RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

sponsored by the

Rutgers University
Department of Mathematics

and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Founded 2003 by Drew Sills and Doron Zeilberger.

Former co-organizers: Drew Sills (2003-2007), Moa ApaGodu (2005-2006), Lara Pudwell (2006-2008), Andrew Baxter (2008-2011), Brian Nakamura (2011-2013), Edinah Gnang (2011-2013), Matthew Russell (2013-2016), Nathan Fox (2016-2017), Bryan Ek (2017-2018), Mingjia Yang (2018-2020), Yonah Biers-Ariel (2018-2020), Robert Dougherty-Bliss (2020-2024), Stoyan Dimitrov (2023-2025)

Current co-organizers:
Doron Zeilberger (doronzeil {at} gmail [dot] com)
Aurora Hiveley (aurora.hiveley {at} scarletmail [dot] rutgers [dot] edu)
Lucy Martinez (lm1154 {at} scarletmail [dot] rutgers [dot] edu)

Archive of Previous Speakers and Talks You can find links to videos of some of these talks as well. Currently, our videos are being posted to our Vimeo page. Previously, we had videos posted on our YouTube page.


If you would like to be added to the weekly mailing list, email Lucy Martinez: lm1154 {at} scarletmail [dot] rutgers [dot] edu

Forthcoming Talks (Fall 2025)

Date: Thu., Sept. 11, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Neil Sloane, The OEIS Foundation and Rutgers University.

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Date: Thu., Sept. 18, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Benoit Cloitre (independent researcher)

Title: A heuristic link between divisor counts and prime densities in sequences

Abstract: I introduce a heuristic principle I call "probabilistic continuation" and conjecture a striking asymptotic equivalence: the density of primes in a well-behaved integer sequence appears to match a structural ratio derived from the divisor counts of its terms. The appeal of this conjecture is practical. Determining prime densities usually demands heavy analytic machinery (as in the Prime Number Theorem), whereas the associated divisor ratio is far easier to evaluate. If the conjecture is correct, this ratio could thus provide a simpler proxy for fundamental density measures. I will present the main conjecture, show its consistency with classical results (PNT, PNT in arithmetic progressions, prime distribution in quadratic-residue sequences), and discuss its coherence with Hardy-Littlewood-type conjectures.

Date: Thu., Sept. 25, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: Thu., Oct. 9, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: Thu., Oct. 16, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: Thu., Oct. 23, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: Thu., Oct. 30, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: Thu., Nov. 6, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: Thu., Nov. 13, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: Thu., Nov. 20, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: Thu., Dec. 4, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: Thu., Dec. 11, 2025, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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