Calendar

Quantum many-body scars have been an active area of research in Condensed Matter Physics for several years. In some many-body systems, the Hilbert space breaks up into a large ergodic sector and a much smaller scar subspace. It has been suggested [K. Pakrouski et al., Phys. Rev. Lett. 125 (2020) 230602] that the two sectors may be distinguished by their transformation properties under a large group whose rank grows with the system size (this group is not a symmetry of the Hamiltonian). The scars are invariant under this group, while all other states are not. We begin by reviewing some many-body systems where group singlet states have special properties: the matrix quantum mechanics and fermionic tensor models. We continue on to appropriately deformed versions of the SU(2) Hubbard model and show that the scar subsector is invariant under a large group, which acts on the lattice sites. More generally, we apply this idea to lattice systems with N sites that contain M Majorana fermions per site. The Hilbert space may be decomposed under the action of the SO(N)xSO(M) group, and the scars are the SO(N) singlets. For any even M, there are two families of scars. One of them, which we call the eta-states, is symmetric under the group O(N) that includes a reflection. The other, the zeta-states, has the SO(N) invariance only. For M=4, where our construction reduces to a deformed SU(2) Hubbard chain with local interactions, the former family are the N+1 eta-pairing states, while the latter are the N+1 states of maximum spin. For M=6, we exhibit explicit formulae for the scar states and calculate the bipartite entanglement entropy analytically. For large N, it grows logarithmically with the region size. In general, the energies of the scars within each family are not equidistant. For M>6 we also find that, with local Hamiltonians, the scars typically have certain degeneracies.

The latter part of the talk is based on the recent paper “Majorana Scars as Group Singlets” by Zimo Sun, Fedor Popov, Igor Klebanov and Kiryl Pakrouski, arXiv:2212.11914

For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantum-matter-seminar/

I will argue on the possibility that the smallness of some physical parameters signal a universe corresponding to a large distance corner in the string landscape of vacua. Such parameters can be the scales of dark energy and supersymmetry breaking, leading to a generalisation of the dark dimension proposal. I will discuss the theoretical framework and some of its main physical implications to particle physics and cosmology.

A conjecture of Orlov predicts the invariance of the Hodge numbers of a smooth projective complex variety under derived equivalence. For instance this has been verified in the case of varieties of general type. In this talk, I will examine the case of varieties that are fibered by varieties of general type through the Albanese map. For this class of varieties I will prove the derived invariance of Hodge numbers of type $h^{0,p}$, together with a few other invariants arising from the Albanese map. This talk is based on a joint work with F. Caucci and G. Pareschi.

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The Central Limit Theorem is an example of the ubiquitous yet still surprising phenomena in probability that many random inputs often combine to give an output insensitive to the input distributions. We will explore an example of how this plays out in the construction of random abelian groups from random integral matrices. As an example we will see the probability, as n goes to infinity, that a random linear map from Z^(n+1) to Z^n is surjective.

This talk includes joint work with Hoi Nguyen.

For more information, please see: https://people.math.harvard.edu/~ana/ons/

In this talk I will explore the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with different near-horizon geometries. For each of these three cases I will analyze small deformations away from extremality, and construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features. The ultracold case in particular shows an interesting interplay between the entropy variation and charge variation, realizing a different symmetry breaking with respect to the other two near-extremal limits.

For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/general-relativity/

I will focus on the interaction between different active matter systems. In particular, I will describe recent experimental and modeling results that reveal how interaction forces between adhesive cells generate activity in the cell layer and lead to a potentially new mode of phase segregation. I will then discuss mechanics of how cells use finger-like protrusions, known as filopodia, to interact with their surrounding medium. First, I will present experimental and theoretical results of active mirror-symmetry breaking in subcellular skeleton of filopodia that allows for rotation, helicity, and buckling of these cellular fingers in a wide variety of cells ranging from epithelial, mesenchymal, cancerous and stem cells. I will then describe in-vivo experiments together with theoretical modeling showing how during embryo development specialized active cells probe and modify other cell layers and integrate within an active epithelium.

This seminar will be held in person and on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/active-matter-seminar/

A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.

Andrew Strominger will give the Third Annual Yip Lecture on February 2, 2023.

For more information, please see: https://cmsa.fas.harvard.edu/event/yip-2023/

For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantum-matter-seminar/

We show that for any closed symplectic manifold, the number of 1-periodic orbits of any non-degenerate Hamiltonian is bounded from below by an integral version of total Betti number which takes account of torsions of all characteristics. The proof is based on a perturbation scheme (FOP perturbations) which produces pseudo-cycles from normally complex derived orbifolds, and a regularization procedure of moduli spaces of J-holomorphic curves (extending recent work of Abouzaid-McLean-Smith) which produces coherent smooth structures on the moduli spaces of Floer trajectories. I will outline the proof and indicate how these results may fit into other topics including Floer homotopy theory. This is based on joint work with Guangbo Xu.