Jul 25, 2022
Monday

09:00 AM  09:15 AM


Introduction to MSRI

 Location
 
 Video


 Abstract
 
 Supplements



09:15 AM  10:15 AM


KKMType Theorems and their Applications Pt I
Shira Zerbib (Iowa State University)

 Location
 
 Video

 Abstract
The KKM theorem, due to Knaster, Kuratowski and Mazurkiewicz in 1929, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fixed point theorem. It has numerous applications in combinatorics, discrete geometry, economics, game theory and other areas. Generalizations of this lemma, in several different directions, were proved over the years (e.g., by Shapley, Gale, ShihLee, Komiya, FrickZerbib, and Soberon) and have been widely applied as well. In my lecture series we will prove several different KKMtype theorems and use them to solve a variety of problems in discrete geometry, combinatorics and game theory. We will also discuss open problems that may benefit from a similar topological approach.
 Supplements



10:15 AM  10:45 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



10:45 AM  12:00 PM


Intersection Patterns in Combinatorics, Geometry, and Topology Pt I
Florian Frick (Carnegie Mellon University)

 Location
 
 Video

 Abstract
Given a collection of sets, we will investigate what can be said about how these sets intersect one another in the presence or absence of additional structure. In the case of no further structure this is a fundamental combinatorial problem with various incarnations, such as graph and hypergraph colorings and combinatorial design theory. In the geometric setting we will encounter the main results of convex geometry, while in the topological setting such questions concern the embeddability of one space into another. We will see that the combinatorial, geometric, and topological settings should not be seen as disjoint, but that they inform one another. This viewpoint will provide us with methods to solve problems of this form and unifying results that explain recurring phenomena.
 Supplements



12:00 PM  01:45 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



01:45 PM  03:00 PM


Using Equivariant Topology Pt I
Pavle Blagojevic (Freie Universität Berlin)

 Location
 
 Video

 Abstract
Various classes of problems from discrete and convex geometry, mathematical mechanics, algorithm complexity theory and approximation theory can be transformed into challenging, and often unsolved problems in equivariant topology. The focus of our lecture series is understanding where these topological problems come from and then demonstrating some of the diverse methods of algebraic topology which are critical to study and subsequently solve them.
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Discussion Session

 Location
 
 Video


 Abstract
 
 Supplements




Jul 26, 2022
Tuesday

09:00 AM  10:15 AM


KKMType Theorems and their Applications Pt II
Shira Zerbib (Iowa State University)

 Location
 
 Video

 Abstract
The KKM theorem, due to Knaster, Kuratowski and Mazurkiewicz in 1929, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fixed point theorem. It has numerous applications in combinatorics, discrete geometry, economics, game theory and other areas. Generalizations of this lemma, in several different directions, were proved over the years (e.g., by Shapley, Gale, ShihLee, Komiya, FrickZerbib, and Soberon) and have been widely applied as well. In my lecture series we will prove several different KKMtype theorems and use them to solve a variety of problems in discrete geometry, combinatorics and game theory. We will also discuss open problems that may benefit from a similar topological approach.
 Supplements



10:15 AM  10:45 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



10:45 AM  12:00 PM


Intersection Patterns in Combinatorics, Geometry, and Topology Pt II
Florian Frick (Carnegie Mellon University)

 Location
 
 Video

 Abstract
Given a collection of sets, we will investigate what can be said about how these sets intersect one another in the presence or absence of additional structure. In the case of no further structure this is a fundamental combinatorial problem with various incarnations, such as graph and hypergraph colorings and combinatorial design theory. In the geometric setting we will encounter the main results of convex geometry, while in the topological setting such questions concern the embeddability of one space into another. We will see that the combinatorial, geometric, and topological settings should not be seen as disjoint, but that they inform one another. This viewpoint will provide us with methods to solve problems of this form and unifying results that explain recurring phenomena.
 Supplements



12:00 PM  01:45 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



01:45 PM  03:00 PM


Using Equivariant Topology Pt II
Pavle Blagojevic (Freie Universität Berlin)

 Location
 
 Video

 Abstract
Various classes of problems from discrete and convex geometry, mathematical mechanics, algorithm complexity theory and approximation theory can be transformed into challenging, and often unsolved problems in equivariant topology. The focus of our lecture series is understanding where these topological problems come from and then demonstrating some of the diverse methods of algebraic topology which are critical to study and subsequently solve them.
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Discussion Session

 Location
 
 Video


 Abstract
 
 Supplements




Jul 27, 2022
Wednesday

09:00 AM  10:15 AM


KKMType Theorems and their Applications Pt III
Shira Zerbib (Iowa State University)

