February 20, 2020
1:50 pm
-
2:50 pm
Cockins Hall 240
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2020-02-20 14:50:00
2020-02-20 15:50:00
Quantum Algebra/Quantum Topology Seminar - Aaron Lauda
Title: Bordered Heegaard-Floer homology, category O, and higher representation theory
Speaker: Aaron Lauda - University of Southern California
Abstract: The Alexander polynomial for knots and links can be interpreted as a quantum knot invariant associated with the quantum group of the Lie superalgebra gl(1|1). This polynomial has been famously categorified to a link homology theory, knot Floer homology, defined within the theory of Heegaard-Floer homology. Andy Manion showed that the Ozsvath-Szabo algebras used to efficiently compute knot Floer homology categorify certain tensor products of gl(1|1) representations. For representation theorists, work of Sartori provides a different categorification of these same tensors products using subquotients of BGG category O. In this talk we will explain joint work with Andy Manion establishing a direct relationship between these two constructions. Given the radically different nature of these two approaches, transporting ideas between them provides a new perspective and allows for results that would not have been apparent otherwise, including a surprising connection between Ozsvath-Szabo theory and hypertoric varieties.
Cockins Hall 240
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America/New_York
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2020-02-20 13:50:00
2020-02-20 14:50:00
Quantum Algebra/Quantum Topology Seminar - Aaron Lauda
Title: Bordered Heegaard-Floer homology, category O, and higher representation theory
Speaker: Aaron Lauda - University of Southern California
Abstract: The Alexander polynomial for knots and links can be interpreted as a quantum knot invariant associated with the quantum group of the Lie superalgebra gl(1|1). This polynomial has been famously categorified to a link homology theory, knot Floer homology, defined within the theory of Heegaard-Floer homology. Andy Manion showed that the Ozsvath-Szabo algebras used to efficiently compute knot Floer homology categorify certain tensor products of gl(1|1) representations. For representation theorists, work of Sartori provides a different categorification of these same tensors products using subquotients of BGG category O. In this talk we will explain joint work with Andy Manion establishing a direct relationship between these two constructions. Given the radically different nature of these two approaches, transporting ideas between them provides a new perspective and allows for results that would not have been apparent otherwise, including a surprising connection between Ozsvath-Szabo theory and hypertoric varieties.
Cockins Hall 240
America/New_York
public
Title: Bordered Heegaard-Floer homology, category O, and higher representation theory
Speaker: Aaron Lauda - University of Southern California
Abstract: The Alexander polynomial for knots and links can be interpreted as a quantum knot invariant associated with the quantum group of the Lie superalgebra gl(1|1). This polynomial has been famously categorified to a link homology theory, knot Floer homology, defined within the theory of Heegaard-Floer homology. Andy Manion showed that the Ozsvath-Szabo algebras used to efficiently compute knot Floer homology categorify certain tensor products of gl(1|1) representations. For representation theorists, work of Sartori provides a different categorification of these same tensors products using subquotients of BGG category O. In this talk we will explain joint work with Andy Manion establishing a direct relationship between these two constructions. Given the radically different nature of these two approaches, transporting ideas between them provides a new perspective and allows for results that would not have been apparent otherwise, including a surprising connection between Ozsvath-Szabo theory and hypertoric varieties.
