General Information
Time and venue
The sessions take place every
Thursday from 17:00 to 18:00 in room
WebEx meeting online.
Aim
Dedicated to PhD students, the PhD Seminar is an important part of the research training offered at the
Department of Mathematics of the
University of Luxembourg. The PhD Seminar has a twofold
objective:
 To give PhD students the opportunity to present their fields of research
and some topics and problems studied in those fields.
The usual audience of the PhD Seminar is composed by PhD students and
young researchers of the Department of Mathematics. The atmosphere is informal, so that all participants
can ask the questions they want.
Comments and suggestions on the presentations are also highly encouraged.
 To provide a good general mathematical background, in relation with the
research interests of groups of PhD students
and other participants of the PhD Seminar.
In this perspective, the PhD Seminar proposes all over the academic year
series of introductory minicourses, held by
the young researchers of the Department of Mathematics.
Who can be a speaker?
All contributions for talks or minicourses are welcome, including from people external to Luxembourg's
Department of Mathematics!
If you want to make a presentation, please provide the organizers with a title and an abstract of your talk.
Lecture notes in any form are welcome as well.
Organisers
Summer semester: Talks

18 February 2020
Organisational meeting

Abstract In this talk I will introduce the basic concepts of group cohomology and elliptic curves, with the goal of presenting a recent result that I have obtained in a joint work with Davide Lombardo, and I will try to outline the main (simple) techniques used in the proof. This result provides a uniform bound for the exponent of certain cohomology groups attached to elliptic curves defined over the field of rational numbers.

Abstract Statisticians have been trying to develop universal estimation techniques with good estimation properties. One of them is the Maximum Likelihood Estimation developed by Sir Ronald Fisher in the 1920's. It has been very successful and is still widely used in practice nowadays. The MLE has excellent asymptotic properties on regular parametric models but it suffers from a certain lack of robustness. I will try to explain what "robustness" means with examples for which the MLE fails, and present what tools have been developed in order to achieve robust estimation.

18 March 2021
Axel SIBEROV,
A first look at quasicategories
Abstract The theory of quasicategories is one of the more fully fledged models of (∞,1)categories. I will give and explain the definition of quasicategories and shed some light on why it might be worthwhile to care about higher categories.

23 March 2021
Hanh VO,
The probabilistic nature of McShane's identity: planar tree coding of simple loops.
Abstract We will discuss McShane's identity and the proof by Labourie François and Tan Ser Peow.

01 April 2021
David CAMARA,
McShane’s, Basmajian’s and an entire family of identities
Abstract We will recall McShane’s identity on cusped hyperbolic surfaces, and Mirzakhani’s generalization to bounded surfaces. Then we will present another great identity on the same kind of surfaces, namely Basmajian’s identity, and sketch its proof. Finally we will see how these two can be seen as limit cases of a bigger family of identities.

22 April 2021
Alisa GOVZMANN,
Exponential Sequence and Sheaf Cohomology
Abstract We consider the problem of finding a branch of the complex algorithm on all of the complex plane without the origin. We make interesting observations which can be reformulated in the beautiful language of sheaves. This gives rise to the exponential sequence and now the question about the existence of a branch of the complex algorithm can be extended and the answer will depend on the vanishing of a certain sheaf cohomology group.

Abstract The Riemann zeta function:
\zeta(s):=\sum_{n=1}^{\infty}\frac{1}{n^s}
was first defined by L. Euler and happens to be one of the central functions in mathematics for centuries. Remarkable that Euler managed to compute the values of this function (even zeta values) at all even numbers:
\zeta(2)=\frac{\pi^2}{6},\quad \zeta(4)=\frac{\pi^4}{90}, \quad \zeta(6)=\frac{\pi^6}{945},\dots
While these nice formulas (proved in 1741) tell us a lot about the structure of even zeta values (all even zeta values are rational multiples of \pi and hence all \zeta(2k) are transcendental numbers) the properties of odd zeta values remain completely mysterious. So far we even do not know if \zeta(3) is transcendental or not!
In my talk, I am going to explain the fundamental Transcendence conjecture which (roughly) states that all odd zeta values are distinct and transcendental numbers and the refinement of this conjecture by D. Zagier. Then following P. Deligne, V. Drinfeld, M. Kontsevich, I will explain how algebraic geometry helps to handle this conjecture and the recent progress of F. Brown towards the proof of it.

Abstract Convergence in distribution is a classical topic in probability theory and there is a plethora of methods and tools to show the convergence of a sequence of random variables towards a limiting distribution. However, it is often harder to find the rate of convergence. In 1972, Charles Stein introduced an idea on how to approach this problem in the Gaussian case. His method is now known as Stein's Method and has found countless applications and generalizations to other distributions.
In this talk I am going to give an introduction to the ideas behind Stein's Method in the Gaussian and Poisson case and I am going to show how to generalize this idea to distributions with absolutely continuous densities.

20 May 2021
Juntong CHEN,
Robust estimation of a regression function in exponential families
Abstract In this talk, we consider the regression framework where the regression function belongs to an exponential family for example logit regression, poisson regression, exponential regression and so on. First, we introduce various examples and some simulation results as a motivation. Then, we present our robust procedure which is based on rhoestimation. We will show the theoretical performance of our estimator under a suitable parametrisation is optimal up to a logarithmic factor.

27 May 2021
Valentin GARINO,
Concentration properties of conic and convex intrinsic volumes
Abstract Intrinsic volumes are fundamental invariants that arise in the fields of convex geometry, and provide important informations about the global shape of a convex body (or alternatively, a convex cone). In this talk, we will focus on the probabilistic interpretation of the intrinsic volumes. In particular, we will discuss about a Central Limit Theorem proved recently, as well as some applications in convex optimization.