# Seminars & Colloquia Calendar

## Comparing models and data using computational algebraic geometry and topology

#### Heather Harrington, Oxford University

Location: ** Hill 425**

Date & time: Friday, 01 February 2019 at 1:30PM - 2:30PM

**Abstract:** I will overview my research for a very general math audience. I will start with motivation of the biological problems we have explored, such as tumor-induced angiogenesis (the growth of blood vessels to nourish a tumor), as well as signaling pathways involved in the dysfunction of cancer (sets of molecules that interact that turn genes on/off and ultimately determine whether a cell lives or dies). Both of these biological problems can be modeled using differential equations. The challenge with analyzing these types of mathematical models is that the rate constants, often referred to as parameter values, are difficult to measure or estimate from available data.

I will present mathematical methods we have developed to enable us to compare mathematical models with experimental data. Depending on the type of data available, and the type of model constructed, we have combined techniques from computational algebraic geometry and topology, with statistics, networks and optimization to compare and classify models without necessarily estimating parameters. Specifically, I will introduce our methods that use computational algebraic geometry (e.g., Grobner bases) and computational algebraic topology (e.g., persistent homology). I will present applications of our methodology on datasets involving cancer. Time permitting, I will conclude with our current work for analyzing spatio-temporal datasets with multiple parameters using computational algebraic topology. Mathematically, this is studying a module over a multivariate polynomial ring, and finding discriminating and computable invariants.

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

Brooke Logan

Wujun Zhang Organizer's webpage

Ziming Shi, Sagun Chanillo, Xiaojun Huang, Chi Li, Jian Song Seminar website Old seminar website

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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