Talks

Abstract An embedded vertexon sequence is the sequence of vertex sets of a sequence of graphs in a connected compact set  $M$ in $R^{m}$ together with an asymptotically dense partition hierarchy of $M$. Vertexon sequences and the associated graph sequences have subsequential limit measures in $M$ and $M^2$ respectively, independent of the partition hierarchy within a large class. The differentiation of functions on vertexon  limits with open support in $M,$ and certain directional derivatives in the support of the associated graphon measure in $M^2,$ may be defined. Consequently, subject to conditions, one may seek stationary node dependent Nash values for Embedded Graphon Mean Field Games (EGMFGs). An example will be given in the case of a class of Linear Quadratic Gaussian EGMFGs.\\ Work with  Rinel Foguen-Tschuendom, Shuang Gao, Minyi Huang

It has been argued astronomy and astrophysics as a research field developed with the first telescope.  At the same time that Galileo observed the phases of Venus and the moons of Jupiter, European Powers will colonizing the Americas and other parts of the world.  This began a relationship between astronomy and colonization that continues today in terms of astronomers and nations building giant telescopes on Indigenous lands.  In the future as private actors develop a new space industry we will see the export of this colonialism to Space, to the Moon and one day even to Mars. We are already seeing this today with the development of satellite constellations, some of which are visible by the unaided eye and with the multinational Artemis Accords for lunar exploration.  In this talk I will review the relation between astronomy and colonization in the past, present, and future; and I will discuss steps educators and astronomers can take to address this in the classroom and how the field of astronomy and space exploration can be inclusive of Indigenous rights and voices.

Zoom link: https://pitp.zoom.us/j/95620288526?pwd=dW9ReW5FUVp3TWFmUVUxZjV5VFhNdz09

Abstract Consider the subgraph sampling model, where we observe a random subgraph of a given (possibly non random) large graph $G_n$, by choosing vertices of $G_n$ independently at random with probability $p_n$. In this setting, we study the question of estimating the number of copies $N(H,G_n)$ of a fixed motif/small graph (think of $H$ as edges, two stars, triangles) in the big graph $G_n$. We derive necessary and sufficient conditions for the consistency and the asymptotic normality of a natural Horvitz-Thompson (HT) type estimator. As it turns out, the asymptotic normality of the HT estimator exhibits an interesting fourth-moment phenomenon, which asserts that the HT estimator (appropriately centered and rescaled) converges in distribution to the standard normal whenever its fourth-moment converges to 3. We apply our results to several natural graph ensembles, such as sparse graphs with bounded degree, Erdős-Renyi random graphs, random regular graphs, and dense graphons. This talk is based on joint work with Bhaswar B. Bhattacharya and Sayan Das.

With over a hundred detections to date, the discoveries of compact binary mergers by gravitational wave observatories LIGO and Virgo have allowed us to start characterizing the astrophysical population of binary black holes. This task requires measuring the fifteen parameters (masses, spins, location, orientation, etc...) that characterize each merger event. However, these high dimensional distributions are challenging to describe due to the presence of nonlinear correlations and multiple modes. In this seminar I will describe a series of coordinate changes that, by identifying parameter combinations that control specific observable signatures in the data, remove these degeneracies and multimodality, making parameter estimation amenable. Among the new coordinates is a spin azimuth that can be measured surprisingly well in several cases, hinting that some black hole spins are misaligned with the orbit. This is very interesting because the degree of spin-orbit alignment is a robust discriminator between isolated and dynamical formation channels, which predict spins preferentially aligned with the orbit or randomly oriented, respectively. At the same time, I will show that the observed proportion of events with spins aligned versus anti-aligned with the orbit disfavors the hypothesis that the spin distribution is isotropic.

Zoom link:  https://pitp.zoom.us/j/91820222881?pwd=YW9vR0xwTlBCVXg4UlRBNWxuUFhCQT09

Abstract   Cographs are by definition $P_4$-free graphs, i.e. graphs avoiding the path $P_4$ as induced subgraph. In this talk, we will consider a uniform random cograph with $n$ vertices, for large $n$. We shall describe the (random) graphon limit of this object, which is constructed using a Brownian excursion. Motivated by some probabilistic work around Erdős-Hajnal conjecture, we also consider large independent sets in uniform cographs. For both aspects, cographs behave differently from most other $H$-free random graphs. Based on joint work with F. Bassino, M. Bouvel, M. Drmota, L. Gerin, M. Maazoun and A. Pierrot.

