Talks

A resource theory imposes a preorder over states, with one state being above another if the first can be converted to the second by a free operation, and where the set of free operations defines the notion of resourcefulness under study. In general, the location of a state in the preorder of one resource theory can constrain its location in the preorder of a different resource theory. It follows that there can be nontrivial dependence relations between different notions of resourcefulness. In this talk, we lay out the conceptual and formal groundwork for the study of resource dependence relations. In particular, we note that the relations holding among a set of monotones that includes a complete set for each resource theory provides a full characterization of resource dependence relations. As an example, we consider three resource theories concerning the about-face asymmetry properties of a qubit along three mutually orthogonal axes on the Bloch ball, where about-face symmetry refers to a representation of $\mathbb{Z}_2$, consisting of the identity map and a $\pi$ rotation about the given axis. This example is sufficiently simple that we are able to derive a complete set of monotones for each resource theory and to determine all of the relations that hold among these monotones, thereby completely solving the problem of determining resource dependence relations. Nonetheless, we show that even in this simplest of examples, these relations are already quite nuanced. At the end of the talk, we will briefly discuss how to witness nonclassicality in quantum resource dependence relations and demonstrate it with the about-face asymmetry example. The talk is based on the preprint: arXiv:2407.00164 and ongoing work.

Intensity Interferometry (II) is a method that can achieve high angular resolution and was first employed in the 1960s by Robert Brown and Richard Q. Twiss (HBT). Since then, significant advancements have been made, particularly in the construction of telescopes with large light collection areas, such as Imaging Atmospheric Cherenkov Telescopes (IACTs), exemplified by instruments like H.E.S.S. , MAGIC and VERITAS. Our II setup was designed to be mounted on the lid of the Phase I H.E.S.S. telescopes in Namibia. In April 2022, our first observation campaign was conducted, during which two telescopes operated in a single wavelength band. In April-May 2023, a third telescope was added, and observations were performed in two colors simultaneously for the first time in II. In this contribution I will introduce our setup and compare the different configurations, as well as present the latest results of four southern hemisphere stars.

In this talk, I will give an introduction to intensity correlations for astrophysical imaging, as pioneered by Hanbury Brown and Twiss. This triggered a wider effort for the field of quantum optics, which I will put into a larger context beyond astrophysical imaging. I will also give an overview of the past results on intensity correlations for astrophysical imaging by our group in Nice and present the ongoing effort towards resolving a white dwarf and to search for signatures of random lasing in space.

In our previous study (TI-Mucciconi-Sasamoto, Forum of Mathematics, Pi 11(e27) 1-101,2023) we introduced a deterministic time evolution of a pair of skew semistandard Young tableaux called the skew RSK dynamics.

In this talk we introduce a variant based on the column bumping in the RSK correspondence, which we call the column skew RSK dynamics. Utilizing (bi) crystal structure in the pair of skew tableaux, we show that the column skew RSK dynamics can be mapped to the single species box and ball system (BBS).  Using the mapping we obtain a relation between restricted Cauchy sums about the modified Hall-Littlewood polynomials and the skew Schur polynomials. This talk is based on the joint work with Matteo Mucciconi, Tomohiro Sasamoto and Travis Scrimshaw.

In [1] we introduced the skew RSK dynamics, which is a time evolution for a pair of skew Young tableaux (P,Q). This gives a connection between the q-Whittaker measure and the periodic Schur measure, which immediately implies a Fredholm determinant formula for various KPZ models[2]. The dynamics exhibits interesting solitonic behaviors similar to box ball systems (BBS) and is related to the theory of crystal. 

In this talk we explain basics of the skew RSK dynamics. The talk is based on a collaboration with T. Imamura, M. Mucciconi. 

[1] T. Imamura, M. Mucciconi, T. Sasamoto, 
Skew RSK dynamics: Greene invariants, affine crystals and applications to $q$-Whittaker polynomials, Forum of Mathematics, Pi (2023), e27 1–10. 

[2] T. Imamura, M. Mucciconi, T. Sasamoto, 
Solvable models in the KPZ, arXiv: 2204.08420

In this series of lectures, I will give an introduction to the theory of moments of L-functions. I will focus on important examples, such as the moments of the Riemann zeta function and Dirichlet L-functions, as well as some GL_2 families. I will also present some of the important tools for understanding moments, as well as applications of moments.

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...

I will revisit some integrable difference equations arising in the study of the distance statistics of random planar maps (discrete surfaces built from polygons). In a paper from 2003 written jointly with P. Di Francesco and E. Guitter, we conjectured a general formula for the so-called ``two-point function'' characterizing these statistics. The first proof of this formula was given much later in a paper from 2012 joint with E. Guitter, where we used bijective arguments and the combinatorial theory of continued fractions. I will present a new elementary and purely analytic proof of the result, obtained by considering orthogonal polynomials with respect to a polynomial deformation of the Wigner semicircle distribution. This talk is based on a work in progress with Sofia Tarricone.