We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

# Research Seminar Series

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.

## Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.

Presented by Joe Perez, University of Vienna

6 December 2010 17:15 in CM221

Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.

It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.