Event Category: Berkeley String-Math Seminar

Berkeley String-Math Seminar

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abstract: In recent work, Aganagic proposed a categorification of quantum link invariants using Lagrangian Floer theory in multiplicative Coulomb branches equipped with a potential. The braid group action arises from monodromy of this potential. We show that in the case g=sl(2), this braid group action agrees with the braid group action constructed by Webster, which proves that Aganagic’s proposal gives … Read More

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Abstract:  Inverse Hamiltonian reduction refers to a series of conjectural relations between W-algebras corresponding to distinct nilpotent orbits in a Lie algebra. I will outline a proof of this conjecture in type A that relies on novel geometric methods. Along the way, we shall encounter the localization of vertex algebras and, time permitting, speak briefly on the deformation theory thereof. … Read More

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This will be a report on a joint project with Yalong Cao, Yehao Zhou, and Zijun Zhou, in which we systematically explore the world of stable envelopes in critical cohomology and critical K-theory. We will compare and contrast old stable envelope to the more general critical stable envelopes, with an emphasis on the contrasting features.

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Abstract: Nahm’s construction of magnetic monopoles produced all monopoles with gauge (structure) group G=U(n).  It was generalized by Hurtubise and Murray to SO and Sp monopoles.  For any compact Lie group G, in principle, Nahm’s construction can be used to obtain monopoles in any given unitary representation of G.  For example, for G=E_8, the smallest such representation has dimension 248, … Read More

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Abstract: A quasimap from a curve to a GIT quotient is a map to the stack quotient that is generically stable. An open subset of quasimaps from P^1 to the flag variety, usually called Laumon space or handsaw quiver variety, is known to be closely related to the representation theory of gl_n. In particular, one can construct an action of … Read More

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Abstract: Inverse Hamiltonian reduction refers to a series of conjectural relations between W-algebras corresponding to distinct nilpotent orbits in a Lie algebra. I will outline a proof of this conjecture in type A that relies on novel geometric methods. Along the way, we shall encounter the localization of vertex algebras and, time permitting, speak briefly on the deformation theory thereof. … Read More

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Abstract:  This is a series of two lectures on categorifying quantum group U_q(g) using Fukaya categories proposed by Mina Aganagic. In the first lecture, we will give an introduction to the theory, focusing on the geometric setup, basic calculations and connection to representation theory; in the second lecture we will discuss the TQFT structures underlying our theory, proposing the definition … Read More

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Abstract: This is the 2nd part of a series of two talks on categorification of quantum group U_q(g) using Fukaya categories proposed by Mina Aganagic. In the first talk, we will give an introduction to the theory, focusing on the geometric setup, basic calculations and connection to representation theory; in the second talk we will discuss the TQFT structures underlying … Read More

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Abstract: For any well-behaved link homology theory for links in the 3-sphere, Morrison–Walker–Wedrich defined an invariant for smooth 4-manifolds called skein lasagna modules, which can be viewed as an upgrade of the input link homology theory. We review the definition and investigate some formal properties of the invariant. We also introduce a few variations of the invariant. In the case where … Read More