## Monthly Online Colloquium

## Mathematics in Lebanon and beyond

### Institute of Mathematics Potsdam

This colloquium will serve as a meeting place for scientific exchange, bringing together mathematicians from the Lebanese diaspora, friends of Lebanon from around the world, and researchers based in Lebanon. By nature, the colloquium will be interdisciplinary and speakers will be asked to prepare pedagogical talks addressed to a wide audience including non experts in the subject. Presentations can be given in French or English.

**Forthcoming talks:**

Tuesday October 10th 2023

as part of the conference

"At the confluence of Geometry, Analysis and Mathematical Physics"

October 10-12, 2023, at the American University of Beirut

https://sites.aub.edu.lb/humboldt/workshops/meeting-2023/"

- 2pm CET (3pm Beirut)
- Isabelle Chalendar (Université Gustave Eiffel, Marne-La-Vallée): "Ideal Properties of the Riemann-Liouville semigroup"

Joint work with I. Alam, F. El Chami, E. Fricain, G. Habib and P. Lefèvre
Abstract:

We consider a classical operator, namely the Volterra operator, which can be embedded into an analytic strongly continuous semi-group acting on the space of L^p or continuous functions on the interval [0,1]. This semi-group has many invariant sub-spaces which can be completely described. We investigate its membership to several ideals of operators including Schatten classes.

**Past talks:**

Wednesday September 13th 2023

- 3pm CET:
- Wael Bahsoun (Loughborough University): "Statistical properties of chaotic dynamical systems via spectral methods" Abstract:

Smooth ergodic theory aims to analyse the long-term statistics of chaotic dynamical systems. There are several analytic and probabilistic tools that are used to answer such questions. Each of these approaches has its advantages and its shortcomings, depending on the system under consideration. In this talk, I will focus on transfer operator techniques and spectral methods. In the first half of this talk, I will explain ideas behind this approach through simple, yet important examples. In the second half of the talk, I will discuss a recent joint work with C. Liverani, whose long-term goal is to provide a good spectral picture for pricewise hyperbolic systems with singularities (e.g. billiard maps) in any dimension.

- 3pm CET:
- Pierre Youssef (New York University, Abu Dhabi): "Phenomena in High Dimensions" Abstract:

What do high dimensional convex bodies look like? How does the spectrum of a random matrix behave as its dimension grows? How does the connectivity of a graph evolve as its size grows? In this talk, I will try to discuss some phenomena that arise as the "dimension" grows in several related contexts.

- 3pm CET:
- Joseph AYOUB (University of Zurich): "Symmetries in algebraic geometry and motives" Abstract:

Starting from the general notion of `symmetry' in mathematics, we give a gentle introduction to the theory of motives, which is the universal cohomology theory for algebraic varieties.

Slides

- 3pm CET:
- Abdallah ASSI (University of Angers): "Numerical semi-groups and applications" Abstract:

A numerical semigroup (NSG for short) is a monoid S of the set N of non negative integers such that the group generated by S in Z is Z (that is, S is stable under addition, 0 is an element of S, and the GCD of the elements of S is 1). Given a NSG S, there exists a finite number of elements, a_1,...,a_n, of S such that S=a_1N+....+a_nN. Moreover, there exists an integer in N\S, denoted F(S), such that every integer > F(S) is in S. We call F(S) the Frobenius number of S. Then we can associate with S many numerical invariants, and this gives rise to many combinatorial problems and conjectures. In addition, NSGs appear in many areas in mathematics, in particular they give us an arithmetic tool in the problem of classification of singularities of plane algebraic curves. The purpose of this talk is to give a review of the results, problems, conjectures, and applications related to this field.

- 4pm-4:50pm CET:
- Karma Dajani (Utrecht University): "Interactions between ergodic theory and number theory: from beta-expansions to the Sierpinski gasket" Abstract

Opening session: Tuesday February 7th 2023

- 3pm-3:50pm CET:
- George Saliba (American University of Beirut): "Revisiting Islamic Science and Renaissance Europe"

- 4pm:-4:50pm CET:
- Hussein Mourtada (IMJ, Université Paris-Cité): "Singularities and integer partitions" Abstract:

An integer partition of an integer number is simply a decreasing sequence of integers whose sum is equal to n. Naturally, integer partitions and their theory are ubiquitous in mathematics. I will report on a link between an algebro-geometric invariant and the theory of integer partitions in the spirit of Ramanujan. The talk is aimed at a wide audience of mathematicians.

**Contact:**

- Sylke Pfeiffer (Potsdam) sypfeiffer@math.uni-potsdam.de

Zoom link:

Join Zoom Meeting

https://uni-potsdam.zoom.us/j/8733076196

Meeting ID: 873 307 6196

Passcode: 29634559

**Organising committee:**

- Georges Habib (Beirut)
- Sylvie Paycha (Potsdam)

Impressum