Analyse Projecten

On this page one finds a number of possible subjects for various projects associated to mathematical exams. Descriptions are very short. Students are invited to drop by and get more info if they are interested.

Bachelor

Tweede jaars projecten

• De nergens differentieerbare, continue functie van Weierstrass en verwante vragen

Bachelor scriptie

• Kakeya's Needle and related problems Hoe groot moet een verzameling in R² zijn om er een interval op continue manier in te keren?
• Overconvergentie en gap series. Machtreeksen convergeren op schijven. Kan een reeks van partieel sommen op een groter gebied convergeren? Hoe krijg je dat voor elkaar, en wat kun je zeggen over de limiet functies

Master

Master's Thesis

• Proper Embedding of one dimensional manifolds in C²
• Approximation on compact sets in C. This topic is classic. Recent work on analytic capacity may open new ways to solve old problems.
• The Cauchy Transform. The integral transformation ∫ 1/(z-ζ) dμ(ζ) has intersting holomorphy properties that are worth studying.
• Gleason's problem: Given a ring of holomorphic functions R on a domain D in C^n. Is the ideal of the functions vanishing at p in D spanned by the functions z_i-p_i (i=1...n)?
• Fine holomorphic functions. An extension of the notion of holomorphic function, or rather of the sets that are considered open. There exists a good basic theory, but on a slightly more advanced level there are many interesting questions.

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