## RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

sponsored by the
and the
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)

Fall 2020 Talks

*Date:* Oct. 22, 2020, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420]

*Speaker:* Christoph Koutschan, Johan Radon Institute (RICAM), Linz, Austria

*Title:* On Christol's Conjecture

*Abstract:* Diagonals of rational functions naturally occur in many applications,
such as lattice statistical mechanics and enumerative combinatorics. In
the mid 1980's Gilles Christol famously conjectured that any globally
bounded D-finite function can be expressed as the diagonal of a rational
function. We study several families of rational functions in three or
four variables and investigate the nature of their diagonals. It is
interesting to compare them with the solutions of the telescopers
associated to these rational functions. The connection with creative
telescoping leads us to eliminate some of the potential counterexamples
to Christol's conjecture that were proposed in the literature. This is
joint work with Youssef Abdelaziz, Salah Boukraa, and Jean-Marie Maillard.

*Date:* Oct. 29, 2020, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

*Speaker:* Edinah Gnang, Johns Hopkins Univesity

*Title:* On Partial Differential encodings of Boolean functions

*Abstract:* We describe how combinatorial enumeration and listing problem in connection with structural properties of hypermatrices
determine critical aspect of the complexity of Boolean function.
The talk will not assume familiarity with Boolean functions nor with hypermatrices.

*Date:* Nov. 5, 2020, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

*Speaker:* Vladimir Retakh, Rutgers University.

*Title:* Noncommutative Catalan numbers, orthogonal polynomials and beyond

*Abstract:* I will discuss an approach to (generalized) orthogonal polynomials
over noncommutative rings by using infinite Hankel matrices. As an
example, I will consider properties of Hankel matrices consisting of
noncommutative analogues of Catalan numbers. This is a joint work with
Arkady Berenstein

*Date:* Nov. 12, 2020, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

*Speaker:* Jonathan Lenchner,
IBM T.J. Watson Research Center, Yorktown Heights, NY

*Title:* Rethinking the Foundations of Mathematics and its Practical Consequences

*Abstract:* In this talk I shall argue that we should recast the foundations of mathematics using the foundational notion of a bit, rather than the much more ambiguous notion of a set, and the axiomatic assumption that infinite sets exist, whatever that might mean. I shall argue that mathematics and physics are inextricably connected and that treating mathematics axiomatically, and believing that mathematical objects like points, lines or even simple infinite decimal expansions like 0.1111 exist in some Platonic idealist sense, is just coercing mathematics into some meaningless ideal form. I will try to convince you that the deepest questions are not about some large cardinals that are inexpressible in the language of set theory (so-called inaccessible cardinals), but about extremely large natural numbers that we are unable to express in any way given a finite universe and so finite rewritable memories and finite computational power. Forget about infinite cardinal numbers, do these finite numbers exist or not? What precisely do we mean by expressibility, specifically expressibility in N bits? What are the limits of our expresibility? What do these questions say about the limitations of what is provable about arithmetic, or about finite structures like graphs?

*Date:* Nov. 19, 2020, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

*Speaker:* Richard Stanley, MIT and the University of Miami.

*Title:* From Stern's triangle to upper homogeneous posets

*Abstract:* Stern's triangle S is an array of numbers similar to Pascal's
triangle, except that in addition to adding two adjacent numbers we also
copy each number down to the next row. We discuss some arithmetic
properties of S that can be greatly generalized.
There is also a natural poset P associated to S. This poset is upper
homogeneous, i.e., for every t in P, the subposet {s: s ≥ t} is
isomorphic to P. As a consequence, the Ehrenborg quasisymmetric function
of P, which is a kind of generating function for counting certain chains
in P, is a symmetric function. This motivates the question of which
symmetric functions can be Ehrenborg quasisymmetric functions of upper
homogeneous posets.