# Seminars & Colloquia Calendar

## Analysis without the Analysis

#### Brian Pinsky - Rutgers University

Location: ** GSL**

Date & time: Friday, 09 November 2018 at 1:40PM - 2:40PM

Abstract: I'd like to share a definitely true story. Once upon a time, there lived a logician named Abraham Robinson. Overall, he had a happy life, but there was one problem: the analysts of his department were constantly being friendly and telling him about their research. This led to far too many conversations involving the letter epsilon for Robinson to live a happy and successful life. Then, one day, Robinson had an idea. "What if I reengineered all of real analysis so that it required a whole course in model theory to understand even the most basic definitions? Surely," he thought, "that would make the analysts stop trying to talk to me".

And with that, he set to work. To succeed with his plan, he knew he would first have to learn how to do analysis. For months, he read paper after paper, and filled entire chalkboards, only to find himself lost in a sea of epsilons and sign errors. As he chased references backwards, he started reading older and older works, until eventually, he found himself all the way back at the beginning, in Leibniz's first formulations of calculus. Back then, before the idea of epsilons, people had been making do with just the idea of "infinitesimal numbers". Most sensible mathematicians of Robinson's day would criticize this as informal and lacking in rigor; and with good reason. Nevertheless, this proved to be the one paper Robinson could read, and so here he began his work.

Some years later, Robinson had perfected an analyst-proof formulation of calculus. Unfortunately for him, it turned out better than standard calculus in many ways, and some of the open minded analysts wanted to actually learn this horrible system he had derived, and they made him spend the rest of his career explaining it to them.

These days, the framework he built is called "non-standard analysis". In my talk, I plan to introduce you to this wonderful world where definitions make intuitive sense without 5 layers of quantifiers, and all the proofs feel like you're definitely cheating. My agenda will be to define the hyperreals properly, then spend the remaining 5 minutes spewing out definitions, and perhaps actually proving a theorem.

R. Shapiro Organizer's Page

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

Yonah Biers-Ariel, Mingjia Yang, and Doron Zeilberger --> homepage

Paul Feehan, Manousos Maridakis, 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

Corrine Yap 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: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song

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

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

Stephen D. Miller

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

Ebru Toprak, Organizer

Fioralba Cakoni Seminar webpage

Organizer: Vladimir Retakh Organizer's webpage

- Show events from all categories

## Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

*Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.*