# Spacetime and Quantum Mechanics Seminar

2019-09-12 17:38 - 17:38

As part of the program on Spacetime and Quantum Mechanics, the CMSA will be hosting a weekly seminar on Thursdays at 2:30pm in room G10.

Date Speaker Title/Abstract
9/12/2019 Pasha Pylyavskyy (University of Minnesota) Title: Vector-relation configurations and plabic graphs
19/18/2019

2:00pm

G02

Francis Brown (University of Oxford) Title: Amplitudes, Polylogs and Moduli Spaces
9/19/2019 Chuck Doran (University of Alberta) Title: Calabi-Yau geometry of the N-loop sunset Feynman integrals

Abstract: I will present an overview of the algebraic and transcendental features of the computation of N-loop sunset Feynman integrals.

Starting from the realization of arbitrary Feynman graph hypersurfaces as (generalized) determinantal varieties, we describe the Calabi-Yau subvarieties of permutohedral varieties that arise from the N-loop sunset Feynman graphs and some key features of their geometry and moduli.

These include: (1) an iterated fibration structure which allows one to “bootstrap” both periods and Picard-Fuchs equations from lower N cases; (2) specialization to and interpretation of coincident mass loci (“jump loci”) in moduli; (3) a significant generalization of the Griffiths-Dwork algorithm via “creative telescoping”; and (4) the realization of Calabi-Yau pencils as Landau-Ginzburg models mirror to weak Fano varieties.

Details of each of these will be discussed in later lectures this semester. This is joint work with Pierre Vanhove and Andrey Novoseltsev.

9/26/2019 Tomasz Taylor (Northeastern) Title: Celestial Amplitudes
10/3/2019 Simon Caron-Huot (McGill) Title: Poincare Duals of Feynman Integrals
10/10/2019

3:30pm

Yutin Huang (National Taiwan University) Title: Dualities of Planar Ising Networks and the Positive Orthogonal Grassmannian
10/15/2019

Tuesday

3:30pm

Sergey Fomin (Univ. of Michigan)

Title: “Morsifications and mutations” (joint work with P. Pylyavskyy, E. Shustin, and D. Thurston).
10/18/2019

Friday

G02

Sebastian Franco (The City College of New York) Title: Graded quivers, generalized dimer models, and topic geometry
10/31/2019 Junjie Rao (Albert Einstein Institute) Title: All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
11/1/2019

SC 232

1:30pm

George Lusztig (MIT) Title: Total positivity in Springer fibres
11/12/2019

Tuesday

G02

3:30pm

Title: Feynman Integrals and Intersection Theory
11/14/2019

G02

Pierpaolo Mastrolia (University of Padova) Title: Feynman Integrals and Intersection Theory Pt. II
11/21/2019 Cristian Vergu (Niels Bohr Institute) Title: The Octagonal Alphabet
11/26/2019 Stephan Stieberger (IAS) Title: Strings on the Celestial Sphere
12/4/2019 Hadleigh Frost (Oxford) Title: BCJ numerators, $\mathcal{M}_{0,n}$, and ABHY

Abstract: We relate the BCJ numerator Jacobi property to the classical fact that the top homology group of $\mathcal{M}_{0,n}$ is isomorphic to a component of the free Lie algebra. We describe ways to get BCJ numerators, and caution that the BCJ Jacobi property doesn’t imply the existence of what has been called a ‘kinematic algebra.’

12/5/2019 David Kosower (IAS) Title: From scattering amplitudes to classical observables
12/10/2019 Ramis Movassagh (MIT) Title: Highly entangled quantum spin chains: Exactly solvable counter-examples to the area law

Abstract: In recent years, there has been a surge of activities in proposing “exactly solvable” quantum spin chains with surprising high amount of ground state entanglement–exponentially more than the critical systems that have $\log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the ground state entanglement entropy scales as $\sqrt(n)$ and in some cases even extensive (i.e., as $n$) despite the underlying Hamiltonian being: (1) Local (2) Having a unique ground state and (3) Translationally invariant in the bulk. These models have rich connections with combinatorics, random walks, Markov chains, and universality of Brownian excursions. Lastly, we develop techniques for proving the gap. As a consequence, the gap of Motzkin and Fredkin spin chains are proved to vanish as 1/n^c with c>2; this rules out the possibility of these models to be relativistic conformal field theories in the continuum limit. Time permitting we will discuss more recent developments in this direction and ‘generic’ aspects of local spin chains.