## SoSe 2024

Title: Algebraic geometry of equilibria in cooperative games Abstract: The classical notion of Nash equilibria imposes the somewhat unnatural assumption of independent non-cooperative acting on the players of a game. In 2005, the philosopher Wolfgang Spohn introduced a new concept, called dependency equilibria, that also takes into consideration cooperation of the players. Dependency…

Read moreTitle: Algebraic Patching for Beginners Abstract: Using the language and the tools of rigid analytic geometry, Harbater (1987) has defined a "patching operation" which can be used to solve the inverse Galois problem over fields like Qₚ(T) or Fₚ((X))(T). Later, Haran and Völklein (1996) rephrased this construction in a purely algebraic language, replacing all geometric arguments with (almost…

Read moreTitle: The distribution of quadratic non-residues: A stroll through the garden Abstract: We shall have a stroll through the garden of classical results about the distribution quadratic (non-)residues modulo a prime with an emphasis on the methods involved. We shall also stress the depressing state of the affairs pertaining to the distribution of quadratic non-residues in non-initial segments,…

Read moreTitle: Symmetries of the set of squarefree integers in a number field Abstract: Let K be a number field. We answer the following question and several generalizations: What are the Z-linear maps O_K -> O_K that send every squarefree algebraic integer to a squarefree algebraic integer? In the talk at 11:15am, Michael Baake will introduce dynamical systems associated to k-free algebraic integers. …

Read moreTitle: Dynamical and spectral properties of some shift spaces of number-theoretic origin Abstract: While B-free systems in one dimension have been studied for a long time, considerably less is known on their higher-dimensional analogues. Starting from the visible points of the integer lattice, a large class of such systems emerge via k-free integers in algebraic number fields. We discuss typical…

Read moreDi, 16. April 2024 in Raum A 3.339 14:15 Uhr - 15:45 Uhr Titel: Fermat's Last Theorem for regular primes Abstract: Definition. For a number field K, let h(K) denote its class number. A prime number p is said to be regular if p ∤ h(Q(ζp)), otherwise irregular. Theorem. (Fermat’s Last Theorem for regular primes) For a regular prime p ≥ 3, the equation xp + yp = zp does not have a solution in…

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