as a sufficient condition for the existence of consistent price systems (CPSs). In this note, we give a weaker sufficient condition for a CPS to exist. We use this condition to describe a mechanism to construct models with CPSs. Using this mechanism we give two examples that admit CPSs but do not have the CFS property.
For more information, e-mail ma-chair@wpi.edu.
December 2009
Abdeslem Lyaghfouri (King Fahd University and Fields Institute) - A Class of Elliptic Free Boundary Problems
Friday, 12/4/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: In this talk I will consider the following class of elliptic free boundary problems $Lu=-div(\chi(u)H(X))$, where $u$ and $\chi$ are nonnegative functions, $\chi=1$ a.e. in $[u>0]$, $L$ is a second order linear elliptic operator, $H=(H_1,H_2)$ is a vector function, and $X=(x,y)$.
When $H_1=0$ and $H_2$ is nondecreasing with respect to $y$, the free boundary $\partial[u>0]$ is the graph of a continuous curve $y=\Phi(x)$. I will discuss the situation when $H$ is a Lipschitz vector function with nonnegative divergence and show that the free boundary $\partial[u>0]$ can be represented locally by a family of continuous functions.
This is a joint work with S. Challal.
For more information, e-mail ma-chair@wpi.edu.
Justin Holmer (Brown University)-Title TBA
Friday, 12/11/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
January 2010
Woo Sun Lee (Pohang University of Science and Technology, Korea) - Title TBA
Friday, 1/22/2010 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
Catherine Roberts (College of the Holy Cross)-Title TBA
Friday, 1/29/2010 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
July 2009
Mingchao Cai (Technical University of Dortmund, Germany)-Decoupled algorithms for the surface-subsurface flow interaction problems
Monday, 7/27/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Research works on the coupling of incompressible surface flow with subsurface porous media flow arouse increasing interest recently. The coupled problems are typical multi-domain problems with multi-physics. Correspondingly, heterogeneous partial differential equations for modeling these problems are coupled together at the interface between two domains. We propose several decoupled algorithms so that numerical computations can be realized in parallel. Specifically, we investigate decoupled preconditioning techniques and two grid algorithms. Numerical examples and mathematical analysis are given to show that our algorithms are effective and efficient.
For more information, e-mail ma-chair@wpi.edu.
August 2009
Patrick Dondl (University of Bonn)-Pinning of interfaces in random media
Friday, 8/28/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: We consider the evolution of an interface, modeled by a parabolic equation, in a random environment. The randomness is given by a distribution of smooth obstacles of random strength. To provide a barrier for the moving interface, we construct a positive, steady state supersolution. This construction depends on the existence, after rescaling, of a Lipschitz hypersurface separating the domain into a top and a bottom part, consisting of boxes that contain at least one obstacle of sufficient strength. We prove this percolation result.
Joint work with N. Dirr (Bath University) and M. Scheutzow (TU Berlin).
For more information, e-mail ma-chair@wpi.edu.
September 2009
Dara Entekhabi (MIT)-Math Awareness Month Talk: Mathematics and the Weather Forecast Problem
Friday, 9/18/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: The atmospheric and oceanic systems are chaotic in nature which, in the context of environmental forecasting, means that small initialization errors will lead to increasing large divergence of model forecasts with respect to true trajectory. That is why weather forecasting is a challenge and the reliability of weather forecasts goes down the farther out in time we look. To reduce model initialization errors the scientific and governmental communities have embarked on unprecedented efforts to increase observing networks, launch Earth-observing satellites, and openly share data in real-time and internationally. We have transitioned from a data-starved state to becoming overwhelmed with observations. How do we ingest the massive volume of observations into models? Both observations and models have errors. Can the two random variables be combined in a Bayesian probabilistic framework? Given the volume of data (millions counts per day) and model sizes (millions of state variables), is this computationally feasible? How do chaotic models respond to observations that d not lie on any possible model trajectory? Everyone complains about the weather, but no-one does anything about it (attributed to Mark Twain). When it comes to weather forecasts however, much has been done about it.