 Location
 
 Video

 Abstract
The KKM theorem, due to Knaster, Kuratowski and Mazurkiewicz in 1929, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fixed point theorem. It has numerous applications in combinatorics, discrete geometry, economics, game theory and other areas. Generalizations of this lemma, in several different directions, were proved over the years (e.g., by Shapley, Gale, ShihLee, Komiya, FrickZerbib, and Soberon) and have been widely applied as well. In my lecture series we will prove several different KKMtype theorems and use them to solve a variety of problems in discrete geometry, combinatorics and game theory. We will also discuss open problems that may benefit from a similar topological approach.
 Supplements



10:15 AM  10:45 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



10:45 AM  12:00 PM


Intersection Patterns in Combinatorics, Geometry, and Topology Pt III
Florian Frick (Carnegie Mellon University)

 Location
 
 Video

 Abstract
Given a collection of sets, we will investigate what can be said about how these sets intersect one another in the presence or absence of additional structure. In the case of no further structure this is a fundamental combinatorial problem with various incarnations, such as graph and hypergraph colorings and combinatorial design theory. In the geometric setting we will encounter the main results of convex geometry, while in the topological setting such questions concern the embeddability of one space into another. We will see that the combinatorial, geometric, and topological settings should not be seen as disjoint, but that they inform one another. This viewpoint will provide us with methods to solve problems of this form and unifying results that explain recurring phenomena.
 Supplements



12:00 PM  01:45 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



01:45 PM  03:00 PM


Using Equivariant Topology Pt III
Pavle Blagojevic (Freie Universität Berlin)

 Location
 
 Video

 Abstract
Various classes of problems from discrete and convex geometry, mathematical mechanics, algorithm complexity theory and approximation theory can be transformed into challenging, and often unsolved problems in equivariant topology. The focus of our lecture series is understanding where these topological problems come from and then demonstrating some of the diverse methods of algebraic topology which are critical to study and subsequently solve them.
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Discussion Session

 Location
 
 Video


 Abstract
 
 Supplements




Jul 28, 2022
Thursday

09:00 AM  10:15 AM


KKMType Theorems and their Applications Pt IV
Shira Zerbib (Iowa State University)

 Location
 
 Video

 Abstract
The KKM theorem, due to Knaster, Kuratowski and Mazurkiewicz in 1929, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fixed point theorem. It has numerous applications in combinatorics, discrete geometry, economics, game theory and other areas. Generalizations of this lemma, in several different directions, were proved over the years (e.g., by Shapley, Gale, ShihLee, Komiya, FrickZerbib, and Soberon) and have been widely applied as well. In my lecture series we will prove several different KKMtype theorems and use them to solve a variety of problems in discrete geometry, combinatorics and game theory. We will also discuss open problems that may benefit from a similar topological approach.
 Supplements



10:15 AM  10:45 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



10:45 AM  12:00 PM


Intersection Patterns in Combinatorics, Geometry, and Topology Pt IV
Florian Frick (Carnegie Mellon University)

 Location
 
 Video

 Abstract
Given a collection of sets, we will investigate what can be said about how these sets intersect one another in the presence or absence of additional structure. In the case of no further structure this is a fundamental combinatorial problem with various incarnations, such as graph and hypergraph colorings and combinatorial design theory. In the geometric setting we will encounter the main results of convex geometry, while in the topological setting such questions concern the embeddability of one space into another. We will see that the combinatorial, geometric, and topological settings should not be seen as disjoint, but that they inform one another. This viewpoint will provide us with methods to solve problems of this form and unifying results that explain recurring phenomena.
 Supplements



12:00 PM  01:45 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



01:45 PM  03:00 PM


Using Equivariant Topology Pt IV
Pavle Blagojevic (Freie Universität Berlin)

 Location
 
 Video

 Abstract
Various classes of problems from discrete and convex geometry, mathematical mechanics, algorithm complexity theory and approximation theory can be transformed into challenging, and often unsolved problems in equivariant topology. The focus of our lecture series is understanding where these topological problems come from and then demonstrating some of the diverse methods of algebraic topology which are critical to study and subsequently solve them.
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Discussion Session

 Location
 
 Video


 Abstract
 
 Supplements




Jul 29, 2022
Friday

09:00 AM  10:15 AM


KKMType Theorems and their Applications Pt V
Shira Zerbib (Iowa State University)

 Location
 
 Video

 Abstract
The KKM theorem, due to Knaster, Kuratowski and Mazurkiewicz in 1929, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fixed point theorem. It has numerous applications in combinatorics, discrete geometry, economics, game theory and other areas. Generalizations of this lemma, in several different directions, were proved over the years (e.g., by Shapley, Gale, ShihLee, Komiya, FrickZerbib, and Soberon) and have been widely applied as well. In my lecture series we will prove several different KKMtype theorems and use them to solve a variety of problems in discrete geometry, combinatorics and game theory. We will also discuss open problems that may benefit from a similar topological approach.
 Supplements



