# Seminars & Colloquia Calendar

## Parametrization and Spacing of Roots of Cubic Congruences

#### Matthew Welsh (Rutgers)

Location: ** Hill 525**

Date & time: Tuesday, 24 April 2018 at 2:00PM - 3:00PM

Roots of quadratic congruences, for example x^2 = -1 (mod m), can be parametrized using binary quadratic forms. This parametrization leads to an approximation, to error less than 1/m, of x/m by a fraction with denominator of size m^{1/2}. This in turn shows that those roots with m at most M are spaced by at least 1/M, a fact crucial to Fouvry and Iwaniec's proof that there are infinitely many primes of the form x^2 + p^2.

In this talk we will discuss similar parametrization, approximation, and spacing results for roots of cubic congruences, focusing on x^3 = 2 (mod m). A main result is that inside any square with side length 1/M in R^2/Z^2, there are O(1) points (x/m, x^2/m) mod 1 with x^3 = 2 (mod m) and m ~M.

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

- 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.*