MAPSS
from
Sunday, July 14, 2024 (6:35 PM)
to
Friday, July 19, 2024 (2:00 PM)
Monday, July 8, 2024
Tuesday, July 9, 2024
Wednesday, July 10, 2024
Thursday, July 11, 2024
Friday, July 12, 2024
Saturday, July 13, 2024
Sunday, July 14, 2024
7:00 PM
Dinner
7:00 PM - 8:30 PM
Monday, July 15, 2024
9:00 AM
Symplectic Geometry
-
Donald Huber-Youmans
(
Heidelberg University
)
Symplectic Geometry
Donald Huber-Youmans
(
Heidelberg University
)
9:00 AM - 9:45 AM
This course is an introduction to the foundations of symplectic geometry. We will discuss a motivating example—Hamiltonian mechanics—before defining what it means to be symplectic. Afterwards we will study some consequences of the general definitions. Importantly, we will show that locally, all symplectic spaces look the same: there are no local symplectic invariants! This is a consequence of Darboux’s theorem. Key words: Hamiltonian mechanics, symplectic manifolds, Darboux theorem
9:45 AM
Coffee Break
9:45 AM - 10:00 AM
10:00 AM
Symplectic Geometry
-
Donald Huber-Youmans
(
Heidelberg University
)
Symplectic Geometry
Donald Huber-Youmans
(
Heidelberg University
)
10:00 AM - 10:45 AM
This course is an introduction to the foundations of symplectic geometry. We will discuss a motivating example—Hamiltonian mechanics—before defining what it means to be symplectic. Afterwards we will study some consequences of the general definitions. Importantly, we will show that locally, all symplectic spaces look the same: there are no local symplectic invariants! This is a consequence of Darboux’s theorem. Key words: Hamiltonian mechanics, symplectic manifolds, Darboux theorem
11:00 AM
Symplectic Geometry
-
Donald Huber-Youmans
(
Heidelberg University
)
Symplectic Geometry
Donald Huber-Youmans
(
Heidelberg University
)
11:00 AM - 11:45 AM
This course is an introduction to the foundations of symplectic geometry. We will discuss a motivating example—Hamiltonian mechanics—before defining what it means to be symplectic. Afterwards we will study some consequences of the general definitions. Importantly, we will show that locally, all symplectic spaces look the same: there are no local symplectic invariants! This is a consequence of Darboux’s theorem. Key words: Hamiltonian mechanics, symplectic manifolds, Darboux theorem
12:00 PM
Lunch
12:00 PM - 1:30 PM
3:55 PM
Coffee Break
3:55 PM - 4:10 PM
4:15 PM
Symplectic reduction and its application in physics
-
Alexander Thomas
(
Heidelberg University
)
Symplectic reduction and its application in physics
Alexander Thomas
(
Heidelberg University
)
4:15 PM - 5:00 PM
After the introductory course in symplectic geometry, we analyze symplectic manifolds which are symmetric under the action of a Lie group, leading in particular to the symplectic quotient construction. The important concept is the notion of the moment map, generalizing the concept of momentum and angular momentum in classical mechanics, and capturing all preserved quantities coming from Noethers theorem. The symplectic quotient, or Marsden-Weinstein quotient, allows then to define reduced phase spaces. We will see many examples both physically and mathematically motivated. Key words: Hamiltonian actions, moment maps, symplectic quotient, Noether theorem, Poisson manifolds
5:15 PM
Symplectic reduction and its application in physics
-
Alexander Thomas
(
Heidelberg University
)
Symplectic reduction and its application in physics
Alexander Thomas
(
Heidelberg University
)
5:15 PM - 6:00 PM
After the introductory course in symplectic geometry, we analyze symplectic manifolds which are symmetric under the action of a Lie group, leading in particular to the symplectic quotient construction. The important concept is the notion of the moment map, generalizing the concept of momentum and angular momentum in classical mechanics, and capturing all preserved quantities coming from Noethers theorem. The symplectic quotient, or Marsden-Weinstein quotient, allows then to define reduced phase spaces. We will see many examples both physically and mathematically motivated. Key words: Hamiltonian actions, moment maps, symplectic quotient, Noether theorem, Poisson manifolds
6:15 PM
Symplectic reduction and its application in physics
-
Alexander Thomas
(
Heidelberg University
)
Symplectic reduction and its application in physics
Alexander Thomas
(
Heidelberg University
