Date: Thu., Jan. 23, 2025, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker: Stoyan Dimitrov, Rutgers University
Title: Picking, posing and attacking natural problems in discrete mathematics: from insightful bijections to black-box help from machine learning
Abstract: We will walk through several combinatorial results. Half of them have important motivation coming from computer science and the other half explain surprising observations made by experimentation. We will begin by a high-level discussion on how one shall pick or pose his problems, and end by sharing more about an exciting machine learning technique that may change the way we approach combinatorial (and mathematical) problems in general. Some exciting open questions will also be mentioned.
Date: Thu., Jan. 30, 2025, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Title: A map of the holonomic forest - searching for irrationality with Conservative Matrix Fields
Abstract: Is this number irrational?
This question has been troubling mathematicians since the time of Pythagoras, and inspired a search for good
rational approximations of constants. Examining the literature on irrationality, we notice a recurring theme: holonomic sequences.
These recursive sequences have dominated this field, generating very good approximations. In this talk we shall detail an experimental journey into the
"forest" of holonomic functions. In our exploration, we will pick up a powerful object - the Conservative Matrix Field. With this map in hand,
we shall re-discover many known Diophantine approximations (Apery, Beukers, Zudilin, Aptekareve), and some new ones as well.
If time permits, we will detail more deeply the conjectured properties of these Matrix Fields.
Speaker: Shachar Weinbaum, Technion (member of the Ramanujan Machine group)
Date: Thu., Feb. 6, 2025, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker:
David Broadhurst, Open University, UK
Title: Resurgent integer sequences
Abstract: In combinatorics, we happily manipulate formal power series, taking no heed of whether they might converge. Applied mathematicians encounter series with no radius of convergence, about which they worry. Jean Ecalle mediates between these communities, by telling us about resurgent trans-series. I shall give an account of how an integer sequence from a problem in physics exhibits resurgence.
Title: A mirror step variant of gambler's ruin
Abstract: Consider a gambler who starts with x dollars. At each gamble, the gambler either wins a dollar with probability 1/2 or loses a dollar with probability 1/2. The gambler's goal is to reach N dollars without first running out of money (i.e., hitting 0 dollars). If the gambler reaches N dollars, we say that they are a winner. The gambler continues to play until they either run out of money or win. This scenario is known as the gambler's ruin problem, first posed by Pascal. We consider a new generalization of the gambler's ruin problem. A particle starts at some point x on a line of length N. At each step, the particle either moves from x to x-1 with probability q1, or moves from x to x+1 with probability q2, or moves from x to N-x with probability p where 0
Title: Ascent sequences avoiding a set of length-3 patterns
Abstract: See here
Title: Young Tableau Reconstruction Via Minors
Abstract:
Starting point of our talk will be a short discussion of the classical 15 puzzle. It turns out that similar problems about sliding numbered tiles around in a box are of enormous relevance to combinatorial algebra in the context of Young tableaux. In particular, we are going\
to present "The Tableau Reconstruction Problem," posed by Monks (2009). Starting with a standard Young tableau T of size n, i.e., an arrangement of n numbered tiles, a 1-minor of T is a tableau obtained by first deleting any tile of T, and then sliding the remaining tiles \
into position and renumbering them according to some rules. This can be iterated to arrive at the set of k-minors of T. The problem is this: given k, what are the values of n such that every tableau of size n can be reconstructed from its set of k-minors? For k=1, the prob\
lem was recently solved by Cain and Lehtonen. In this talk, we discuss the problem for k=2, proving the sharp lower bound n ≥ 8. In the case of multisets of k-minors, we also give a lower bound for arbitrary k, as a first step toward a sharp bound in the general multis\
et case
Title: The Mathematics of Adriano Garsia (1928-2024)
Abstract: Adriano Garsia (wiki) started out
in Harmonic Analysis, but soon enough saw the light and became one of the leaders of Enumerative and Algebraic Combinatorics. In this tribute,
students, collaborators, and colleagues, will try and describe some of his seminal contrubutions. After the end of the formal part,
there would be plenty of time for an "open stage" where everyone (including his 36 PhD students) would have the opportunity to
say a few words in Adriano's memory.