10:15 AM  10:45 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



10:45 AM  12:00 PM


Intersection Patterns in Combinatorics, Geometry, and Topology Pt V
Florian Frick (Carnegie Mellon University)

 Location
 
 Video

 Abstract
Given a collection of sets, we will investigate what can be said about how these sets intersect one another in the presence or absence of additional structure. In the case of no further structure this is a fundamental combinatorial problem with various incarnations, such as graph and hypergraph colorings and combinatorial design theory. In the geometric setting we will encounter the main results of convex geometry, while in the topological setting such questions concern the embeddability of one space into another. We will see that the combinatorial, geometric, and topological settings should not be seen as disjoint, but that they inform one another. This viewpoint will provide us with methods to solve problems of this form and unifying results that explain recurring phenomena.
 Supplements



12:00 PM  01:45 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



01:45 PM  03:00 PM


Using Equivariant Topology Pt V
Pavle Blagojevic (Freie Universität Berlin)

 Location
 
 Video

 Abstract
Various classes of problems from discrete and convex geometry, mathematical mechanics, algorithm complexity theory and approximation theory can be transformed into challenging, and often unsolved problems in equivariant topology. The focus of our lecture series is understanding where these topological problems come from and then demonstrating some of the diverse methods of algebraic topology which are critical to study and subsequently solve them.
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Discussion Session

 Location
 
 Video


 Abstract
 
 Supplements




Aug 01, 2022
Monday

09:00 AM  10:15 AM


KKMType Theorems and their Applications Pt VI
Shira Zerbib (Iowa State University)

 Location
 
 Video

 Abstract
The KKM theorem, due to Knaster, Kuratowski and Mazurkiewicz in 1929, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fixed point theorem. It has numerous applications in combinatorics, discrete geometry, economics, game theory and other areas. Generalizations of this lemma, in several different directions, were proved over the years (e.g., by Shapley, Gale, ShihLee, Komiya, FrickZerbib, and Soberon) and have been widely applied as well. In my lecture series we will prove several different KKMtype theorems and use them to solve a variety of problems in discrete geometry, combinatorics and game theory. We will also discuss open problems that may benefit from a similar topological approach.
 Supplements



10:15 AM  10:45 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



10:45 AM  12:00 PM


Intersection Patterns in Combinatorics, Geometry, and Topology Pt VI
Florian Frick (Carnegie Mellon University)

 Location
 
 Video

 Abstract
Given a collection of sets, we will investigate what can be said about how these sets intersect one another in the presence or absence of additional structure. In the case of no further structure this is a fundamental combinatorial problem with various incarnations, such as graph and hypergraph colorings and combinatorial design theory. In the geometric setting we will encounter the main results of convex geometry, while in the topological setting such questions concern the embeddability of one space into another. We will see that the combinatorial, geometric, and topological settings should not be seen as disjoint, but that they inform one another. This viewpoint will provide us with methods to solve problems of this form and unifying results that explain recurring phenomena.
 Supplements



12:00 PM  01:45 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



01:45 PM  03:00 PM


Discussion Session

 Location
 
 Video


 Abstract
 
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Problem Session

 Location
 
 Video


 Abstract
 
 Supplements




Aug 02, 2022
Tuesday

09:00 AM  10:15 AM


Using Equivariant Topology Pt VI
Pavle Blagojevic (Freie Universität Berlin)

 Location
 
 Video

 Abstract
Various classes of problems from discrete and convex geometry, mathematical mechanics, algorithm complexity theory and approximation theory can be transformed into challenging, and often unsolved problems in equivariant topology. The focus of our lecture series is understanding where these topological problems come from and then demonstrating some of the diverse methods of algebraic topology which are critical to study and subsequently solve them.
 Supplements



10:15 AM  10:45 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



10:45 AM  12:00 PM


KKMType Theorems and their Applications Pt VII
Shira Zerbib (Iowa State University)

 Location
 
 Video

 Abstract
The KKM theorem, due to Knaster, Kuratowski and Mazurkiewicz in 1929, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fixed point theorem. It has numerous applications in combinatorics, discrete geometry, economics, game theory and other areas. Generalizations of this lemma, in several different directions, were proved over the years (e.g., by Shapley, Gale, ShihLee, Komiya, FrickZerbib, and Soberon) and have been widely applied as well. In my lecture series we will prove several different KKMtype theorems and use them to solve a variety of problems in discrete geometry, combinatorics and game theory. We will also discuss open problems that may benefit from a similar topological approach.
 Supplements



12:00 PM  01:45 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



01:45 PM  03:00 PM


Discussion Session

 Location
 
 Video


 Abstract
 
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Problem Session

 Location
 
 Video


 Abstract
 
 Supplements




Aug 03, 2022
Wednesday

09:00 AM  10:15 AM


Intersection Patterns in Combinatorics, Geometry, and Topology Pt VII
Florian Frick (Carnegie Mellon University)

