Talks

In modern astronomy, artificial intelligence (AI) is increasingly utilized to analyze large volumes of data, significantly reducing the need for human computational resources and time. Machine learning (ML) techniques are at the forefront of revealing astronomical mysteries by analyzing observed data. Here, we will introduce the application of machine learning to Intensity Interferometry (II) data for high-resolution optical astronomy, aiming to overcome the limitations of traditional image reconstruction methods. In this presentation, we demonstrate successful image reconstruction of a fast-rotating star using conditional Generative Adversarial Networks (cGANs), a supervised machine learning approach. Simulations of II are based on an assembly of four telescopes similar to existing arrays. However, the sensitivity of the signal and high resolution are expected to improve with additional baselines. It makes the current and future Cherenkov Telescope Array Observatory (CTAO) an ideal candidate for II applications. Our approach is highly relevant and innovative, addressing key challenges in phase reconstruction and proposing novel solutions that could revolutionize high-resolution imaging in astronomy.

Even with dense sampling of the uv plane intensity correlations only contain half the information required to reconstruct an image. Intensity correlations do contain the full information of the image power spectrum and therefore of the image 2-point correlation function. With some practice one can gain intuitive understanding in interpreting 2-point correlation function "images". This is illustrated with both toy examples and modeling of real astronomical images. In some assumptions one can even interpret these 2-point correlation function "images" with only a few baselines.

With the observation of gravitational waves (GW's) at high, kilohertz frequencies by LIGO and the evidence for GW's at low, nanohertz frequencies from NANOGrav there is a new emphasis on exploring the GW landscape at intermediate frequency ranges. Beyond the two measurement methods used in these observations, i.e. laser metrology in LIGO and pulsar timing offsets in NANOGrav, we have been developing a third approach of observing astrometric GW signatures, which is very well suited to the intermediate microhertz frequency range. While astrometric GW observations have been discussed in the context of survey missions, e.g. GAIA, this presentation will exhibit a potentially superior approach using long baseline two-photon interferometry, with both space-based and ground-based platforms. The practicalities of a near-future experiment will be particularly highlighted

In this talk, I'll describe some recently discovered connections between one-dimensional interacting particle models (the ASEP and the TAZRP) and Macdonald polynomials and show the combinatorial objects that make these connections explicit. Recently, a new tableau formula was found for the modified Macdonald polynomial $\widetilde{H}_{\lambda}$ in terms of a queue inversion statistic that is naturally related to the dynamics of the TAZRP. We give a new compact tableau formula for the symmetric Macdonald polynomials $P_{\lambda}(X;q,t)$ using the same queue inversion statistic on certain sorted non-attacking tableaux. The nonsymmetric components of our formula are the ASEP polynomials, which specialize to the probabilities of the asymmetric simple exclusion process (ASEP) on a circle, and the queue inversion statistic encodes to the dynamics of the ASEP.  Our tableaux are in bijection with Martin's multiline queues, from which we obtain an alternative multiline queue formula for $P_{\la...

The notion of congruence (modulo an integer q) was formalised by C. F. Gauss in his Disquisitiones arithmeticae. This is a basic yet fundamental concept in all aspects of number theory. Indeed congruences allow to evaluate and compare integers in way considerably richer than the archimedean order alone permits.

In analytic number theory, several outstanding question -starting with Dirichlet’s theorem on primes in arithmetic progressions- reduce to the of measuring whether some classical arithmetic function (say the characteristic function of prime numbers) correlate with suitable q periodic functions for instance Gauss sums, Jacobi sums or Kloosterman sums. It turns out that these functions, when the modulus q is a prime (to which one can reduce via the Chinese Reminder Theorem) can be recognised as « trace functions». The study of trace functions was initiated by A. Weil in the 1940’s and was pursued by A. Grothendieck in the second half of the century with his refoundation of alge...

In this talk, the problem of constructing the stationary states of the multispecies asymmetric simple exclusion process on a one-dimensional periodic lattice is revisited. A central role is played by a quantum oscillator-weighted five vertex model, which features an unusual weight conservation distinct from the conventional one. This approach clarifies the interrelations among several known results and refines their derivations, including the multiline queue construction and matrix product formulas. (Joint work with Masato Okado and Travis Scrimshaw)