Talks

I will first review the construction of quiver Yangians for the quiver and superpotential from string theory on general toric Calabi-Yau threefolds; they serve as BPS algebras of these systems and their characters reproduce the unrefined BPS indices. I will then explain how to generalize the construction to arbitrary quivers and how to incorporate refined BPS indices. The entire construction allows for straightforward generalizations to trigonometric, elliptic, and generalized cohomologies. Time permitting, I will discuss some applications, such as on BPS counting and on Gauge/Bethe correspondence. 

Zoom link:  https://pitp.zoom.us/j/96812116687?pwd=RjlsSVhDaUVBREtUUnd5S04rQjhpZz09

Causal reasoning is vital for effective reasoning in many domains, from healthcare to economics. In medical diagnosis, for example, a doctor aims to explain a patient’s symptoms by determining the diseases causing them. This is because causal relations, unlike correlations, allow one to reason about the consequences of possible treatments and to answer counterfactual queries. In this talk I will present two recent causal inference projects done with my collaborators deriving new algorithms to solve problems that arise when applying causal inference in the real world.

"Linear structural equation models relate random variables of interest via a linear equation system that features stochastic noise. The models are naturally represented by directed graphs whose edges indicate non-zero coefficients in the linear equations. In this talk I will report on progress on combinatorial conditions for parameter identifiability in models with latent (i.e., unobserved) variables. Identifiability holds if the coefficients associated with the edges of the graph can be uniquely recovered from the covariance matrix they define. Paper: https://doi.org/10.1214/22-AOS2221 or https://arxiv.org/abs/2201.04457"

There has been recent interest in extending the concept of contextuality to cases of disturbance or inconsistent connectedness. This talk will describe an approach using probabilistic causal models, which generalize the hidden-variables models of Bell and Kochen & Specker, following recent work by Cavalcanti. I first prove an equivalence between three conditions on an arbitrary measurement system: (1) existence of a model minimizing all causal influences of context upon measurement outcomes, (2) prohibition of a form of "hidden" causal influence, and (3) noncontextuality as defined in the Contextuality-by-Default (CbD) theory of Dzhafarov and Kujala. The no-hidden-influence principle thus confers a physical interpretation to CbD-contextuality, paralleling Bell's local causality and Kochen & Specker's classical embeddability. I then extend this analysis to other causal graph topologies, showing that different graphs yield different notions of contextuality, but only the one corresponding to CbD agrees with traditional contextuality when restricted to non-disturbing systems.

I will discuss several issues related to the computation of Poisson brackets in field theories. I will show that by choosing appropriate functional spaces as configuration manifolds, it is possible to avoid the use of distributions. This is relevant, for instance, in the context of Loop Quantum Gravity, where the basic holonomy/flux variables play a central role. I will illustrate the main ideas by using simple examples based on Sobolev spaces.

Zoom link:  https://pitp.zoom.us/j/92794475242?pwd=T2Fjbk1lTXRCNnBxVDZabnJqWlAzUT09