There are no events at the Simons Center today. Here are the events for this week

Monday, October 15th, 2018

Exactly Solvable Program Seminar: Jean-Marie Stephan

Time: 11:30 AM - 12:30 PM

Location: 313

Description:

__Title__: Effective descriptions of inhomogeneous systems in condensed matter and statistical mechanics

__Abstract__: I will discuss the ground state physics of 1d integrable and non integrable inhomogeneous quantum critical systems. By inhomogeneous I mean that the couplings in the underlying model may now depend on position. Examples include spin chains in a position-dependent magnetic field, Lieb-Liniger models in a trapping potential, or entanglement Hamiltonians of homogeneous systems. Studying those models naturally leads to conformal field theories in a curved metric. I will also discuss the universal properties that may be found at the edge, and how all those problems are related to the limit shape phenomenon in statistical mechanics.

Weekly Physics Meeting: Yuya Tanizaki

Time: 2:30 PM - 3:30 PM

Location: 313

Description:

__Title__: Applications of anomaly matching to SU(N) spin chains and generalization of Haldane conjecture

__Abstract__: We discuss an application of anomaly matching to study the phase structure of SU(N) spin chain. Anomaly matching is a field-theoretic avatar of Lieb-Schultz-Mattis theorem, and gives a useful tool to understand nonperturbative aspects of strongly-coupled systems. Low-energy effective theory of SU(N) anti-ferromagnetic Heisenberg chain of p-box representation is described by SU(N)/U(1)^{N-1} nonlinear sigma model with the specific theta angles, and we show that its phase diagram in terms of theta angles is almost completely determined only by symmetry, anomaly, and global inconsistency. We further show that if we have Z_N lattice translation, the anomaly matching suggests that the low-energy limit is described by SU(N)_gcd(N,p) Wess-Zumino-Witten model.

Tuesday, October 16th, 2018

SCGP Weekly Talk: Michael Anderson

Time: 1:00 PM - 2:00 PM

Location:

Description:

__Title__: Boundaries in Euclidean and Lorentzian Gravity

__Abstract__: There is no existence theory for Riemannian Einstein metrics on compact manifolds, while there is an excellent theory for Lorentzian Einstein metrics (GR). What happens when one puts in a boundary, creating a boundary value problem - at finite or infinite distance? What are the correct boundary data? This makes the Riemannian existence problem more amenable - one can start to build a theory, but the Lorentzian problem becomes more difficult. The talk will discuss some results, perspectives and open problems in this area.

Wednesday, October 17th, 2018

Physics Seminar: Avner Karasik

Time: 1:30 PM - 2:30 PM

Location: SCGP 313

Description:

__Title__: On the phase diagram of SU(N)XSU(N) gauge theory with bifundamental Fermion.

__Abstract__: We study the phase diagram of SU(N)XSU(N) gauge theory with massive bifundamental Fermion at zero temperature. Assuming that the theory is confining and gapped, some constraints that come from anomalies can be put on the phase diagram as a function of the two theta- angles. We combine these constraints with computations that are valid in the large mass and small mass limits to construct the phase diagram also for intermediate mass.

**Math Event:**Algebraic Geometry: Matt Kerr - Hodge theory of degenerations

Time: 4:00 PM - 5:30 PM

Location: Math Tower P-131

Description:

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__Title__: Hodge theory of degenerations

__Speaker__: Matt Kerr [Washington University in St Louis]

__Abstract__: The asymptotics and monodromy of periods in degenerating families of algebraic varieties are encountered in many settings -- for example, in comparing (GIT, KSBA, Hodge-theoretic) compactifications of moduli, in computing limits of geometric normal functions, and in topological string theory. In this talk, based on work with Radu Laza, we shall describe several tools (beginning with classical ones) for comparing the Hodge theory of singular fibers to that of their nearby fibers, and touch on some relations to birational geometry.

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Thursday, October 18th, 2018

Exactly Solvable Program Seminar: Fabio Franchini

Time: 2:00 PM - 3:00 PM

Location: 313

Description:

__Title__: The Frustration in being Odd: area law violation in local systems

__Abstract__: We demonstrate the existence of a new quantum phase of matter that arises in antiferromagnetic spin chains with a weak frustration -just one bond in a large chain-. This is the case, for instance, of systems with an odd number of spins with periodic boundary conditions. Such new phase is extended, gapless, but not relativistic: the low-energy excitations have a quadratic (Galilean) spectrum. Locally, the correlation functions on the ground state do not show significant deviations compared to the non-frustrated case, but correlators involving a number of sites (or distances) scaling like the system size display new behaviors. In particular, the von Neumann entanglement entropy is found to follow new rules, for which neither area law applies, nor one has a divergence of the entropy with the system size. Such very long-range correlations are novel and of potential technological interest. We display such new phase in a few prototypical chains using numerical simulations and we study analytically the paradigmatic example of the Ising chain. Through these examples we argue that this phase emerges generally in (weakly) frustrated systems with discrete symmetries. - Salvatore Marco Giampaolo, Flávia Braga Ramos, Fabio Franchini: arXiv:1807.07055

**Math Event:**Math Colloquium: Ailana Fraser - Geometries that optimize eigenvalues

Time: 4:00 PM - 5:00 PM

Location: Math Tower P-131

Description:

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__Title__: Geometries that optimize eigenvalues

__Speaker__: Ailana Fraser [UBC]

__Abstract__: When we choose a metric on a manifold we determine the spectrum of the Laplace operator. Thus an eigenvalue may be considered as a functional on the space of metrics. For example the first eigenvalue would be the fundamental vibrational frequency. In some cases the normalized eigenvalues are bounded independent of the metric. In such cases it makes sense to attempt to find critical points in the space of metrics. For surfaces, the critical metrics turn out to be the induced metrics on certain special classes of minimal (mean curvature zero) surfaces in spheres and Euclidean balls. The eigenvalue extremal problem is thus related to other questions arising in the theory of minimal surfaces. In this talk we will give an overview of progress that has been made for surfaces with boundary, and contrast this with some recent results in higher dimensions. This is joint work with R. Schoen.

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Friday, October 19th, 2018

Exactly Solvable Program Seminar: Jacopo Viti

Time: 11:00 AM - 12:00 PM

Location: 313

Description:

__Title__: Exact logarithmic boundary connectivities in 2d critical percolation

__Abstract__: I will conjecture an exact form for an universal ratio of four-point cluster connectivities in the critical two-dimensional Q-color Potts model. I in particular will provide results for the limit Q->1 that corresponds to percolation, a non-unitary CFT where the observable has a logarithmic singularity. These conjectures are tested against Monte Carlo simulations showing excellent agreement for Q=1,2 and 3.