Three Bachelor´s Degree Project presentations: Simon Vågberg, Zakarias Brounéus, Viggo Laaksoharju och Philip Åberg

  • Date: 5 June 2024, 10:15–15:00
  • Location: Ångström Laboratory, 4003
  • Type: Course
  • Lecturer: Simon Vågberg, Zakarias Brounéus, Viggo Laaksoharju och Philip Åberg
  • Organiser: Matematiska instituitonen
  • Contact person: Martin Herschend

Simon Vågberg, Zakarias Brounéus, Viggo Laaksoharju och Philip Åberg presents their bachelor´s degree projects. Welcome to join!

Time: 10:15-11:00

  • Place: 4003
  • Student: Simon Vågberg
  • Title: Classical representation through the lens of positive self adjoint Hopf algebras

Abstract: Representation theory has become an important area in modern mathematics. In this presentation we will restrict ourselves to study finite dimensional representations over the complex numbers of some classical groups - mostly the symmetric groups Sn - but will do so through the use of so called positive self adjoint Hopf algebras, or PSH-algebra for short. We will define a PSH-algebra, develop some general theory surrounding them, and then apply this general theory to specific PSH-algebras constructed from objects related to representation theory.

 

TIme: 11:15-12:00

  • Place: 4003
  • Student: Zakarias Brounéus
  • Title: Grassmannianer
  • Abstract: see the Swedish version of the page

Time: 13:15-14:00

  • Place: 4003
  • Student: Viggo Laaksoharju
  • Title: A guide to the étale cohomology of curves

Abstract: Étale cohomology is an important tool in modern algebraic geometry that was introduced by A. Grothendieck in an attempt to exhibit a Weil cohomology theory and ultimately to prove the Weil conjectures. One of the appealing aspects of this theory is that it provides algebro-geometric analogues to some arguments in differential topology. In this talk I will outline the fundamental constructions underlying this theory and the core arguments used in the computation of the cohomology for some selected curves.

 

Time: 14:15-15:00

  • Place: 4003
  • Student: Philip Åberg
  • Title: Fourier analysis on finite groups.

Abstract: In this bachelor's thesis we discuss Fourier analysis on finite groups with the aim of reaching the famous Peter-Weyl theorem. On the road we also discuss the general theory of class functions, the character-basis of $L^2(G)_G$, and the differences between the abelian and nonabelian theory.

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