)
6:15 PM - 7:00 PM
After the introductory course in symplectic geometry, we analyze symplectic manifolds which are symmetric under the action of a Lie group, leading in particular to the symplectic quotient construction. The important concept is the notion of the moment map, generalizing the concept of momentum and angular momentum in classical mechanics, and capturing all preserved quantities coming from Noethers theorem. The symplectic quotient, or Marsden-Weinstein quotient, allows then to define reduced phase spaces. We will see many examples both physically and mathematically motivated. Key words: Hamiltonian actions, moment maps, symplectic quotient, Noether theorem, Poisson manifolds
7:15 PM
Dinner
7:15 PM - 8:45 PM
Tuesday, July 16, 2024
9:00 AM
Algebraic Topology
-
Nikita Nikolaev
(
University of Birmingham
)
Algebraic Topology
Nikita Nikolaev
(
University of Birmingham
)
9:00 AM - 9:45 AM
9:45 AM
Coffee Break
9:45 AM - 10:00 AM
10:00 AM
Algebraic Topology
-
Nikita Nikolaev
(
University of Birmingham
)
Algebraic Topology
Nikita Nikolaev
(
University of Birmingham
)
10:00 AM - 10:45 AM
11:00 AM
Algebraic Topology
-
Nikita Nikolaev
(
University of Birmingham
)
Algebraic Topology
Nikita Nikolaev
(
University of Birmingham
)
11:00 AM - 11:45 AM
12:00 PM
Lunch
12:00 PM - 1:30 PM
4:00 PM
Coffee Break
4:00 PM - 4:15 PM
4:15 PM
Supergeometry - oddities of the square
-
Donald Huber-Youmans
Supergeometry - oddities of the square
Donald Huber-Youmans
4:15 PM - 5:00 PM
This course is an excursion into the marvelous world of supergeometry which plays an important role in mathematics and physics. On one hand, it is a natural, albeit at first glance unintuitive, generalization of ordinary geometry. On the other hand it plays a pivotal role in the theory of supersymmetry. Naively, one can replace “super” by “Z/2Z”-graded, alongside introducing the Koszul sign-rule. This naive idea has far reaching consequences leading to the definition of supermanifolds and supersymmetry. Key words: Super algebras, super manifolds, odd coordinates, fuzzy points, Supersymmetry, super quantum mechanics
5:15 PM
Supergeometry - oddities of the square
-
Donald Huber-Youmans
Supergeometry - oddities of the square
Donald Huber-Youmans
5:15 PM - 6:00 PM
This course is an excursion into the marvelous world of supergeometry which plays an important role in mathematics and physics. On one hand, it is a natural, albeit at first glance unintuitive, generalization of ordinary geometry. On the other hand it plays a pivotal role in the theory of supersymmetry. Naively, one can replace “super” by “Z/2Z”-graded, alongside introducing the Koszul sign-rule. This naive idea has far reaching consequences leading to the definition of supermanifolds and supersymmetry. Key words: Super algebras, super manifolds, odd coordinates, fuzzy points, Supersymmetry, super quantum mechanics
6:15 PM
Supergeometry - oddities of the square
-
Donald Huber-Youmans
Supergeometry - oddities of the square
Donald Huber-Youmans
6:15 PM - 7:00 PM
This course is an excursion into the marvelous world of supergeometry which plays an important role in mathematics and physics. On one hand, it is a natural, albeit at first glance unintuitive, generalization of ordinary geometry. On the other hand it plays a pivotal role in the theory of supersymmetry. Naively, one can replace “super” by “Z/2Z”-graded, alongside introducing the Koszul sign-rule. This naive idea has far reaching consequences leading to the definition of supermanifolds and supersymmetry. Key words: Super algebras, super manifolds, odd coordinates, fuzzy points, Supersymmetry, super quantum mechanics
7:00 PM
Dinner
7:00 PM - 8:30 PM
Wednesday, July 17, 2024
12:00 PM
Lunch
12:00 PM - 1:30 PM
7:15 PM
Dinner
7:15 PM - 8:45 PM
Thursday, July 18, 2024
9:00 AM
Differential Geometry
-
Olga Chekeres
Differential Geometry
Olga Chekeres
9:00 AM - 9:45 AM
Differential geometry in 1, 2, 3 and more dimensions. Imagine an n-dimensional Riemannian manifold and then set n=1, 2, 3, 4+. Prerequisites: Come as you are. Understanding the notion of a differentiable manifold is assumed though. Consequences: To embrace the mightiness of general relativity prepared thou shall be. Key words: Riemannian and pseudo-Riemannian manifolds, metric tensor, connection, covariant derivative, curvature.
