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)

Current co-organizers:
Doron Zeilberger (doronzeil {at} gmail [dot] com)
Robert Dougherty-Bliss (robert {dot} w {dot} bliss {at} gmail [dot] com)

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 Robert Dougherty-Bliss (robert {dot} w {dot} bliss {at} gmail [dot] com)

Note: due to Dr. Z.'s sabbatical this academic year, this seminar only meets every other Thurs. It will go back to being weekly in Fall 2023.

Forthcoming Talks (Spring 2023)


Date: Feb. 2, 2023, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Jinyoung Park, Courant Institute, New York University.

Title: Thresholds

Abstract: For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a "threshold." Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). In this talk, I will present recent progress on this topic. Based on joint work with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham.



Date: Feb. 16, 2023, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Robert Dougherty-Bliss, Rutgers University

Title: Gosper's algorithm and Bell numbers

Abstract: Computers are now very good at evaluating finite sums in closed form. They can do them almost instantly and can often prove that a sum cannot be evaluated in closed form, like the partial sums of k!. Just like in calculus, we can fix summands that don't yield closed forms by multiplying them by a suitable "summation factor." I will show that this idea, applied to sums of falling factorials, produces sequences of polynomials closely related to the Bell numbers.



Date: March 2, 2023, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Vladimir Retakh, Rutgers University

Title: Noncommutative generalized Catalan numbers and their generating functions

Abstract: In 1999 M. Aigner defined Catalan-like numbers as North-West entries of powers of semi-infinite three-diagonal matrices. In this talk I will generalize this construction to various matrices over noncommutative rings and discuss properties of the corresponding generating functions. I will also consider orthogonal polynomials associated with these "numbers". Most of the results are new even in the commutative case. Joint work with A. Berenstein and M. Gekhtman.



Date: March 23, 2023, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: March 30, 2023, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: April 13, 2023, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: April 27, 2023, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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