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seminar:top [2019-07-13]
gereonq [Spring 2019 - Upcoming Talks]
seminar:top [2019-10-03] (nåværende versjon)
runegha [Fall 2019 - Upcoming Talks]
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 ====== Seminars in geometry/​topology ====== ====== Seminars in geometry/​topology ======
-The Topology Seminar ​Spring ​2019 will be on **Mondays** 13:15 - 14:15 (or 14:00 - 15:00) in room 734, Sentralbygg 2.+The Topology Seminar ​Fall 2019 will be on **Mondays** 13:15 - 14:15 (or 14:00 - 15:00) in room 734, Sentralbygg 2.
-===== Spring ​2019 - Upcoming Talks =====+===== Fall 2019 - Upcoming Talks =====
-<​infoboks fill|August 513:15 - 14:15, room 734, Sentralbygg 2>+<​infoboks fill|November 710:15 - 11:15, room 656, Sentralbygg 2>
-**Benjamin Collas ​(University of Bayreuth): //TBA//**+**Martin Frankland ​(University of Regina): //TBA//**
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-**Abstract:​** TBA+**Abstract:​** TBA.
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 +<​infoboks fill|November 8, 13:00 - 14:00, room 734, Sentralbygg 2>
-<​infoboks fill|August 12, 13:15 - 14:15, room 734, Sentralbygg 2> +**Irakli Patchkoria ​(University ​of Aberdeen): //TBA//**
- +
-**Tomer Schlank ​(Hebrew ​University, Jerusalem): //TBA//**+
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-**Abstract:​** TBA+**Abstract:​** TBA.
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-===== Spring 2019 - Previous Talks ===== 
-<​infoboks fill|February 25, 13:15 - 14:15, room 734, Sentralbygg 2>+<​infoboks fill|November 18, 13:15 - 14:15, room 734, Sentralbygg 2>
-**Jarl Gunnar Taxerås Flaten ​(NTNU): //Programming with Category Theory//**+**Hongyi Chu (Max Planck Institute for Mathematics): //TBA//**
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-**Abstract:​** ​Haskell is a programming language heavily inspired by category theoryWe'll start by seeing how basic category theory is represented in this language, before having a deeper look at what monads are and their different uses here. Anyone with some familiarity with algebra is welcome---especially those who don't believe pure mathematics has real, practical uses!+**Abstract:​** ​TBA.
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-<​infoboks fill|March 4, 13:15 14:15, room 734, Sentralbygg 2>+===== Fall 2019 Previous Talks =====
-**Viktoriya Ozornova (Ruhr-Universität Bochum): //Homotopy theory for 2-categories//​** +<​infoboks fill|August 5, 13:15 - 14:15, room 734, Sentralbygg 2>
- +
-**Abstract:​** Grothendieck and Quillen introduced a notion of homotopy equivalences for categories using a by-now-standard tool called "​nerve"​ of a category. This idea leads to various models of categories-up-to-homotopy. In a joint ongoing project with Martina Rovelli, we study variants of the Roberts-Street-nerve for 2-categories and notions of homotopy equivalences arising from this nerve, with an eye towards 2-categories-up-to-homotopy. +
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-<​infoboks fill|April 1, 13:15 - 14:15, room 734, Sentralbygg 2>+
-**Ambrus Pal (Imperial College London): //An arithmetic Yau-Zaslow formula//**+**Benjamin Collas ​(University of Bayreuth): //Moduli Stacks of Curves: Arithmetic and Motives//**
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-**Abstract:​** ​We prove an arithmetic ​refinement ​of the Yau–Zaslow formula by replacing ​the classical Euler characteristic ​in Beauville’s argument by variant ​of Levine’s ​motivic ​Euler characteristicWe derive several similar formulas for other related invariantsincluding Saito’s determinant ​of cohomology, and a generalisation ​of a formula ​of Kharlamov and Rasdeaconu on counting real rational curves on real K3 surfaces. Joint work with Frank Neumann.+**Abstract:​** ​Thanks to the arithmetic of their Knudsen-Mumford stratification, ​the tower of moduli stacks of curves is a key object in the study of geometric Galois theory and of the Tannakian category of mixed Tate motives. 
