Scientific Series

The Heisenberg algebra plays an important role in many areas of mathematics and physics. Khovanov constructed a categorical analogue of this algebra which emphasizes its connections to representation theory and combinatorics. Recently, Brundan, Savage, and Webster have shown that the Grothendieck group of this category is isomorphic to the Heisenberg algebra. However, applying an alternative decategorification functor called the trace to the Heisenberg category yields a richer structure: a W-algebra, an infinite-dimensional Lie algebra related to conformal field theory. In this talk, we will describe recent work extending this latter result to a generalized version of the Heisenberg category associated to an arbitrary graded Frobenius algebra F. The decategorifications of this Frobenius Heisenberg category conjecturally provide connections to alternative Heisenberg algebras and W-algebras associated to the algebra F. This is joint work with Alistair Savage (University of Ottawa).

Sexual harassment and sexual assault in the workplace is almost always a severe betrayal of trust.  I will describe research and theory that my students and I have developed over the last 25 years regarding interpersonal and institutional betrayals of trust.  My presentation will include an explanation of betrayal trauma theory and information about institutional betrayal.   I will present data from some of our research studies, including results from a study of sexual harassment of graduate students.   Included will be research-based recommendations for how to respond well to disclosures of harassment and sexual violence as well as steps individuals and institutions can take to constructively address sexual violence and promote institutional courage.  

Jennifer J. Freyd, PhD, is a Fellow at the Center for Advanced Study in the Behavioral Sciences at Stanford University and a Professor of Psychology at the University of Oregon.

From earliest infancy, we live in and learn to function in a world of causes and effects. Yet science has had an ambivalent, even hostile attitude toward causation for more than a century. Statistics courses teach us that “correlation is not causation,” yet they are strangely silent about what is causation.

A central reason for this silence is that causation does not reside in data alone, but in the process that generates the data. In order to answer causal questions, like “What would happen if we lowered the price of toothpaste?” or “Should I brake for this object?” we need a model of causes and effects. Judea Pearl has developed a simple calculus for expressing our cause-effect knowledge in a diagram and using that diagram to tell us how to interpret the data we gather from the real world. His methods are already transforming the practice of statistics and could equip future artificial intelligences with causal reasoning abilities they currently lack.

This talk is largely based on Mackenzie’s book co-written with Pearl, The Book of Why.

From arXiv: 1806.04937, with Carlo Sparaciari, Carlo Maria Scandolo, Philippe Faist and Jonathan Oppenheim

We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of the physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. 

This seminar will be a continued discussion on the topic of last week's seminar: 

I will describe some general mathematical structures expected to arise from field theories with boundary conditions in terms of factorization algebras, and outline some results and future directions in the study of boundary chiral algebras for 3d N=4 theories following the work of Costello and Gaiotto.

Given by Dylan Butson.

Black hole entropy is a robust prediction of quantum gravity with no observational test to date. We use the Bekenstein-Hawking entropy formula to determine the probability distribution of the spin of black holes at equilibrium in the microcanonical ensemble. We argue that this ensemble is relevant for black holes formed in the early universe and predicts the existence of a population of black holes with zero spin. Observations of such a population at LIGO, Virgo, and future gravitational wave observatories would provide the first experimental test of the statistical nature of black hole entropy.

The source of about half of the heaviest elements in the Universe has been a mystery for a long time. Although the general picture of element formation is well understood, many questions about the nuclear physics processes and particularly the astrophysical details remain to be answered. Here I focus on recent advances in our understanding of the origin of the heaviest and rarest elements in the Universe.

The precise relationship between post-selected classical and 
post-selected quantum computation is an open problem in complexity 
theory. Post-selection has proven to be a useful tool in uncovering some 
of the differences between quantum and classical theories, in 
foundations and elsewhere. This is no less true in the area of 
computational complexity -- quantum computations augmented with 
post-selection are thought to be vastly more powerful than their 
classical counterparts. However, the precise reasons why this might be 
the case are not well understood, and no rigorous separations between 
the two have been found. In this talk, I will consider the difference in 
computational power of classical and quantum post-selection in the 
computational query complexity setting.

We define post-selected classical query algorithms, and relate them to 
rational approximations of Boolean functions; in particular, by showing 
that the post-selected classical query complexity of a Boolean function 
is equal to the minimal degree of a rational function with nonnegative 
coefficients that approximates it (up to a factor of two). For 
post-selected quantum query algorithms, a similar relationship was shown 
by Mahadev and de Wolf, where the rational approximations are allowed to 
have negative coefficients. Using our characterisation, we find an 
exponentially large separation between post-selected classical query 
complexity and post-selected quantum query complexity, by proving a 
lower bound on the degree of rational approximations to the Majority 
function.

One long standing question on quantum non-locality is the quest for an informational principle explaining quantum correlations. Many candidates for such a principle have been proposed with partial success, but none fully explaining quantum correlation. Most of these principles rely on the analysis of the multipartite conditional probabilities. In this talk I will briefly review a few results we had when, instead of analysing multipartite probabilities, we analysed sequences of results from non-local boxes. First, that non-local deterministic boxes cannot be computable. Second, that pseudorandom inputs allow for a local model explaining non-local correlations. Finally, I will present a simple principle that rules out many non-physical sequences of experiments, and a unified view of local and non-signalling correlations based on sequences.

I will describe some general mathematical structures expected to arise from field theories with boundary conditions in terms of factorization algebras, and outline some results and future directions in the study of boundary chiral algebras for 3d N=4 theories following the work of Costello and Gaiotto.

In crystals, quantum electrons can be spatially distributed in a way that the bulk solid supports macroscopic electric multipole moments, which are deeply 

related with emergence of topology insulators in condensed matter systems. However, unlike the classical electric multipoles in open space, 

defining electric multipoles in crystals is a non-trivial task. So far, only the dipolar moment, namely polarization, has been successfully defined and served as a classic example of topological insulators. 

In this talk, we propose the general definition, i.e., many-body invariants, for electric multipoles in crystals, which are related with recently-discovererd higher-order topological insulators. 

Our invariants are designed to measure the distribution of electron charge in unit cells and thus can detect multipole moments purely from the bulk ground state wavefunctions. 

We provide analytic as well as numerical proofs for our invariants. Application of our invariants to spin systems as well as various other aspects of the many-body invariants will be briefly discussed.

I argue that we do not understand gauge theory as well as we think when boundaries are present. I will briefly explain the conceptual and technical issues that arise at the boundary.  I will then propose a tentative resolution, which requires us to think of theories not in spacetime, but in field-space.