For more information, e-mail ma-chair@wpi.edu.
Lucian Beznea (Simion Stoilow Institute of Mathematics of the Romanian Academy)-Nonlinear PDE and Measure-Valued Branching Processes
Tuesday, 9/22/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: We intend to present relations between two classes of measure-valued Markov processes (superprocesses and processes with discrete branching) and nonlinear operators of the form Lu + Phi(u), where L is a second order elliptic differential operator and Phi is a "branching mechanism"; in particular we may take Phi(u)= u^2. We follow the pioneering works of M. Nagasawa, S. Watanabe, M.L. Silverstein, and the approaches of E.B. Dynkin and P. Fitzsimmons. We shall develop potential theoretical methods in the construction of the measure-valued branching processes.
For more information, e-mail ma-chair@wpi.edu.
Katharine Ott (University of Kentucky)-The Netflix Prize: How Mathematics Can Predict Movies You'll Love
Wednesday, 9/23/2009 4:00 PM-5:00 PM
Stratton Hall, 308
ABSTRACT: Recommendation engines are programs that use a set of ratings from a particular customer, along with ratings from the whole customer base, to predict new items that a consumer will like. Online stores such as Netflix, Amazon and iTunes employ recommendation systems to encourage users to make future purchases. In October 2006 Netflix offered $1,000,000 to anyone who can improve their current recommendation engine by 10%. Within the first month of the competition a mathematical technique from linear algebra called singular value decomposition (SVD) improved the recommendation engine by almost 4%. In this talk I will discuss how user data collected by Netflix is arranged into a matrix, how to factor a matrix into its singular value decomposition, and why the SVD can find connections between movies a particular user likes and dislikes. I'll also discuss why, despite early advances via singular value techniques, the Netflix prize remained unclaimed until July 2009.
Undergraduate students are welcome and encouraged to attend this talk.
For more information, e-mail ma-chair@wpi.edu.
Katharine Ott (University of Kentucky) - The mixed boundary value problem for the Laplacian in Lipschitz domains
Friday, 9/25/2009 11:00 AM-12:00 PM
Stratton Hall, 203
TITLE: The mixed boundary value problem for the Laplacian in Lipschitz domains
ABSTRACT: Two classical boundary value problems for the Laplacian are the Dirichlet and Neumann problems. A third type of boundary value problem is the mixed problem, or Zaremba's problem, where we specify Dirichlet data on a portion of the boundary and Neumann data on the remaining portion. In this talk I will discuss existence, uniqueness, and regularity of solutions to the mixed boundary value problem for the Laplacian in Lipschitz domains.
For more information, e-mail ma-chair@wpi.edu.
Mike Hill (Harvard University, University of Virgina)-Ruler, Compass, and Origami Constructions: Trisecting and Angle and Doubling a Cube
Wednesday, 9/30/2009 4:00 PM-5:00 PM
Stratton Hall, 308
ABSTRACT: We'll see in this talk how techniques in origami can be used to do the impossible: trisect and arbitrary angle and double a cube. Along the way, we'll play with the mathematical side of paper folding and try our hand at understanding the basic axiomatic approach.
Undergraduate students are welcome and encouraged to attend this talk.
For more information, e-mail ma-chair@wpi.edu.
October 2009
Irina Mitrea (WPI) - On the global regularity of conformal maps
Friday, 10/9/2009 11:00 AM-12:00 PM
Stratton Hall, 203
TITLE: On the global regularity of conformal maps
ABSTRACT: The Riemann mapping theorem, one of the most celebrated results in complex analysis, states that any bounded, connected and simply connected domain $D$ in ${\Bbb R}^2$ can be conformally mapped onto the unit disk. It has long been understood that there are subtle connections between the smoothness of the conformal transformation $\Phi$ near the boundary of the domain and the degree of regularity of $D$. In this talk we address the issue of global regularity of $\Phi$ on Sobolev-Besov scales, in the case when the domain $D$ is allowed to have a Lipschitz graph-like boundary. The approach employed relies on powerful tools from Harmonic Analysis and PDE's, in particular on boundary layer potentials and sharp estimates for the solution of the Dirichlet Laplacian with Besov data in Lipschitz domains.