Title: A central limit theorem in the framework of the Thompson group F
Abstract: The classical central limit theorem states that the average of an infinite sequence of independent and identically distributed random variables, when suitably rescaled, tends to a normal distribution. In fact, this classical result can be stated purely alg\
ebraically, using the combinatorics of pair partitions. In the 1980s, Voiculescu proved an analog of the central limit theorem in free probability theory, wherein the normal distribution is replaced by Wigner's semicircle distribution. Later, Speicher provided an
algebraic proof of the free central limit theorem, based on the combinatorics of non-crossing pair partitions. Since then,
various algebraic central limit theorems have been studied in noncommutative probability, for instance, in the context of symmetric groups. My talk will discus\
s a central limit theorem for the Thompson group F, and show that the central limit law of a naturally defined sequence in the group algebra of F is the normal distribution. Our combinatorial approach employs abstract reduction systems to arrive at this result.
Title: Combinatorial exploration and permutation classes
Abstract:
Permutations, words, set partitions, and other such families of objects often play a role in diverse subfields of mathematics, physics and computer science. When the structure of the object under investigation is known there are well-established tools, such as symbolic and \
analytic combinatorics, that derive an enumeration, asymptotics, and the ability to randomly generate instances of the objects. However, the initial step from a definition of the object to a structural description is often ad-hoc, human-staring-at-a-blackboard type of work.\
This is the gap combinatorial exploration attempts to fill.
Combinatorial exploration is a domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions. We describe how it works and provide an open-source Python impleme\
ntation. As a prerequisite, we build up a new theoretical foundation for combinatorial decomposition strategies and combinatorial specifications.
Combinatorial exploration has been most extensively applied to permutation classes, rederiving hundreds of results in the literature as well as discovering many novel results (which can be found on permpal.com). As well as unifying earlier methods, one key advantage of our \
approach is its ability to utilise a growing library of strategies in a simultaneous manner to build a greater understanding of the structure of the permutation classes.
Date: Thu.,April 3, 2025, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Title: Some positivity conjectures for symmetric functions motivated by
classical theorems from the analytic theory of polynomials
Abstract:
I recall some classical theorems from the analytic theory of polynomials,
and then ask whether they can be "upgraded" from pointwise positivity
to coefficientwise positivity. This leads to a series of positivity
conjectures for symmetric functions. This is joint work with Yusra Naqvi.
Title: Some surprises in lattice problems
Abstract: I present some (idealized) problems from condensed matter physics and cluster chemistry that lead to mathematical insights that seem to fly in the face of the scientists' intuition
Date: Thu.,April 24, 2025, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Title: Modular arithmetic with trinomial moduli
Abstract:
A popular approach to speed up computations is to reduce the input modulo several relatively prime numbers, do arithmetic on the residues, then reconstruct the result at the end. This improves the running time if the moduli (and their pairwise inverses) have "nice" binary s\
hapes, but only a limited number of such moduli are known. I will discuss a new system of moduli related to a family of trinomials. This system has shown promising real-world performance, can produce arbitrarily many moduli, and its elements can be computed quickly. I will \
mention some theoretical limitations of the system based on roots of unity and graph colorings, and point out what remains to be discovered.
Joint work with Mits Kobayashi, Natalya Ter-Saakov, and Eugene Zima.
Date: Thu., Feb. 20, 2025, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker: Toufik Mansour, University of Haifa
Date: Thu., Feb. 27, 2025, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker: Daniel Herden, Baylor University
i>Date: Thu., March 6, 2025, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
coordinator and MC: Angela Hicks. Here is the program
(that includes the list of speakers)
Date: Thu., March 13, 2025, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker:
Arundhathi Krishnan,Mary Immaculate College, Thurles, Ireland
Date: Thu., March 27, 2025, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker: Christian Bean, Keele University
Speaker: Alan Sokal, University College London.
Date: Thu.,April 17, 2025, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker: Michael Kiessling, Rutgers University
Speaker: Robert Dougherty-Bliss, Dartmouth College