# Seminars & Colloquia Calendar

## Computing linear extensions of partial orders subject to algebraic constraints

#### Shane Kepley, Rutgers University

Location: ** Hill 425**

Date & time: Friday, 13 September 2019 at 12:00PM - 1:00PM

**Abstract:** Switching systems have been extensively used for modeling the dynamics of gene regulation. This is partially due to the natural decomposition of phase space into rectangles on which the dynamics can be completely understood. Recent work has shown that the parameter space can also be decomposed into ``nice'' subsets. However, computing these subsets, or even determining if they are empty turns out to be a difficult problem.

We will show that computing a parameter space decomposition is equivalent to computing all linear extensions of a certain poset. The elements of this poset are polynomials and this structure induces additional algebraic constraints on the allowable linear extensions. We will describe an algorithm for efficiently solving this problem when the polynomials are linear. A more general class of polynomials can also be handled efficiently through a transformation which reduces to the linear case. Finally, we present several open problems and conjectures which arise when one generalizes this problem to subsets of arbitrary polynomial rings.

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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