 Location
 
 Video

 Abstract
Given a collection of sets, we will investigate what can be said about how these sets intersect one another in the presence or absence of additional structure. In the case of no further structure this is a fundamental combinatorial problem with various incarnations, such as graph and hypergraph colorings and combinatorial design theory. In the geometric setting we will encounter the main results of convex geometry, while in the topological setting such questions concern the embeddability of one space into another. We will see that the combinatorial, geometric, and topological settings should not be seen as disjoint, but that they inform one another. This viewpoint will provide us with methods to solve problems of this form and unifying results that explain recurring phenomena.
 Supplements



10:15 AM  10:45 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



10:45 AM  12:00 PM


Using Equivariant Topology Pt VII
Pavle Blagojevic (Freie Universität Berlin)

 Location
 
 Video

 Abstract
Various classes of problems from discrete and convex geometry, mathematical mechanics, algorithm complexity theory and approximation theory can be transformed into challenging, and often unsolved problems in equivariant topology. The focus of our lecture series is understanding where these topological problems come from and then demonstrating some of the diverse methods of algebraic topology which are critical to study and subsequently solve them.
 Supplements



12:00 PM  01:45 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



01:45 PM  03:00 PM


Discussion Session

 Location
 
 Video


 Abstract
 
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Problem Session

 Location
 
 Video


 Abstract
 
 Supplements




Aug 04, 2022
Thursday

09:00 AM  10:15 AM


KKMType Theorems and their Applications Pt VIII
Shira Zerbib (Iowa State University)

 Location
 
 Video

 Abstract
The KKM theorem, due to Knaster, Kuratowski and Mazurkiewicz in 1929, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fixed point theorem. It has numerous applications in combinatorics, discrete geometry, economics, game theory and other areas. Generalizations of this lemma, in several different directions, were proved over the years (e.g., by Shapley, Gale, ShihLee, Komiya, FrickZerbib, and Soberon) and have been widely applied as well. In my lecture series we will prove several different KKMtype theorems and use them to solve a variety of problems in discrete geometry, combinatorics and game theory. We will also discuss open problems that may benefit from a similar topological approach.
 Supplements



10:15 AM  10:45 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



10:45 AM  12:00 PM


Intersection Patterns in Combinatorics, Geometry, and Topology Pt VIII
Florian Frick (Carnegie Mellon University)

 Location
 
 Video

 Abstract
Given a collection of sets, we will investigate what can be said about how these sets intersect one another in the presence or absence of additional structure. In the case of no further structure this is a fundamental combinatorial problem with various incarnations, such as graph and hypergraph colorings and combinatorial design theory. In the geometric setting we will encounter the main results of convex geometry, while in the topological setting such questions concern the embeddability of one space into another. We will see that the combinatorial, geometric, and topological settings should not be seen as disjoint, but that they inform one another. This viewpoint will provide us with methods to solve problems of this form and unifying results that explain recurring phenomena.
 Supplements



12:00 PM  01:45 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



01:45 PM  03:00 PM


Discussion Session

 Location
 
 Video


 Abstract
 
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Problem Session

 Location
 
 Video


 Abstract
 
 Supplements




Aug 05, 2022
Friday

09:00 AM  10:15 AM


Using Equivariant Topology Pt VIII
Pavle Blagojevic (Freie Universität Berlin)

 Location
 
 Video

 Abstract
Various classes of problems from discrete and convex geometry, mathematical mechanics, algorithm complexity theory and approximation theory can be transformed into challenging, and often unsolved problems in equivariant topology. The focus of our lecture series is understanding where these topological problems come from and then demonstrating some of the diverse methods of algebraic topology which are critical to study and subsequently solve them.
 Supplements



10:15 AM  10:45 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



10:45 AM  12:00 PM


KKMType Theorems and their Applications Pt IX
Shira Zerbib (Iowa State University)

 Location
 
 Video

 Abstract
The KKM theorem, due to Knaster, Kuratowski and Mazurkiewicz in 1929, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fixed point theorem. It has numerous applications in combinatorics, discrete geometry, economics, game theory and other areas. Generalizations of this lemma, in several different directions, were proved over the years (e.g., by Shapley, Gale, ShihLee, Komiya, FrickZerbib, and Soberon) and have been widely applied as well. In my lecture series we will prove several different KKMtype theorems and use them to solve a variety of problems in discrete geometry, combinatorics and game theory. We will also discuss open problems that may benefit from a similar topological approach.
 Supplements



12:00 PM  01:45 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



01:45 PM  03:00 PM


Discussion Session

 Location
 
 Video


 Abstract
 
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Problem Session

 Location
 
 Video


 Abstract
 
 Supplements



