## April 2014

**Levi L. Conant Lecture-John Huerta (Centre for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Técnico, Lisbon)-Symmetry in Mathematics and Physics**

Friday, 4/18/2014 3:00 PM-5:00 PM

Fuller Laboratories, Upper Perreault

ABSTRACT: Deep at the heart of any discipline lies the idea of symmetry. We will explore the fascinating tale of symmetry, from its codification into a powerful tool called group theory by mathematicians in the 19th century, to its rise to the center of fundamental physics in the 20th century, and its evolution and influence today. Group theory begins with intuitive, pictorial ideas of what it means to have symmetry. In the 1830s, the 20 year old genius Evariste Galois invented group theory and turned it into a powerful tool in pure mathematics, but one devoid of apparent practical use. Much later, after decades of mathematical development, Albert Einstein introduced symmetry to physics with his theory of relativity. Yet it was only in the latter half of the 20th century that we discovered the true importance of symmetry in physics: particle physicists discovered it at the heart of the laws of nature, essentially giving our most basic laws their form. It has continued to have a central place ever since, and today, new mathematical ideas about symmetry, with exotic names like quantum groups and higher categories, may be poised to revolutionize the physics of the 21st century.

John Huerta earned his PhD in 2011 in mathematics from the University of California, Riverside. Huerta is a mathematical physicist, currently a postdoctoral fellow at Centre for Mathematical Analysis, Geometry, and Dynamical Systems in Lisbon. In 2013 he shared the Levi L. Conant Prize with his advisor, John Baez, at University of California, Riverside, for the paper The Algebra of Grand Unified Theories. (Bulletin of the American Mathematical Society 47:483-552, 2010.)

For more information, e-mail ma-chair@wpi.edu.

**Stochastic Analysis Common-Anja Richter (Baruch College, CUNY)-Discrete Term Structure Models**

Wednesday, 4/23/2014 3:00 PM-4:00 PM

Stratton Hall, 203

ABSTRACT: In the classic approach to option pricing one models the dynamics of the underlying and then calibrates the model to today's option prices. However, option prices derived from the model are often inconsistent with the observed prices in the market. To overcome this problem we model the dynamics of both the underlying and liquidly traded options together using forward characteristic processes. We develop theory and applications of forward characteristic processes in discrete time. In particular we provide a no-arbitrage characterization of our model and a rich class of examples. Finally we show how to implement our model. This is joint work with Josef Teichmann (ETH Zurich).

For more information, e-mail ma-chair@wpi.edu.

**Harold J. Gay Lecture-Viorel Barbu (University of Iasi, Romania)-PDEs and variational based models for image restoring**

Friday, 4/25/2014 3:00 PM-5:00 PM

Kaven Hall, 116

ABSTRACT: One surveys here a few nonlinear diffusion models in image restoration and denoising with main emphasis on that described by nonlinear parabolic equations of gradient type. The well-posedness of the corresponding Cauchy problem as well as stability of the derived finite difference scheme is studied from perspectives of nonlinear semigroup theory. Most of denoising PDE procedures existing in literature, though apparently are efficient at experimental level, are however mathematically ill posed and our effort here is to put them on more rigorous mathematical basis.

For more information, e-mail ma-chair@wpi.edu.

**Math Bio Seminar-Mike Neubert (Woods Hole Oceanographic Institute)-Bioeconomics of Marine Reserves**

Tuesday, 4/29/2014 4:00 PM-5:00 PM

Stratton Hall, 203

ABSTRACT: Spatially explicit fisheries management is a hot topic. Of particular interest is the role that closed areas (a.k.a. marine protected areas or marine reserves), should play in the regulation of fishing. Theoretical work in this area has shown that the establishment of marine reserves for conservation purposes does not necessarily require a reduction in economic productivity. It is fair to say that the implementation and design of actual marine reserve networks has been motivated and guided in large part by bioeconomic theory.

As is appropriate, the mathematical models that are currently used to understand the economic and biological costs and benefits of marine reserves make a number of simplifying assumptions. These include assumptions about the goal of management, the impacts of harvest on habitat, the number of harvesters, the nature of regulatory constraints, etc. In my talk, I will present the results of my analysis of a simple, spatially-explicit, bioeconomic model for a harvested renewable resource. Even this model can have complicated dynamics. Then, depending on time and audience interests, I will discuss the consequences of relaxing various of these assumptions.

For more information, e-mail ma-chair@wpi.edu.

## May 2014

**Colloquium-Rohini Kumar (Wayne State University)-Title TBA**

Friday, 5/2/2014 11:00 AM-12:00 PM

Stratton Hall, 203

ABSTRACT: TBA

For more information, e-mail ma-chair@wpi.edu.

