The Electronic Computational Homotopy Theory Seminar is an international research seminar on the topic of computational homotopy theory. Topics include any part of homotopy theory that has a computational flavor, including but not limited to stable homotopy theory, unstable homotopy theory, chromatic homotopy theory, equivariant homotopy theory, motivic homotopy theory, and Ktheory. The seminar meets on Thursdays at 11:30am in Detroit (Eastern Time). Contact Dan Isaksen (isaksen@wayne.edu) for more information, or to be added to the seminar mailing list. The ECHT calendar lists all scheduled talks. See below for the schedule of talks, in reverse chronological order. 14 December 2017 Speaker: Teena Gerhardt, Michigan State University 30 November 2017 Speaker: Paul Goerss, Northwestern University 16 November 2017 Speaker: Dan Dugger, University of Oregon 2 November 2017 Speaker: Vitaly Lorman, University of Rochester 19 October 2017 Speaker: Glen Wilson, University of Oslo 5 October 2017 Speaker: Prasit Bhattacharya, University of Virginia 21 September 2017 Speaker: Bogdan Gheorghe, Max Planck Institute Abstract: The setting is motivic homotopy theory over Spec C. After pcompleting, the Tate twist originating in the motivic mod p cohomology of a point lifts to an element \tau in the stable homotopy groups of the (pcompleted) motivic sphere. Inverting this element recovers classical homotopy theory, while killing it produces a homotopy theory that is equivalent to the (algebraic) derived category of the Hopf algebroid BP_* BP. One can use this element tau to formulate an obstruction theory to construct motivic spectra which starts in the algebraic category, and with obstructions in algebraic Extgroups (similar to Toda's obstruction theory). We will illustrate this obstruction theory by reconstructing the motivic spectrum kq representing hermitian Ktheory, and by also computing the cooperations of kq/tau along the way, which proves to be similar but easier to the classical computation for kO.
7 September 2017 Speaker: Dan Isaksen, Wayne State University; Guozhen Wang, Fudan University Abstract: In the past year, Guozhen Wang, Zhouli Xu, and I have computed approximately thirty new stable homotopy groups, in dimensions 6293. Our methodology uses motivic techniques to leverage computer calculations of both the Adams and AdamsNovikov E2pages. I will describe our computational approach, and I will point out some interesting phenomena in the stable stems that we have uncovered. Guozhen Wang will also present some information about our computer code. 1 June 2017 Speaker: Mark Behrens, University of Notre Dame Abstract: The Ebased Adams Spectral Sequence (EASS) famously has E_2term given by Ext over E_*E if E_*E is flat over E_*. What do you do if this is not the case?? LellmannMahowald, in their analysis of the boASS, had to figure this out. In their case, the E_1 term decomposed into a v_1periodic summand and an EilenbergMacLane summand. They completely computed the cohomology of the v_1periodic summand, and left Don Davis to use a computer to attack the EilenbergMacLane summand (which petered out around the 20 stem). I will discuss a new technique, joint with Agnes Beaudry, Prasit Bhattacharya, Dominic Culver, and Zhouli Xu, which instead computes the EilenbergMacLane summand in terms of Ext over the Steenrod algebra (and thus is much more robust). This technique applies whenever such a decomposition occurs, and I will discuss applications to the BP<2>ASS and the tmfASS. 18 May 2017 Speaker: Nat Stapleton, Universitaet Regensburg Abstract: In the 90's Goerss, Hopkins, and Miller proved that the Morava Etheories are E_\inftyring spectra in a unique way. Since then several people including Ando, Hopkins, Strickland, and Rezk have worked on explaining the affect of this structure on the homotopy groups of the spectrum. In this talk, I will present joint work with Barthel that shows how a form of character theory due to Hopkins, Kuhn, and Ravenel can be used to reduce this problem to a combination of combinatorics and the GL_n(Q_p)action on the Drinfeld ring of full level structures which shows up in the local Langlands correspondence. 4 May 2017 Speaker: Oliver Roendigs, Universitaet Osnabrueck 20 April 2017 Speaker: Kyle Ormsby, Reed College Abstract: Recent work of RöndigsSpitzweckØstvær sharpens the connection between the slice and Novikov spectral sequences. Using classical vanishing lines for the E_2page of the AdamsNovikov spectral sequence and the work of AndrewsMiller on the alpha_1periodic ANSS, I will deduce some new vanishing theorems in the bigraded homotopy groups of the etacomplete motivic sphere spectrum. In particular, I will show that the mth etacomplete MilnorWitt stem is bounded above (by an explicit piecewise linear function) when m = 1 or 2 mod 4, and then lift this result to integral MilnorWitt stems (where an additional constraint on m appears). This is joint work with Oliver Röndigs and Paul Arne Østvær. 13 April 2017 Speaker: Andrew Salch, Wayne State University 23 March 2017 Speaker: Bert Guillou, University of Kentucky 9 March 2017 Speaker: Doug Ravenel, University of Rochester 2 March 2017 Speaker: Vesna Stojanoska, UIUC 16 February 2017 Speaker: Michael Hill, UCLA Abstract: I'll talk about a genuine equivariant notion of a derivation which not only takes products to sums but also takes norms to transfers. This arises naturally from genuine equivariant multiplicative filtrations, like the slice filtration, and gives some techniques for producing differentials. As an application, I'll discuss in some detail the slice spectral sequence for a $C_4$analogue of $BP\langle 1\rangle 1$, the simplified $C_4$ version of the spectrum used in the solution of the Kervaire invariant one problem. 19 January 2017 Speaker: Lennart Meier, Universitaet Bonn 15 December 2016 Speaker: Agnes Beaudry, University of Colorado

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