For more information, e-mail ma-chair@wpi.edu.
November 2009
Abdelmalek Abdesselam (University of Virginia)-Introduction to the Renormalization Group
Friday, 11/6/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Ever since its introduction by Kenneth G. Wilson in the seventies, the renormalization group has been the main conceptual tool used by physicists in order to make meaningful calculations with functional integrals. The latter are, largely conjectural, infinite-dimensional probability measures over spaces of functions which one can try to construct rigorously using a scaling limit of similar measures where the continuum is discretized by finer and finer grids.
The renormalization group is a dynamical system corresponding to averaging over the short distance fluctuations of the random function and zooming out by a fixed scale ratio. Fixed points of this dynamical system correspond to the possible scaling limits one can achieve. The renormalization group provides a far reaching generalization of the familiar central limit theorem, in a situation where the random variables are dependent, in a way which is subordinated to the geometry of the space labeling these variables. In this nontechnical presentation, we will provide an introduction to the basic ideas of the renormalization group on the example of the usual central limit theorem, and the next simplest example: the so-called hierarchical model.
For more information, e-mail ma-chair@wpi.edu.
Johnny Guzman (Brown University) - Mixed methods for linear elasticity
Friday, 11/13/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Mixed methods are a class of finite element methods. Applied to elasticity problems, mixed methods approximate both the stress and displacement variables and the resulting approximation to the stress variable converges faster than displacement-based finite element methods. This is important since in many applications the stress variable is the quantity of interest. Mixed methods also have the advantage that they perform better than displacement-based finite element methods for nearly incompressible materials.
In this talk I will discuss a class of mixed methods for linear elasticity. The methods we consider are known as weakly imposed symmetry methods since the approximation to the stress variable will in general not be symmetric. This allows one to borrow stable mixed finite element spaces for the Poisson problem, which are well known, and modify them in order to obtain stable spaces for the elasticity problem.
For more information, e-mail ma-chair@wpi.edu.
Hasanjan Sayit (WPI) - On the Existence of Consistent Price Systems
Friday, 11/20/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: In a recent paper by Guasoni, Rasonyi, and Schachermayer, the conditional full support (CFS) condition was introduced as a sufficient condition for the existence of consistent price systems (CPSs). In this note, we give a weaker sufficient condition for a CPS to exist. We use this condition to describe a mechanism to construct models with CPSs. Using this mechanism we give two examples that admit CPSs but do not have the CFS property.
For more information, e-mail ma-chair@wpi.edu.
December 2009
Abdeslem Lyaghfouri (King Fahd University and Fields Institute) - A Class of Elliptic Free Boundary Problems
Friday, 12/4/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: In this talk I will consider the following class of elliptic free boundary problems $Lu=-div(\chi(u)H(X))$, where $u$ and $\chi$ are nonnegative functions, $\chi=1$ a.e. in $[u>0]$, $L$ is a second order linear elliptic operator, $H=(H_1,H_2)$ is a vector function, and $X=(x,y)$.
When $H_1=0$ and $H_2$ is nondecreasing with respect to $y$, the free boundary $\partial[u>0]$ is the graph of a continuous curve $y=\Phi(x)$. I will discuss the situation when $H$ is a Lipschitz vector function with nonnegative divergence and show that the free boundary $\partial[u>0]$ can be represented locally by a family of continuous functions.
This is a joint work with S. Challal.
For more information, e-mail ma-chair@wpi.edu.
Justin Holmer (Brown University)-Title TBA
Friday, 12/11/2009 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
January 2010
Woo Sun Lee (Pohang University of Science and Technology, Korea) - Title TBA
Friday, 1/22/2010 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
Catherine Roberts (College of the Holy Cross)-Title TBA
Friday, 1/29/2010 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.