Calendar
- 01April 1, 2020
CMSA Quantum Matter/Quantum Field Theory Seminar: Exploration on Deconfined Fractionalized Particles at Quantum Criticality — Fractional Chern Insulators and Shastry-Sutherland Quantum Magnets
via Zoom Video Conferencing: https://harvard.zoom.us/j/977347126
One of the most exotic phenomena in condensed matter systems is the emergence of fractionalized particles. However, until now, only a few experimental systems are known to realize fractionalized excitations. This calls for more systematic ways to find and understand systems with fractionalization. One natural starting point is to look for an exotic quantum criticality, where the fundamental degrees of freedom become insufficient to describe the system accurately. Furthermore, understandings in exotic quantum critical phenomena would provide a unified perspective on nearby gapped phases, i.e. a guiding principle to engineer the system in a desirable direction that may host anyons. In this talk, I would present my works on two different types of quantum criticality: (1) Deconfined quantum critical point (DQCP) between plaquette valence-bond solids and Neel ordered state in Shastry-Sutherland lattice models [PRX 9, 041037 (2019)], where two distinct symmetry breaking order parameters become unified by the fractionalized degree of freedom. (2) Transitions between fractional Chern/Quantum Hall insulators tuned by the strength of lattice potential [PRX 8, 031015 (2018)]. Here, the low-lying excitations are already fractionalized; therefore, the deconfined fractional excitations follows more naturally, which is described by Chern-Simons quantum electrodynamics. The numerical results using iDMRG as well as theoretical analysis of their emergent critical properties would be presented. In the end, I would discuss their spectroscopic signatures, providing a full analysis of experimental verification.
- 01April 1, 2020
Joint Math Department and CMSA Random Matrix and Probability Theory Seminar: A simplified approach to interacting Bose gases
will speak on:
A Simplified Approach to Interacting Bose Gases
via Zoom Video Conferencing: https://harvard.zoom.us/j/147308224
I will discuss some new results about an effective theory introduced by Lieb in 1963 to approximate the ground state energy of interacting Bosons at low density. In this regime, it agrees with the predictions of Bogolyubov. At high densities, Hartree theory provides a good approximation. In this talk, I will show that the ’63 effective theory is actually exact at both low and high densities, and numerically accurate to within a few percents in between, thus providing a new approach to the quantum many body problem that bridges the gap between low and high density.
- 01April 1, 2020
Wiles defect for Hecke algebras that are not complete intersections
via Zoom Video Conferencing: https://harvard.zoom.us/j/136830668
In his work on modularity theorems, Wiles proved a numerical criterion for a map of rings R->T to be an isomorphism of complete intersections. In addition to proving modularity theorems, this numerical criterion also implies a connection between the order of a certain Selmer group and a special value of an L-function.In this talk I will consider the case of a Hecke algebra acting on the cohomology a Shimura curve associated to a quaternion algebra. In this case, one has an analogous map of rings R->T which is known to be an isomorphism, but in many cases the rings R and T fail to be complete intersections. This means that Wiles’s numerical criterion will fail to hold.I will describe a method for precisely computing the extent to which the numerical criterion fails (i.e. the ‘Wiles defect”) at a newform f which gives rise to an augmentation T -> Z_p. The defect turns out to be determined entirely by local information of the newform f at the primes q dividing the discriminant of the quaternion algebra at which the mod p representation arising from f is “trivial”. (For instance if
f corresponds to a semistable elliptic curve, then the local defect at q is related to the
“tame regulator” of the Tate period of the elliptic curve at q.)This is joint work with Gebhard Boeckle and Jeffrey Manning.
- 01April 1, 2020
Heights
via Zoom Video Conferencing: https://harvard.zoom.us/j/972495373
We will describe how the problem of finding periodic trajectories in a regular pentagon can be solved using a new height on P^1 coming from real multiplication.
- 01April 1, 2020
CMSA Colloquium: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring
Online via Zoom Video Conferencing: https://harvard.zoom.us/meeting/977347126
I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.