# Seminars & Colloquia Calendar

## The bar flavor of monopole Floer homology and homological algebra

#### Mike Miller Eismeier (Columbia University)

Location: ** zoom**

Date & time: Tuesday, 21 September 2021 at 11:00AM - 12:00PM

Abstract: Kronheimer and Mrowka define three flavors of monopole Floer homology (HM-to, HM-from, and HM-bar, which are known to be isomorphic to HF^+, HF^-, and HF^oo, respectively). The third of these they show depends on much less than the 3-manifold we plug in: HM-bar(Y) can be computed as the "coupled Morse homology" of the torus T(Y) = T^{b_1 Y}, and show that it only depends on the cohomology ring of Y. They also relate this to what might be called the twisted simplicial homology of said torus T(Y). Over the rationals, Kronheimer and Mrowka show that this is enough to completely determine the homology groups HM-bar(Y). However, their techniques cannot be applied integrally.

I will explain recent joint work of myself and Francesco Lin, where we investigate this twisted simplicial homology for its own sake. By proving a formality property for twisted homology of spaces with torsion-free cohomology, we are able to show that Kronheimer and Mrowka's answer holds over the integers as well (bypassing the spectral sequence and thus avoiding extension problems). Passing through the isomorphism HM-bar = HF^oo, this confirms a conjecture of Oszvath and Szabo. We show that this is lucky to T(Y) and twisted homology may be quite complicated in general.

Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

P. Gupta, X.Huang and J. Song Organizer's webpage

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

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