Calendar
- 23September 23, 2021
CMSA Interdisciplinary Science Seminar: The number of n-queens configurations
The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n x n board. The problem has a storied history and was studied by such eminent mathematicians as Gauss and Polya. The problem has also found applications in fields such as algorithm design and circuit development.Despite much study, until recently very little was known regarding the asymptotics of Q(n). We apply modern methods from probabilistic combinatorics to reduce understanding Q(n) to the study of a particular infinite-dimensional convex optimization problem. The chief implication is that (in an appropriate sense) for a~1.94, Q(n) is approximately (ne^(-a))^n. Furthermore, our methods allow us to study the typical “shape” of n-queens configurations.Zoom ID: 950 2372 5230 (Password: cmsa)CMSA Quantum Matter in Mathematics & Physics Seminar: Applications of instantons, sphalerons and instanton-dyons in QCD
I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons,
instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave
functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.https://harvard.zoom.us/j/977347126
Password: cmsaCMSA Active Matter Seminar: The many phases of a cell
I will begin by introducing an emerging paradigm of cellular organization – the dynamic compartmentalization of biochemical pathways and molecules by phase separation into distinct and multi-phase condensates. Motivated by this, I will discuss two largely orthogonal problems, united by the theme of phase separation in multi-component and chemically active fluid mixtures.1. I will propose a theoretical model based on Random-Matrix Theory, validated by phase-field simulations, to characterizes the rich emergent dynamics, compositions, and steady-state properties that underlie multi-phase coexistence in fluid mixtures with many randomly interacting components.2. Motivated by puzzles in gene-regulation and nuclear organization, I will propose a role for how liquid-like nuclear condensates can be organized and regulated by the active process of RNA synthesis (transcription) and RNA-protein coacervation. Here, I will describe theory and simulations based on a Landau formalism and recent experimental results from collaborators.Zoom link: https://harvard.zoom.us/j/96657833341*rescheduled from 9/16/21Quantitative Logarithmic Equidistribution and S-Integrality
Given a rational map defined over a number field, the Galois orbits of points with canonical height tending to zero will equidistribute to a measure supported on the Julia set. If one is able to extend the space of test functions to include those with certain logarithmic poles, then it is possible to obtain finiteness results on S-integral points. In this talk, we will study quantitative versions of logarithmic equidistribution in some special situations and their implications.