Search Talks

The physics proof of the Atiyah-Singer index theorem relates the Hamiltonian and Lagrangian approaches to quantization of N=1 supersymmetric mechanics. Similar ideas applied to the N=(0,1) supersymmetric sigma model construct two versions of elliptic cohomology: elliptic cohomology at the Tate curve over the integers and the universal elliptic cohomology theory over the complex numbers. Quantization procedures give analytic constructions of wrong-way maps in these cohomology theories. Relating these to the Ando-Hopkins-Strickland-Rezk string orientation of topological modular points to intricate torsion invariants associated with these sigma models. 

Quantum annealing with superconducting qubits: status and prospects
Adrian Lupascu, Institute for Quantum Computing

Quantum-enhanced Gibbs sampling in statistical relational learning
Peter Wittek, Institute of Photonic Sciences, University of Boras

Mathematics can be tasty! It’s a way of thinking, and not just about numbers. Through unexpectedly connected examples from music, juggling, and baking, Dr. Eugenia Cheng will demonstrate that math can be made fun and intriguing for all. Her interactive talk will feature hands-on activities, examples that everyone can relate to, and funny stories. She will present surprisingly high-level mathematics, including some advanced abstract algebra usually only seen by math majors and graduate students. There will be a distinct emphasis on edible examples.

In 1983, Nielsen and Ninomiya predicted that the Adler-Bell-Jakiw (or chiral) anomaly should be observable in a crystal that has protected Dirac states in the bulk (3+1 D). Following recent progress in the field of Topological Quantum Matter, the anomaly has now been observed, most clearly in the two semimetals Na3Bi and GdPtBi. I will discuss the general problem of realizing Weyl Fermions in semimetals, and explain what the chiral anomaly is in condensed matter. I will remark on its historical context, starting with pion decay. Several tests that support our conclusion will be described.

*Supported by the Moore Foundation, ARO and NSF.

Quantum triangles can work as interferometers. Depending on their geometric size and interactions between paths, “beats” and/or “steps”

patterns are observed. We show that when inter-level distances between level positions in quantum triangles periodically change with time, formation of beats and/or steps no longer depends only on the geometric size of the triangles but also on the characteristic frequency of the transverse signal. For large-size triangles, we observe the coexistence of beats and steps for moderated frequencies of the signal and for large frequencies a maximum of four steps instead of two as in the case with constant interactions are observed.

Small-size triangles also revealed counter-intuitive interesting dynamics for large frequencies of the field: unexpected two-step patterns are observed. When the frequency is large and tuned such that it matches the uniaxial anisotropy, three-step patterns are observed.

We have equally observed that when the transverse signal possesses a static part, steps maximize to six. These effects are semi-classically explained in terms of Fresnel integrals and quantum mechanically in terms of quantized fields with a photon-induced tunneling process. Our expressions for populations are in excellent agreement with the gross temporal profiles of exact numerical solutions. We compare the semi-classical and quantum dynamics in the triangle and establish the conditions for their equivalence.