Abstract We will present out attempts thus far to develop a theory of graphon-valued stochastic processes. We will present a brief review of theory Graphons and dynamics constructed on the space of graphons. We shall construct and analyse a natural class of such processes arising from population genetics. In conclusion we shall present the challenges in our ongoing work on constructing dynamics where the edges and vertices interact with each other. This is joint work with Frank den Hollander and Adrian Roellin

Abstract In this talk, I will present the multivariate normal approximation for the centered subgraph counts in dense random graphs. The main motivation to investigate these statistics is the fact that they are key to understanding fluctuations of regular subgraph counts since they act as an orthogonal basis of a corresponding L2 space. We also identify the resulting limiting Gaussian stochastic measures by means of the theory of generalised U-statistics and Gaussian Hilbert spaces, which we think is a suitable framework to describe and understand higher-order fluctuations in dense random graph models. This is joint work with Adrian Roellin.

In this talk  will develop Rafael D. Sorkin's heuristic that a partially ordered process of the birth of spacetime atoms in causal set quantum gravity can provide an objective physical correlate of our perception of time passing. I will argue that one cannot have an external, fully objective picture of the birth process because the order in which the spacetime atoms are born is a partial order. I propose that live experience in causal set theory is an internal ``view'' of the objective birth process in which events that are neural correlates of consciousness occur. In causal set theory, what ``breathes fire'' into a neural correlate of consciousness is that which breathes fire into the whole universe: the unceasing, partially ordered process of the birth of spacetime atoms.

Zoom link: https://pitp.zoom.us/j/95170823205?pwd=QW9YM3QrZU12Ti9HTUQ4TDlVNmN5Zz09

Abstract For any given graph $H$, one may define a natural corresponding functional $\|.\|_H$ for real(or complex) valued functions by using the homomorphism density of $H$. We say that $H$ is \emph{norming} if $\|.\|_H$ is a norm. This generalises the Gowers octahedral norms, a widely used tool in extremal combinatorics to quantify quasirandomness. In 2008, Lov\'{a}sz asked what graphs are norming. This has been a central question in the theory of dense graph limits and also connects to Sidorenko's conjecture, a major open problem in extremal graph theory. For the recent few years, there have been interesting developments on the Lovász question, where algebraic combinatorics, extremal graph theory and functional analysis meet. In this talk, I will discuss some of the progress. Based on joint work with David Conlon, Frederik Garbe, Jan Hladk\'{y}, Bjarne Sch\"{u}lke, and Sasha Sidorenko.

The degree-restricted random process is a natural algorithmic model for generating graphs with degree sequence D_n=(d_1,...,d_n): starting with an empty n-vertex graph, it sequentially adds new random edges so that the degree of each vertex v_i remains at most d_i.  It is natural to ask whether the final graph of this process is similar to a uniform random graph with degree sequence D_n (for d-regular degree sequences D_n this was already raised by Wormald in the mid 1990s). We show that, for degree sequences D_n that are not nearly regular, the final graph of the degree-restricted random process differs substantially from a uniform random graph with degree sequence D_n.  Our proof uses the switching method, which is usually only applied to uniform random graph models -- rather than to stochastic processes. Based on joint work with Mike Molloy and Erlang Surya.

The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of non-trivial complexity (with complexity measured by the quantum circuit depth preparing the state). Our recent work https://arxiv.org/abs/2206.13228 (with Nikolas Breuckmann and Chinmay Nirkhe) proves this conjecture by showing that the recently discovered families of constant-rate and linear-distance QLDPC codes correspond to NLTS local Hamiltonians. This talk will provide background on the conjecture, its relevance to quantum many-body physics and quantum complexity theory, and touch upon the proof techniques.

Zoom link: https://pitp.zoom.us/j/94224635225?pwd=SUovNXA3MWlkRUJlcTIxV0pLQzQxdz09