Mathematics

Spectra and Smash Products 1

Speaker: 
Cary Malkiewich
Date: 
Mon, Jul 18, 2022
Location: 
PIMS, University of British Columbia, Zoom, Online
Conference: 
Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
Abstract: 

A lecture titled "Spectra and Smash Products" by Cary Malkiewich, Binghamton University. This is the 1st in a series of 4.

General Description:
The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last decade that this idea became a key tool in low-dimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)-equivariant Seiberg–Witten Floer homotopy type to resolve the Triangulation Conjecture and Abouzaid-Blumberg's use of Floer homotopy theory and Morava K-theory to prove the general Arnol'd Conjecture in finite characteristic. During this period, a range of related techniques, included under the umbrella of Floer homotopy theory, have also led to important advances, including involutive Heegaard Floer homology, Smith theory for Lagrangian intersections, homotopy coherence, and further connections between string topology and Floer theory. These in turn have sparked developments in algebraic topology, ranging from developments on Lie algebras in derived algebraic geometry to new computations of equivariant Mahowald invariants to new results on topological Hochschild homology.

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

Class: 
Subject: 

Floer Homology Fundamentals 9

Speaker: 
Catherine Cannizzo
Date: 
Fri, Jul 15, 2022
Location: 
PIMS, University of British Columbia, Zoom, Online
Conference: 
Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
Abstract: 

A lecture titled "Floer Homology Fundamentals" by Catherine Cannizzo, SCGP. This is the 9th in a series of 9.

General Description:
The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last decade that this idea became a key tool in low-dimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)-equivariant Seiberg–Witten Floer homotopy type to resolve the Triangulation Conjecture and Abouzaid-Blumberg's use of Floer homotopy theory and Morava K-theory to prove the general Arnol'd Conjecture in finite characteristic. During this period, a range of related techniques, included under the umbrella of Floer homotopy theory, have also led to important advances, including involutive Heegaard Floer homology, Smith theory for Lagrangian intersections, homotopy coherence, and further connections between string topology and Floer theory. These in turn have sparked developments in algebraic topology, ranging from developments on Lie algebras in derived algebraic geometry to new computations of equivariant Mahowald invariants to new results on topological Hochschild homology.

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

Class: 
Subject: 

Floer Homology Fundamentals 8

Speaker: 
Nate Bottman
Date: 
Fri, Jul 15, 2022
Location: 
PIMS, University of British Columbia, Zoom, Online
Conference: 
Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
Abstract: 

A lecture titled "Floer Homology Fundamentals" by Nate Bottman, Max Planck. This is the 8th in a series of 9.

General Description:
The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last decade that this idea became a key tool in low-dimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)-equivariant Seiberg–Witten Floer homotopy type to resolve the Triangulation Conjecture and Abouzaid-Blumberg's use of Floer homotopy theory and Morava K-theory to prove the general Arnol'd Conjecture in finite characteristic. During this period, a range of related techniques, included under the umbrella of Floer homotopy theory, have also led to important advances, including involutive Heegaard Floer homology, Smith theory for Lagrangian intersections, homotopy coherence, and further connections between string topology and Floer theory. These in turn have sparked developments in algebraic topology, ranging from developments on Lie algebras in derived algebraic geometry to new computations of equivariant Mahowald invariants to new results on topological Hochschild homology.

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

Class: 
Subject: 

Math to Power Industry 2022 Gala

Speaker: 
Kristine Bauer
Dhavide Aruliah
Date: 
Thu, Jul 28, 2022
Location: 
Zoom
Online
Conference: 
m2pi2022
Abstract: 

Math^Industry is an annual workshop organized by the Pacific Institute for the Mathematical Sciences to bring together graduate students, academics and industrial partners to work on real world problems. Practical problems from industry are framed by industry partners and project teams are formed to tackle them. The workshop culminates in a gala event where the results of the work on each project is presented.

The gala event took place on zoom and the project reports were presented in three breakout rooms. In the video below, the recordings from these rooms have been placed one after the other and the start time of each is give in square brackets below.

Subject: 

Symplectomorphisms mirror to birational transformations of P^2

Speaker: 
Abigail Ward
Date: 
Thu, Jul 14, 2022
Location: 
PIMS, University of British Columbia, Zoom, Online
Conference: 
Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
Abstract: 

We construct a non-finite type four-dimensional Weinstein domain M_{univ} and describe a HMS-type correspondence between certain birational transformations of P^2 preserving a standard holomorphic volume form and symplectomorphisms of M_{univ}. The space M_{univ} is universal in the sense it admits every Liouville four-manifold mirror to a log Calabi-Yau surface as a Weinstein subdomain; our construction recovers a mirror correspondence between the automorphism group of any open log Calabi-Yau surface and the group of symplectomorphisms of its mirror by restriction to these subdomains. This is joint work in progress with Ailsa Keating.

Class: 
Subject: 

Floer Homology Fundamentals 7

Speaker: 
Nate Bottman
Date: 
Thu, Jul 14, 2022
Location: 
PIMS, University of British Columbia, Zoom, Online
Conference: 
Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
Abstract: 

A lecture titled "Floer Homology Fundamentals" by Nate Bottman, Max Planck. This is the 7th in a series of 9.

