The Mathematical Sciences Seminar is a seminar for all of the Department of Mathematical Sciences, GU/Chalmers. This is the arena for seminars of interest to a broader audience. It complements the colloquium in that it is a freer form of event and is not subject to the colloquium’s long term planning. The seminar is usually 60 minutes, but 2*45 minutes is also an option. Should you have a visitor who would like to present results of interest to the entire department, and/or they are visiting on short notice, please consider suggesting them for the Mathematical Sciences Seminar.

##### Mathematical Sciences Seminars Spring 2020

**20-03-05 (13:15 in Euler) Nicolai Reshetikhin, University of California, Berkeley**

*Mixing representation theory and statistics*

The tensor product of finite dimensional representations of a simple Lie algebra decomposes into the sum of irreducible components with some multiplicities. These multiplicities are hard to compute in general, but it turns out that their asymptotic in large tensor products can be described explicitly. As a consequence the statistics of irreducible components in such large tensor products can also be described quite explicitly. This was first studied in particular cases by S. Kerov and A. Vershik, in a more general framework by Ph. Biane; T. Tate and S. Zelditch and other people. The talk is based on a joint work with O. Postnova.

##### Mathematical Sciences Seminars Fall 2019

1

**9-08-30 (10:00 in MVH12)****Grégoire Allaire (**

**CMAP, Ecole Polytechnique)**

*Topology optimization of structures: old and new*

In this talk I will review for a non-expert audience the history of shape and topology optimization of mechanical structures. I will first explain the classical Hadamard method of shape optimization, which amounts to geometrical variations of the shape boundary, but does not permit any topology changes of the shape. Then I will recall what is the so-called homogenization method, which was invented in the 80's to circumvent this drawback and to effectively optimize both the topology and the geometry of shapes. This method is based on the introduction of composite materials (characterized by a material density and a microstructure) as admissible designs. This revolutionary idea was somehow complicated to implement in practice because it required, as a preliminary step, the computation of the homogenized or effective properties of these composite materials which are often anisotropic when they are optimal. Thus, in the 90's the homogenization method was outperformed by a much simpler approach, called SIMP (solid isotropic material with penalization), which uses a material density as design variable and does not feature any microstructure.

However, the appearance of mature additive manufacturing technologies (also known as 3-d printing) which are able to build finely graded microstructures (called lattice materials) drastically changes the picture and there is a resurrection of the homogenization method for such applications. Indeed, homogenization is the right technique to deal with microstructured materials where anisotropy plays a key role, a feature which is absent from SIMP.

I will describe recent work on the topology optimization of these lattice materials, based on a combination of homogenization theory and geometrical methods for the overall deformation of the lattice grid. My talk will be abundantly illustrated by numerical results, including movies, which are often better explanations than long mathematical developments.

##### Mathematical Sciences Seminars Spring 2019

**19-03-06 (15:15 in Pascal)**

Klas Modin (Chalmers/GU)

Klas Modin (Chalmers/GU)

*The work of the Fields medallists 2018: Alessio Figalli*

**19-03-13 (15:15 in Pascal)**

Christian Johansson (Chalmers/GU)

Christian Johansson (Chalmers/GU)

*The work of the Fields medallists 2018: Peter Scholze*

**19-03-27 (1515 in Pascal)**

Anders Södergren (Chalmers/GU)

Anders Södergren (Chalmers/GU)

*The work of the Fields medallists 2018: Akshay Venkatesh*

**19-04-10 (1515 in Pascal)**

**Ove Granstrand (Chalmers/GU)**

*Technology, IP and Innovation – thoughts on the 2018 Nobel Laureates in Economics*

19-05-08 (1515 in Euler)

Bo Berndtsson (Chalmers/GU)

Bo Berndtsson (Chalmers/GU)

*The work of the Abel laureate 2019: Karen Uhlenbeck*##### Mathematical Sciences Seminars Spring 2018

**18-05-21 (1515 in Pascal)**

Martin Raum (Chalmers/GU)

Martin Raum (Chalmers/GU)

*The Langlands Program - The life and work of Robert P. Langlands*

Robert Langlands in the course of his career has brought to flourish a whole domain of mathematics. For good reasons, mathematics connected with his efforts is referred to as being part of the Langlands Program. Langlands will receive the Abel Prize on May 22. We will take this as an excuse to catch a glimpse of the beautiful mathematics he has created and advanced.

##### Mathematical Sciences Seminars Autumn 2017

**17-11-22 (1515 in Euler)**

Adam Rennie (University of Wollongong)

Adam Rennie (University of Wollongong)

*A mathematical view of the quantum Hall effect*

Last year's physics Nobel was awarded for study of topological insulators. Subsequently the press was full of strange stories of doughnuts, electrons and other strange beasts.

In this talk I will describe the simplest topological insulator, called the quantum Hall effect. I will show where the `topology' gets into the game, and report on recent work by my colleagues Chris Bourne, Alan Carey, Johannes Kellendonk and myself.

**Funded by the Gothenburg Centre for Advanced Studies in Science and Technology.**