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Homotopy Theory Seminar - Phillip Jedlovec

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November 2, 2017
11:30AM - 12:30PM
Math Tower 154

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Add to Calendar 2017-11-02 11:30:00 2017-11-02 12:30:00 Homotopy Theory Seminar - Phillip Jedlovec Title: The generalized homology of $BU\langle 2k\rangle$Speaker: Phillip Jedlovec (University of Notre Dame)Abstract: In their 2001 paper, "Elliptic spectra, the Witten genus and the theorem of the cube,'' Ando, Hopkins, and Strickland use an algebro-geometric perspective to give a partial description of the generalized homology of the connective covers of BU. For any complex-orientable cohomology theory, E, they define homology elements $b_{i_1, ..., i_k}$ in $E_*BU\langle 2k\rangle$, prove the so called ``cocycle relations'' and ``symmetry relations'' on these elements, and show that when $E=H\mathbb{Q}$ or $k=1, 2,$ or $3$, these are in fact the defining relations for $E_*BU\langle 2k\rangle$. In this talk, I will sketch a new proof of these results that uses no algebraic geometry, but instead uses facts about Hopf rings and the work of Ravenel and Wilson on the homology of the spaces in the $\Omega$-spectrum for Brown-Peterson cohomology. Time permitting, I will also discuss how this approach gives a similarly nice description of $E_* E(1)_{k}$, for $k>0$ and $E$ Landweber exact.Seminar URL: https://people.math.osu.edu/valenzuelavasquez.2/hts/ Math Tower 154 Department of Mathematics math@osu.edu America/New_York public

Title: The generalized homology of $BU\langle 2k\rangle$

Speaker: Phillip Jedlovec (University of Notre Dame)

Abstract: In their 2001 paper, "Elliptic spectra, the Witten genus and the theorem of the cube,'' Ando, Hopkins, and Strickland use an algebro-geometric perspective to give a partial description of the generalized homology of the connective covers of BU. For any complex-orientable cohomology theory, E, they define homology elements $b_{i_1, ..., i_k}$ in $E_*BU\langle 2k\rangle$, prove the so called ``cocycle relations'' and ``symmetry relations'' on these elements, and show that when $E=H\mathbb{Q}$ or $k=1, 2,$ or $3$, these are in fact the defining relations for $E_*BU\langle 2k\rangle$. In this talk, I will sketch a new proof of these results that uses no algebraic geometry, but instead uses facts about Hopf rings and the work of Ravenel and Wilson on the homology of the spaces in the $\Omega$-spectrum for Brown-Peterson cohomology. Time permitting, I will also discuss how this approach gives a similarly nice description of $E_* E(1)_{k}$, for $k>0$ and $E$ Landweber exact.

Seminar URLhttps://people.math.osu.edu/valenzuelavasquez.2/hts/

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