Seminar

Tutte colloquium-Stephen Melczer

Cody Miller-Sweeney — Thu, 03 Jul 2025 17:56:08 +0000

Tutte colloquium-Stephen Melczer Cody Miller-Sweeney Thu, 07/03/2025 - 13:56

Title:Automated Sequence Asymptotics

Speaker:	Stephen Melczer
Affiliation:	University of ��ݮ��Ƶ
Location:	MC 5501

Abstract:Computing with any sort of object requires a way of encoding it on a computer, which poses a problem in enumerative combinatorics where the objects of interest are (infinite) combinatorial sequences. Thankfully, the generating function of a combinatorial sequence often satisfies natural algebraic/differential/functional equations, which can then be viewed as data structures for the sequence. In this talk we survey methods to take a sequence encoded by such data structures and automatically determine asymptotic behaviour using techniques from the field of analytic combinatorics. We also discuss methods to automatically characterize the asymptotic behaviour of multivariate sequences using analytic combinatorics in several variables (ACSV). The focus of each topic will be rigorous algorithms that have already been implemented in computer algebra systems and can be easily used by anyone.

Algebraic and enumerative combinatorics seminar-Karen Yeats

Cody Miller-Sweeney — Thu, 03 Jul 2025 13:21:29 +0000

Algebraic and enumerative combinatorics seminar-Karen Yeats Cody Miller-Sweeney Thu, 07/03/2025 - 09:21

Title:Sizes of witnesses in covtree

Speaker	Karen Yeats
Affiliation	University of ��ݮ��Ƶ
Location	MC 5479

Abstract: Here is a purely combinatorial problem that arose in causal set theory. Let {P_1, ... , P_k} be distinct unlabelled posets all with n elements. Suppose there is a poset Q such that {P_1, ... , P_k} is exactly the set of downsets of Q of size n up to isomorphism. Given n and k can we give a tight upper bound on the minimum size of such a Q? As with newspaper headlines, the answer to the question is no, at least for the moment, but I'll explain what we do know. Joint work with Jette Gutzeit, Kimia Shaban, and Stav Zalel.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm,

Algebraic and enumerative combinatorics seminar-Farhad Soltani

Cody Miller-Sweeney — Fri, 27 Jun 2025 13:22:36 +0000

Algebraic and enumerative combinatorics seminar-Farhad Soltani Cody Miller-Sweeney Fri, 06/27/2025 - 09:22

Title:Quasisymmetric Harmonics in Superspace

Speaker	Farhad Soltani
Affiliation	York University
Location	MC 5479

Abstract: The harmonics of quasisymmetric polynomials in superspace are the orthogonal complement of the ideal generated by quasisymmetric polynomials without constant term. In this talk, I will discuss the harmonics and present the first basis of this space, which is indexed by a specific family of nested forests.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm,

Tutte colloquium-Henry Wolkowicz

Cody Miller-Sweeney — Thu, 26 Jun 2025 13:21:07 +0000

Tutte colloquium-Henry Wolkowicz Cody Miller-Sweeney Thu, 06/26/2025 - 09:21

Title:The omega-Condition Number: Applications to Preconditioning and Low Rank Generalized Jacobian Updating

Speaker:	Henry Wolkowicz
Affiliation:	University of ��ݮ��Ƶ
Location:	MC 5501

Abstract: Preconditioning is essential in iterative methods for solving linear systems. It is also the implicit objective in updating approximations of Jacobians in optimization methods, e.g.,~in quasi-Newton methods. We study a nonclassic matrix condition number, the omega-condition number}, omega for short. omega is the ratio of: the arithmetic and geometric means of the singular values, rather than the largest and smallest for the classical kappa-condition number. The simple functions in omega allow one to exploit first order optimality conditions. We use this fact to derive explicit formulae for (i) omega-optimal low rank updating of generalized Jacobians arising in the context of nonsmooth Newton methods; and (ii) omega-optimal preconditioners of special structure for iterative methods for linear systems. In the latter context, we analyze the benefits of omega for (a) improving the clustering of eigenvalues; (b) reducing the number of iterations; and (c) estimating the actual condition of a linear system. Moreover we show strong theoretical connections between the omega-optimal preconditioners and incomplete Cholesky factorizations, and highlight the misleading effects arising from the inverse invariance of kappa. Our results confirm the efficacy of using the omega-condition number compared to the kappa-condition number.