General Description:
The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last decade that this idea became a key tool in low-dimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)-equivariant Seiberg–Witten Floer homotopy type to resolve the Triangulation Conjecture and Abouzaid-Blumberg's use of Floer homotopy theory and Morava K-theory to prove the general Arnol'd Conjecture in finite characteristic. During this period, a range of related techniques, included under the umbrella of Floer homotopy theory, have also led to important advances, including involutive Heegaard Floer homology, Smith theory for Lagrangian intersections, homotopy coherence, and further connections between string topology and Floer theory. These in turn have sparked developments in algebraic topology, ranging from developments on Lie algebras in derived algebraic geometry to new computations of equivariant Mahowald invariants to new results on topological Hochschild homology.

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

Class: 
Subject: 

String Topology 3

Speaker: 
Katherine Poirier
Date: 
Thu, Jul 14, 2022
Location: 
PIMS, University of British Columbia, Zoom, Online
Conference: 
Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
Abstract: 

A lecture titled "String Topology" by Katherine Poirier, New York City College of Technology. This is the 3rd in a series of 3.

General Description:
The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last decade that this idea became a key tool in low-dimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)-equivariant Seiberg–Witten Floer homotopy type to resolve the Triangulation Conjecture and Abouzaid-Blumberg's use of Floer homotopy theory and Morava K-theory to prove the general Arnol'd Conjecture in finite characteristic. During this period, a range of related techniques, included under the umbrella of Floer homotopy theory, have also led to important advances, including involutive Heegaard Floer homology, Smith theory for Lagrangian intersections, homotopy coherence, and further connections between string topology and Floer theory. These in turn have sparked developments in algebraic topology, ranging from developments on Lie algebras in derived algebraic geometry to new computations of equivariant Mahowald invariants to new results on topological Hochschild homology.

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

Class: 
Subject: 

Floer Homology Fundamentals 6

Speaker: 
Nate Bottman
Date: 
Thu, Jul 14, 2022
Location: 
PIMS, University of British Columbia, Zoom, Online
Conference: 
Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
Abstract: 

A lecture titled "Floer Homology Fundamentals" by Nate Bottman, Max Planck. This is the 6th in a series of 9.

General Description:
The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last decade that this idea became a key tool in low-dimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)-equivariant Seiberg–Witten Floer homotopy type to resolve the Triangulation Conjecture and Abouzaid-Blumberg's use of Floer homotopy theory and Morava K-theory to prove the general Arnol'd Conjecture in finite characteristic. During this period, a range of related techniques, included under the umbrella of Floer homotopy theory, have also led to important advances, including involutive Heegaard Floer homology, Smith theory for Lagrangian intersections, homotopy coherence, and further connections between string topology and Floer theory. These in turn have sparked developments in algebraic topology, ranging from developments on Lie algebras in derived algebraic geometry to new computations of equivariant Mahowald invariants to new results on topological Hochschild homology.

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

Class: 
Subject: 

String Topology 2

Speaker: 
Katherine Poirier
Date: 
Wed, Jul 13, 2022
Location: 
PIMS, University of British Columbia, Zoom, Online
Conference: 
Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
Abstract: 

A lecture titled "String Topology" by Katherine Poirier, New York City College of Technology. This is the 2nd in a series of 3.

General Description:
The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last decade that this idea became a key tool in low-dimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)-equivariant Seiberg–Witten Floer homotopy type to resolve the Triangulation Conjecture and Abouzaid-Blumberg's use of Floer homotopy theory and Morava K-theory to prove the general Arnol'd Conjecture in finite characteristic. During this period, a range of related techniques, included under the umbrella of Floer homotopy theory, have also led to important advances, including involutive Heegaard Floer homology, Smith theory for Lagrangian intersections, homotopy coherence, and further connections between string topology and Floer theory. These in turn have sparked developments in algebraic topology, ranging from developments on Lie algebras in derived algebraic geometry to new computations of equivariant Mahowald invariants to new results on topological Hochschild homology.

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

Class: 
Subject: 

Floer Homology Fundamentals 4

Speaker: 
Nate Bottman
Date: 
Tue, Jul 12, 2022
Location: 
PIMS, University of British Columbia, Zoom, Online
Conference: 
Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
Abstract: 

A lecture titled "Floer Homology Fundamentals" by Nate Bottman, Max Planck. This is the 4th in a series of 9.

General Description:
The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last decade that this idea became a key tool in low-dimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)-equivariant Seiberg–Witten Floer homotopy type to resolve the Triangulation Conjecture and Abouzaid-Blumberg's use of Floer homotopy theory and Morava K-theory to prove the general Arnol'd Conjecture in finite characteristic. During this period, a range of related techniques, included under the umbrella of Floer homotopy theory, have also led to important advances, including involutive Heegaard Floer homology, Smith theory for Lagrangian intersections, homotopy coherence, and further connections between string topology and Floer theory. These in turn have sparked developments in algebraic topology, ranging from developments on Lie algebras in derived algebraic geometry to new computations of equivariant Mahowald invariants to new results on topological Hochschild homology.

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

Class: 
Subject: 

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