## Search

## Probability and Statistics

First Come, First Served Queues with Two Classes of Impatient Customers.

*V. G. Kulkarni*, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.

## Abstract

We study systems with two classes of impatient customers who differ across the classes in their distribution of service times and patience times. The customers are served on a first-come, first served basis (FCFS), regardless of their class. Such systems are common in customer call centers, which often segment their arrivals into classes of callers whose requests may differ greatly in their complexity and criticality. We first consider an $M/G/1 + M$ queue and then analyze the $M/M/k + M$ case. Analyzing these systems using a queue length process proves intractable as it would require us to keep track of the class of each customer at each position in queue. Consequently, we introduce a virtual waiting time process where the service times of customers who will eventually abandon the system are not considered. We analyze this process to obtain performance characteristics such as the percentage of customers who receive service in each class, the expected waiting times of customers in each class, and the average number of customers waiting in queue. We use our characterization of the system to perform a numerical analysis of the $M/M/k + M$ system, and find several managerial implications of administering a FCFS system with multiple classes of impatient customers. Finally, we compare the performance a system based on data from a call center with the steady-state performance measures of a comparable $M/M/k + M$ system. We find that the performance measures of the $M/M/k + M$ system serve as good approximations of the system based on real data.

Joint work with:

Ivo Adan, Eindhoven University of Technology, the Netherlands,

and

Brett Hathaway, Kenan-Flagler School of Business, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.

## Functional Analysis, Linear Structures and Applications

Fourier-type operators, new convolutions and their applicability to integral equations.

*Rita Guerra*, CIDMA, Universidade de Aveiro.

## Abstract

Considering new generalizations of the Fourier transform, besides studying their general properties, we construct new convolutions associated with such operators. Moreover, for the convolutions we obtain corresponding factorization identities and some norm inequalities. These convolutions allow us to consider new classes of integral equations and to study the solvability of different types of integral equations. Conditions for the existence of unique solutions of those equations are presented, as well as the corresponding explicit solutions.

## Quantum Computation and Information

Realistic resource estimations of fault-tolerant quantum computations.

*Alexandru Paler*, Johannes Kepler University Linz.

## Abstract

It is important to reduce the physical resource costs for interesting quantum algorithms as quickly as possible. Small-scale, cloud-based NISQ machines sparked the interest of exact, realistic and non asymptotic resource estimations. It is still uncertain if any valuable quantum algorithm is possible without incorporating costly error-correction protocols that make estimation far more complex. This talk presents the methodology basics and the software tools for estimating the number of physical qubits and the time necessary to execute fault-tolerant quantum computations.## String Theory

Designing matrix models for zeta functions.

*Debashis Ghoshal*, Jawaharlal Nehru University.

## Abstract

The apparently random pattern of the non-trivial zeroes of the Riemann zeta function (all on the critical line, according to the Riemann hypothesis) has led to the suggestion that they may be related to the spectrum of an operator. It has also been known for some time that the statistical properties of the eigenvalue distribution of an ensemble of random matrices resemble those of the zeroes of the zeta function. With the objective to identify a suitable operator, we start by assuming the Riemann hypothesis and construct a unitary matrix model (UMM) for the zeta function. Our approach, however, could be termed *piecemeal*, in the sense that, we consider each factor (in the Euler product representation) of the zeta function to get a UMM for each prime, and then assemble these to get a matrix model for the full zeta function. This way we can write the partition function as a trace of an operator. Similar construction works for a family of related zeta functions.

Note: unusual date

## Geometria em Lisboa

On a conjecture about curve semistable Higgs bundles.

*Ugo Bruzzo*, SISSA, Itália & Universidade Federal da Paraíba, Brazil.

## Abstract

We say that a Higgs bundle $E$ over a projective variety $X$ is curve semistable if for every morphism $f : C \to X$, where $C$ is a smooth irreducible projective curve, the pullback $f^\ast E$ is semistable. We study this class of Higgs bundles, reviewing the status of a conjecture about their Chern classes.

## Probability and Statistics

To be announced.

*Soraia Pereira*, University of Lisbon, Portugal.

## String Theory

Quantum Line Defects and Refined BPS Spectra.

*Michele Cirafici*, University of Trieste.

## Abstract

We study refined BPS invariants associated with certain quantum line defects in quantum field theories.

Note: unusual date

## Mathematical Relativity

Decay of solutions to the Klein-Gordon equation on some expanding cosmological spacetimes.

*Amol Sasane*, London School of Economics.

## Abstract

The decay of solutions to the Klein-Gordon equation is studied in two expanding cosmological spacetimes, namely the de Sitter universe in flat Friedmann-Lemaître-Robertson-Walker (FLRW) form, and the cosmological region of the Reissner-Nordström-de Sitter (RNdS) model. Using energy methods, for initial data with finite higher order energies, decay rates for the solution are obtained. Also, a previously established decay rate of the time derivative of the solution to the wave equation, in an expanding de Sitter universe in flat FLRW form, is improved, proving Rendall's conjecture. A similar improvement is also given for the wave equation in the cosmological region of the RNdS spacetime.

## String Theory

$3d$ Modularity.

*Francesca Ferrari*, SISSA Trieste.

## Abstract

We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of $3d$ $N=2$ theories, where such structures a priori are not manifest.

## Geometria em Lisboa

To be announced.

*Bruno Colbois*, Université de Neuchâtel.