The new PhD colloquium is organized by Ruben Stienstra and Milan Lopuhaä. The new website can be found here.

- Organization
- Johan Commelin

- Thu, 16 Apr (HG03.085)
- Julius Witte
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*Lattices and representations of $\textrm{GL}_2$.*Let $p$ be a prime. Let $\mathbb{Q}_p$ be the $p$-adic field corresponding with $p$, i.e. the completion of the rational numbers with respect to a norm related to $p$. First we will look at lattices in the 2-dimensional vector space over $\mathbb{Q}_p$. Then we will apply the theory about lattices to study certain irreducible representations of $\textrm{GL}_2(\mathbb{Q}_p)$. - Thu, 21 Apr (HG03.085)
- Abel Stern
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*AF algebras and discrete approximations of (smooth) manifolds.*Motivated by regularization of quantum gravity, we aim to view a (smooth, Riemannian) manifold as a limit of finite-dimensional spectral triples. This means in particular that the topology of said manifold should be accurately captured in an AF algebra. In the process we encounter a way to (functorially) associate an AF algebra to a countable poset. - Thu, 31 Mar (HG03.085)
- Peter Hochs
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*Introduction to index theory.*Index theory has its origins in Atiyah and Singerâ€™s index theorem from the 1960s. This states that analytic information, related to solution spaces of differential equations on manifolds, equals topological/geometrical information. An example is the Gauss-Bonnet theorem, which states that the Euler characteristic of a compact surface equals its average scalar curvature (modulo a constant factor). If a group acts on all relevant structure, this leads to a link with representation theory. I will give an informal overview of this area, and focus on the basics. - Thu, 17 Mar (HG03.085)
- Giovanni Caviglia —
*Operads and homotopy theory.*Operads are mathematical objects that are used to present and to handle algebraic structures in symmetric monoidal categories. In this introductory talk on operad theory I will recall the basic definitions, give some examples and present some applications to homotopy theory. - Thu, 03 Mar (HG01.139)
- Frank Roumen —
*Circles.* - Mon, 14 Dec (HG03.085)
- Bert Lindenhovius —
*Commutative C*-subalgebras and Boolean subalgebras.*Given a unital C*-algebra A, we discuss the poset C(A) of all commutative C*-subalgebras of A ordered by inclusion. In a similar way, we can consider the poset B(P) of Boolean subalgebras of an orthomodular poset P. We will compare Gelfand duality (between commutative C*-algebras and compact Hausdorff spaces) and Stone duality (between Boolean algebras and totally disconnected compact Hausdorff spaces) in order to obtain a relation between C(A) and B(P), which allows us to reconstruct the projections of a C*-algebra A from C(A). - Mon, 7 Dec (HG03.085)
- Joost Nuiten —
*Lie algebroids in deformation theory.*Given any sort of geometric object (e.g. a curve in the plane), one usually likes to study what can happen if one slightly perturbs this geometric structure. In this talk I want to sketch how (infinitesimally) small deformations of such geometric objects are controlled by a certain algebraic gadget called a (derived) Lie algebroid. - Mon, 30 Nov (HG02.028)
- Johan Commelin —
*Periods (and why the fundamental theorem of calculus conjecturely is a fundamental theorem).*In 2001 M. Kontsevich and D. Zagier posed a conjecture on algebraic integrals, which rougly says that the theorem of Stokes (the fundamental theorem of calculus in higher dimensions) is the only non-trivial relation between such integrals. In this talk I will formulate this conjecture, and indicate how it relates to conjectures and research in other fields. - Mon, 23 Nov (HG03.085)
- Ruben Stienstra — Connection and Gauge theory: a long introduction
- Mon, 16 Nov (HG03.085)
- Ruben Stienstra — Connection and Gauge theory: an introduction
- Mon, 2 Nov (HG03.632)
- Ruben Stienstra — Connection and Gauge theory: a brief introduction
- Mon, 12 Oct (HG03.632)
- Peter Badea — An Introduction to the Local Langlands Conjecture
- Mon, 28 Sep (HG03.632)
- Milan Lopuhaä —
*The number of field topologies on a given field.*Let F be a field. A field topology on F is a topology such that addition, multiplication and inversion are continuous. In 1973 (Podewski, Kiltinen) it was proven that an infinite field F admits exactly 2^(2^#F) field topologies. The countable case is radically different from the uncountable case. In this talk I will sketch the proofs of both of these cases and talk about the number of Galois invariant topologies.