# Difference between revisions of "Probability Seminar"

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Abstract: It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe. | Abstract: It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe. | ||

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+ | == October 8, 2020, [http://sites.harvard.edu/~sus977/index.html Subhabrata Sen], [https://statistics.fas.harvard.edu/ Harvard] == | ||

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+ | Title: '''TBA''' | ||

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+ | Abstract: TBA | ||

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+ | == November 12, 2020, [http://stanford.edu/~ajdunl2/ Alexander Dunlap], [https://cims.nyu.edu/ NYU Courant Institute] == | ||

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+ | Title: '''TBA''' | ||

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+ | Abstract: TBA | ||

[[Past Seminars]] | [[Past Seminars]] |

## Revision as of 11:28, 31 August 2020

# Fall 2020

**Thursdays in 901 Van Vleck Hall at 2:30 PM**, unless otherwise noted.
**We usually end for questions at 3:20 PM.**

** IMPORTANT: ** In Fall 2020 the seminar is being run online.

If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu

## September 15, 2020, Boris Hanin (Princeton and Texas A&M)

## September 23, 2020, Neil O'Connell (Dublin)

## October 1, 2020, Marcus Michelen, UIC

Title: **Roots of random polynomials near the unit circle**

Abstract: It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.

## October 8, 2020, Subhabrata Sen, Harvard

Title: **TBA**

Abstract: TBA

## November 12, 2020, Alexander Dunlap, NYU Courant Institute

Title: **TBA**

Abstract: TBA