## April 2014

Levi L. Conant Lecture-John Huerta (Centre for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Técnico, Lisbon)-Symmetry in Mathematics and PhysicsFriday, 4/18/2014 3:00 PM-5:00 PM

Fuller Laboratories, Upper Perreault

ABSTRACT: Deep at the heart of any discipline lies the idea of symmetry. We will explore the fascinating tale of symmetry, from its codification into a powerful tool called group theory by mathematicians in the 19th century, to its rise to the center of fundamental physics in the 20th century, and its evolution and influence today. Group theory begins with intuitive, pictorial ideas of what it means to have symmetry. In the 1830s, the 20 year old genius Evariste Galois invented group theory and turned it into a powerful tool in pure mathematics, but one devoid of apparent practical use. Much later, after decades of mathematical development, Albert Einstein introduced symmetry to physics with his theory of relativity. Yet it was only in the latter half of the 20th century that we discovered the true importance of symmetry in physics: particle physicists discovered it at the heart of the laws of nature, essentially giving our most basic laws their form. It has continued to have a central place ever since, and today, new mathematical ideas about symmetry, with exotic names like quantum groups and higher categories, may be poised to revolutionize the physics of the 21st century.

John Huerta earned his PhD in 2011 in mathematics from the University of California, Riverside. Huerta is a mathematical physicist, currently a postdoctoral fellow at Centre for Mathematical Analysis, Geometry, and Dynamical Systems in Lisbon. In 2013 he shared the Levi L. Conant Prize with his advisor, John Baez, at University of California, Riverside, for the paper The Algebra of Grand Unified Theories. (Bulletin of the American Mathematical Society 47:483-552, 2010.)

For more information, e-mail ma-chair@wpi.edu.

Stochastic Analysis Common-Anja Richter (Baruch College, CUNY)-Discrete Term Structure ModelsWednesday, 4/23/2014 3:00 PM-4:00 PM

Stratton Hall, 203

ABSTRACT: In the classic approach to option pricing one models the dynamics of the underlying and then calibrates the model to today's option prices. However, option prices derived from the model are often inconsistent with the observed prices in the market. To overcome this problem we model the dynamics of both the underlying and liquidly traded options together using forward characteristic processes. We develop theory and applications of forward characteristic processes in discrete time. In particular we provide a no-arbitrage characterization of our model and a rich class of examples. Finally we show how to implement our model. This is joint work with Josef Teichmann (ETH Zurich).

For more information, e-mail ma-chair@wpi.edu.

Harold J. Gay Lecture-Viorel Barbu (University of Iasi, Romania)-PDEs and variational based models for image restoringFriday, 4/25/2014 3:00 PM-5:00 PM

Kaven Hall, 116

ABSTRACT: One surveys here a few nonlinear diffusion models in image restoration and denoising with main emphasis on that described by nonlinear parabolic equations of gradient type. The well-posedness of the corresponding Cauchy problem as well as stability of the derived finite difference scheme is studied from perspectives of nonlinear semigroup theory. Most of denoising PDE procedures existing in literature, though apparently are efficient at experimental level, are however mathematically ill posed and our effort here is to put them on more rigorous mathematical basis.

For more information, e-mail ma-chair@wpi.edu.

Math Bio Seminar-Mike Neubert (Woods Hole Oceanographic Institute)-Bioeconomics of Marine ReservesTuesday, 4/29/2014 4:00 PM-5:00 PM

Stratton Hall, 203

ABSTRACT: Spatially explicit fisheries management is a hot topic. Of particular interest is the role that closed areas (a.k.a. marine protected areas or marine reserves), should play in the regulation of fishing. Theoretical work in this area has shown that the establishment of marine reserves for conservation purposes does not necessarily require a reduction in economic productivity. It is fair to say that the implementation and design of actual marine reserve networks has been motivated and guided in large part by bioeconomic theory.

As is appropriate, the mathematical models that are currently used to understand the economic and biological costs and benefits of marine reserves make a number of simplifying assumptions. These include assumptions about the goal of management, the impacts of harvest on habitat, the number of harvesters, the nature of regulatory constraints, etc. In my talk, I will present the results of my analysis of a simple, spatially-explicit, bioeconomic model for a harvested renewable resource. Even this model can have complicated dynamics. Then, depending on time and audience interests, I will discuss the consequences of relaxing various of these assumptions.

For more information, e-mail ma-chair@wpi.edu.

## May 2014

Colloquium-Rohini Kumar (Wayne State University)-Title TBAFriday, 5/2/2014 11:00 AM-12:00 PM

Stratton Hall, 203

ABSTRACT: TBA

For more information, e-mail ma-chair@wpi.edu.