 +The goal of this talk is to introduce a similar perspective ​in terms of the stack stratification of the spaces. As motivation, we will first present how the first cyclic stack inertia strata are endowed with a Galois action ​of Tate-type, then how Artin-Mazur and Morel-Vovedsky simplicial and homotopical theories provide a fruitful context for some "​stack" ​motivic ​decomposition and Tannakian results that reflect this arithmetic result. 
 +In genus 0these approach leads in particular to an interpretation ​of the mixed Tate motivic Galois group as loop-group, and to the definition ​of computable (hidden) periods ​of stack nature.
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-<​infoboks fill|June 4 <color #​ed1c24>​(!!!Tuesday!!!)</​color>​, 13:15 - 14:15, room 734, Sentralbygg 2>+<​infoboks fill|August 12, 13:15 - 14:15, room 734, Sentralbygg 2>
-**Antoine Touzé ​(Université de Lille): //Structure and applications of exponential functors//**+**Tomer Schlank ​(Hebrew University, Jerusalem): //Ambidexterity in the T(n)-Local Stable Homotopy Theory//**
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-**Abstract:​** ​Exponential functors are functors from k-vector spaces to k-vector spaces which turn direct sums into tensor products, just as the exterior algebra does. In this talkwe will explain some structure results on these exponential functors, which show that these objects have a rather rigid structureWe will explain on a concrete ​example ​how our rigidity results ​can be used in practical computations ​of homological nature.+**Abstract:​** ​Chromatic homotopy is the study of the \(\infty\)-category of Spectra trough a filtration by so-called "​chromatic primes" ​  The pieces of this filtration (monochromatic layers), that is- The K(n)-local (stable \(\infty\)-)categories \(Sp_{K(n)}\) enjoy many remarkable propertiesOne example ​is the vanishing 
 +of the Tate construction due to  Hovey-Greenlees-Sadofsky. ​ The vanishing of Tate construction ​can be considered as a natural equivalence between the colimits and limits ​in \(Sp_{K(n)}\) ​ parametrized by finite groupoids. Hopkins and Lurie proved a generalization ​of this result where finite groupoids are replaced by arbitrary \(\pi\)-finite ​ \(\infty\)-groupoids.  
 +There is another possible sequence of  (stable \(\infty\)-)categories who can be considered as "​monochromatic layers",​ Those are the T(n)-local \(\infty\)-categories \(Sp_{T(n)}\).  
 +For the \(Sp_{T(n)}\) the vanishing of the Tate construction was proved by Kuhn. We shall prove that the analog of  Hopkins and Lurie'​s result in for \(Sp_{T(n)}\). 
 +Our proof will also give an alternative proof for the K(n)-local case.  
 +This is joint work with Shachar Carmeli and Lior Yanovski
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-<​infoboks fill|June 17, 13:15 - 14:15, room 734, Sentralbygg 2>+<​infoboks fill|August 26, 13:15 - 14:15, room 734, Sentralbygg 2>
-** Joachim Kock, Universitat Autònoma de Barcelona: //Infinity operads ​as polynomial monads//**+**Barbara Giunti (University of Pavia): //Parametrised chain complexes ​as a model category//**
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-**Abstract:​** ​I'll present ​new model for ∞-operads,​ namely as analytic monadsIn the ∞-world (unlike what happens in the classical case)analytic functors are polynomial, and therefore the theory can be developed within the setting of polynomial functorsI'll talk about some of the features ​of this theory, and explain ​nerve theoremwhich implies ​that the ∞-category of analytic monads ​is equivalent to the ∞-category of dendroidal Segal spaces of Cisinski ​and Moerdijkone of the known equivalent models for ∞-operads. This is joint work with David Gepner and Rune Haugseng.+**Abstract:​** ​Persistent homology has proven to be useful tool to extract information from data setsHomologyhoweveris a drastic simplification ​and in certain situations might remove too much informationThis prompts us to study parametrised chain complexes. Dwyer and Spalinski proved that the category ​of chain complexes allows ​model category structure. Following their examplewe showed ​that also the category of parametrised chain complexes ​is a model category, for some distinguished classes ​of morphisms. 
 +In this seminar, I will present this result ​and show why it is useful. In particularI will present two types of invariants, very natural in any model category, that apply to any parametrised chain complex, while the standard decomposition of persistent modules can be applied only on a restricted set of parametrised chain complexes
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2019-07-13, Gereon Quick