Triangle Seminars
Tuesday, 26 Nov 2019
TBA
Congkao Wen
Reflections and sum-rules for CFTs and modular forms
📍 London
David McGady
(NORDITA)
Abstract:
In this talk, we discuss conformal field theories in two dimensions (2d CFTs) and aspects of the theory of modular forms. Physical considerations lead us to study two extensions to the theory of modular forms: modular forms for GL2(Z) that are defined on the double half-plane (in distinction to SL2(Z) modular forms defined on the upper half-plane), and L-functions for modular forms with poles *within* the fundamental domain. We introduce both concepts, and discuss their consistency, both with each other and with the physical considerations which led to them. Finally, we note that very similar physical considerations may apply to finite-temperature path integrals for generic QFTs in higher dimensions, and comment on possible consequences of this.
In this talk, we discuss conformal field theories in two dimensions (2d CFTs) and aspects of the theory of modular forms. Physical considerations lead us to study two extensions to the theory of modular forms: modular forms for GL2(Z) that are defined on the double half-plane (in distinction to SL2(Z) modular forms defined on the upper half-plane), and L-functions for modular forms with poles *within* the fundamental domain. We introduce both concepts, and discuss their consistency, both with each other and with the physical considerations which led to them. Finally, we note that very similar physical considerations may apply to finite-temperature path integrals for generic QFTs in higher dimensions, and comment on possible consequences of this.
Posted by: KCL
TBA
Laure Daviaud
(City)
Abstract:
Postponed due to strike
Postponed due to strike
Posted by: CityU2
Wednesday, 27 Nov 2019
Modularity of 3-manifold invariants
📍 London
Francesca Ferrari
(SISSA)
Abstract:
Since the 1980s, the study of invariants of 3-dimensional manifolds has
benefited from the connections between topology, physics and number
theory. Recently, a new topological invariant has been discovered: the
homological block (also known as the half-index of certain 3d N=2
theories). When the 3-manifold is a Seifert manifold given by a
negative-definite plumbing the homological block turned out to be
related to false theta functions and characters of logarithmic VOA's. In
this talk I describe the role of quantum modular forms, false and mock
theta functions in the study of the topology of 3-manifolds. The talk is
based on the article 1809.10148 and work in progress with Cheng, Chun,
Feigin, Gukov, and Harrison.
Since the 1980s, the study of invariants of 3-dimensional manifolds has
benefited from the connections between topology, physics and number
theory. Recently, a new topological invariant has been discovered: the
homological block (also known as the half-index of certain 3d N=2
theories). When the 3-manifold is a Seifert manifold given by a
negative-definite plumbing the homological block turned out to be
related to false theta functions and characters of logarithmic VOA's. In
this talk I describe the role of quantum modular forms, false and mock
theta functions in the study of the topology of 3-manifolds. The talk is
based on the article 1809.10148 and work in progress with Cheng, Chun,
Feigin, Gukov, and Harrison.
Posted by: KCL
TBA
Schlomo Razamat
(Technion)
Thursday, 28 Nov 2019
Cluster Adjacency, Tropical Geometry, and Scattering Amplitudes
Jack Foster
(University of Southampton)
Abstract:
I will discuss two new areas of interest in scattering amplitudes: cluster adjacency and tropical geometry. The former describes how the analytic structure of planar amplitudes in N=4 Super Yang-Mills is controlled by mathematical objects called cluster algebras. The latter has been used to calculate amplitudes in the biadjoint phi^3 theory, which I will discuss briefly, but it also has implications for cluster adjacency.
I will discuss two new areas of interest in scattering amplitudes: cluster adjacency and tropical geometry. The former describes how the analytic structure of planar amplitudes in N=4 Super Yang-Mills is controlled by mathematical objects called cluster algebras. The latter has been used to calculate amplitudes in the biadjoint phi^3 theory, which I will discuss briefly, but it also has implications for cluster adjacency.
Posted by: QMW