Forskjeller

Her vises forskjeller mellom den valgte versjonen og den nåværende versjonen av dokumentet.

--- seminar:top [2019-07-13]
gereonq [Spring 2019 - Upcoming Talks]
+++ seminar:top [2019-09-11]
mariusth
@@ Linje 3: / Linje 3: @@
 ====== 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 5, 13:15 - 14:15, room 734, Sentralbygg 2>
+<infoboks fill|November 7, 10:15 - 11:15, room 656, Sentralbygg 2>
-**Benjamin Collas (University of Bayreuth): //TBA//**
+**Martin Frankland (University of Regina): //TBA//**
 ----
-**Abstract:** TBA
+**Abstract:** TBA.
 </infoboks>
+===== Fall 2019 - Previous Talks =====
-<infoboks fill|August 12, 13:15 - 14:15, room 734, Sentralbygg 2>
+<infoboks fill|August 5, 13:15 - 14:15, room 734, Sentralbygg 2>
-**Tomer Schlank (Hebrew University, Jerusalem): //TBA//**
+**Benjamin Collas (University of Bayreuth): //Moduli Stacks of Curves: Arithmetic and Motives//**
 ----
-**Abstract:** TBA
+**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 a 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 0, these 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.
 </infoboks>
-===== Spring 2019 - Previous Talks =====
-<infoboks fill|February 25, 13:15 - 14:15, room 734, Sentralbygg 2>
+<infoboks fill|August 12, 13:15 - 14:15, room 734, Sentralbygg 2>
-**Jarl Gunnar Taxerås Flaten (NTNU): //Programming with Category Theory//**
+**Tomer Schlank (Hebrew University, Jerusalem): //Ambidexterity in the T(n)-Local Stable Homotopy Theory//**
 ----
-**Abstract:** Haskell is a programming language heavily inspired by category theory. We'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:** 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 properties. One 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.
-</infoboks>
-<infoboks fill|March 4, 13:15 - 14:15, room 734, Sentralbygg 2>
-**Viktoriya Ozornova (Ruhr-Universität Bochum): //Homotopy theory for 2-categories//**
-**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.
-</infoboks>
-<infoboks fill|April 1, 13:15 - 14:15, room 734, Sentralbygg 2>
-**Ambrus Pal (Imperial College London): //An arithmetic Yau-Zaslow formula//**
-----
-**Abstract:** We prove an arithmetic refinement of the Yau–Zaslow formula by replacing the classical Euler characteristic in Beauville’s argument by a variant of Levine’s motivic Euler characteristic. We derive several similar formulas for other related invariants, including 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.
-</infoboks>
-<infoboks fill|June 4 <color #ed1c24>(!!!Tuesday!!!)</color>, 13:15 - 14:15, room 734, Sentralbygg 2>
-**Antoine Touzé (Université de Lille): //Structure and applications of exponential functors//**
-----
-**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 talk, we will explain some structure results on these exponential functors, which show that these objects have a rather rigid structure. We will explain on a concrete example how our rigidity results can be used in practical computations of homological nature.
+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.
 </infoboks>
-<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//**
 ----
-**Abstract:** I'll present a new model for ∞-operads, namely as analytic monads. In 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 functors. I'll talk about some of the features of this theory, and explain a nerve theorem, which implies that the ∞-category of analytic monads is equivalent to the ∞-category of dendroidal Segal spaces of Cisinski and Moerdijk, one of the known equivalent models for ∞-operads. This is joint work with David Gepner and Rune Haugseng.
+**Abstract:** Persistent homology has proven to be a useful tool to extract information from data sets. Homology, however, is a drastic simplification and in certain situations might remove too much information. This prompts us to study parametrised chain complexes. Dwyer and Spalinski proved that the category of chain complexes allows a model category structure. Following their example, we 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 particular, I 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.
 </infoboks>