9:45 AM
Coffee Break
9:45 AM - 10:00 AM
10:00 AM
Differential Geometry
-
Olga Chekeres
Differential Geometry
Olga Chekeres
10:00 AM - 10:45 AM
Differential geometry in 1, 2, 3 and more dimensions. Imagine an n-dimensional Riemannian manifold and then set n=1, 2, 3, 4+. Prerequisites: Come as you are. Understanding the notion of a differentiable manifold is assumed though. Consequences: To embrace the mightiness of general relativity prepared thou shall be. Key words: Riemannian and pseudo-Riemannian manifolds, metric tensor, connection, covariant derivative, curvature.
11:00 AM
Differential Geometry
-
Olga Chekeres
Differential Geometry
Olga Chekeres
11:00 AM - 11:45 AM
Differential geometry in 1, 2, 3 and more dimensions. Imagine an n-dimensional Riemannian manifold and then set n=1, 2, 3, 4+. Prerequisites: Come as you are. Understanding the notion of a differentiable manifold is assumed though. Consequences: To embrace the mightiness of general relativity prepared thou shall be. Key words: Riemannian and pseudo-Riemannian manifolds, metric tensor, connection, covariant derivative, curvature.
12:00 PM
Lunch
12:00 PM - 1:30 PM
4:00 PM
Coffee Break
4:00 PM - 4:15 PM
4:15 PM
General Relativity
-
Fridrich Valach
(
University of Hertfordshire
)
General Relativity
Fridrich Valach
(
University of Hertfordshire
)
4:15 PM - 5:00 PM
Abstract: General relativity is a beautifully geometric and mathematically rigorous theory describing our universe on large scales, where gravity plays a crucial role. After an introduction to differential and Riemannian geometry we will look in more detail at the mathematical underpinnings of this theory and talk about geodesics, normal coordinates, Einstein equations, and other interesting topics. Keywords: spacetime, metric, curvature, geodesics, normal coordinates, Einstein equations
5:15 PM
General Relativity
-
Fridrich Valach
(
University of Hertfordshire
)
General Relativity
Fridrich Valach
(
University of Hertfordshire
)
5:15 PM - 6:00 PM
Abstract: General relativity is a beautifully geometric and mathematically rigorous theory describing our universe on large scales, where gravity plays a crucial role. After an introduction to differential and Riemannian geometry we will look in more detail at the mathematical underpinnings of this theory and talk about geodesics, normal coordinates, Einstein equations, and other interesting topics. Keywords: spacetime, metric, curvature, geodesics, normal coordinates, Einstein equations
6:15 PM
General Relativity
-
Fridrich Valach
(
University of Hertfordshire
)
General Relativity
Fridrich Valach
(
University of Hertfordshire
)
6:15 PM - 7:00 PM
Abstract: General relativity is a beautifully geometric and mathematically rigorous theory describing our universe on large scales, where gravity plays a crucial role. After an introduction to differential and Riemannian geometry we will look in more detail at the mathematical underpinnings of this theory and talk about geodesics, normal coordinates, Einstein equations, and other interesting topics. Keywords: spacetime, metric, curvature, geodesics, normal coordinates, Einstein equations
7:15 PM
Dinner
7:15 PM - 8:45 PM
Friday, July 19, 2024
9:00 AM
Singular ODes
-
Nikita Nikolaev
(
University of Birmingham
)
Singular ODes
Nikita Nikolaev
(
University of Birmingham
)
9:00 AM - 9:45 AM
9:45 AM
Coffee Break
9:45 AM - 10:00 AM
10:00 AM
Singular ODes
-
Nikita Nikolaev
(
University of Birmingham
)
Singular ODes
Nikita Nikolaev
(
University of Birmingham
)
10:00 AM - 10:45 AM
11:00 AM
Singular ODes
-
Nikita Nikolaev
(
University of Birmingham
)
Singular ODes
Nikita Nikolaev
(
University of Birmingham
)
11:00 AM - 11:45 AM
12:00 PM
Lunch
12:00 PM - 1:30 PM