(Joint work with: Woosuk L. Jung, David Torregrosa-Belen.)

Algebraic and enumerative combinatorics seminar-Leo Jiang

Cody Miller-Sweeney — Fri, 20 Jun 2025 17:13:59 +0000

Algebraic and enumerative combinatorics seminar-Leo Jiang Cody Miller-Sweeney Fri, 06/20/2025 - 13:13

Title:Oriented graded Möbius algebras

Speaker	Leo Jiang
Affiliation	University of Toronto
Location	MC 5479

Abstract:The graded Möbius algebra B(M) of a matroid M contains much combinatorial information about the flats of M. Its algebraic properties were instrumental in the proof of the Dowling—Wilson top-heavy conjecture. We will introduce a skew-commutative analogue OB(M) associated to every oriented matroid M, and discuss its algebraic structure. This is part of ongoing work joint with Yu Li.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm

Tutte colloquium-Gary Au

Cody Miller-Sweeney — Thu, 19 Jun 2025 13:35:30 +0000

Tutte colloquium-Gary Au Cody Miller-Sweeney Thu, 06/19/2025 - 09:35

Title:Worst-case instances of the stable set problem of graphs for the Lovász–Schrijver SDP hierarchy

Speaker:	Gary Au
Affiliation:	University of Saskatchewan
Location:	MC 5501

Abstract:(Based on joint work with Levent Tunçel.)

In this talk, we discuss semidefinite relaxations of the stable set problem of graphs generated by the lift-and-project operator LS_+ (due to Lovász and Schrijver), and present some of our recent progress on this front. In particular, we show that for every positive integer k, the smallest graph with LS_+-rank k contains exactly 3k vertices. This result is sharp and settles a conjecture posed by Lipták and Tunçel from 2003.

The talk will be accessible to a general audience, and does not assume any prior knowledge of lift-and-project methods.

Algebraic Graph Theory-Eric Culver

Cody Miller-Sweeney — Thu, 12 Jun 2025 14:05:19 +0000

Algebraic Graph Theory-Eric Culver Cody Miller-Sweeney Thu, 06/12/2025 - 10:05

Title: Two Distinct Eigenvalues from a New Graph Product

Speaker:	Eric Culver
Affiliation:	Brigham Young University
Location:	Please contact Sabrina Lato for Zoom link.

Abstract:The parameter q(G) of a graph G is the minimum number of distinct eigenvalues of a symmetric matrix whose pattern is given by G. We introduce a novel graph product by which we construct new infinite families of graphs that achieve q(G)=2. Several graph families for which it is already known that q(G)=2 can also be thought of as arising from this new product.

Tutte colloquium-Sepehr Hajebi

Cody Miller-Sweeney — Thu, 12 Jun 2025 13:16:55 +0000

Tutte colloquium-Sepehr Hajebi Cody Miller-Sweeney Thu, 06/12/2025 - 09:16

Title:Complete bipartite induced minors (and treewidth)

Speaker:	Sepehr Hajebi
Affiliation:	University of ��ݮ��Ƶ
Location:	MC 5501

Abstract:I will present a result that describes the unavoidable induced subgraphs of graphs with a large complete bipartite induced minor, and will discuss the connections and applications to bounding the treewidth in hereditary classes of graphs. If time permits, I will also sketch some proofs.

Joint work with Maria Chudnovsky and Sophie Spirkl.

Algebraic and enumerative combinatorics seminar-Elana Kalashnikov

Cody Miller-Sweeney — Mon, 09 Jun 2025 12:41:07 +0000

Algebraic and enumerative combinatorics seminar-Elana Kalashnikov Cody Miller-Sweeney Mon, 06/09/2025 - 08:41

Title:The Abelian/non-Abelian correspondence and Littlewood-Richardson

Speaker	Elana Kalashnikov
Affiliation	University of ��ݮ��Ƶ
Location	MC 5479

Abstract:The Abelian/non-Abelian correspondence gives rise to a natural basis for the cohomology of flag varieties, which - except for Grassmannians - is distinct from the Schubert basis. I will describe this basis and its multiplication rules, and explain how to relate it to the Schubert basis for two-step flag varieties. I will then explain how this leads to new tableaux Littlewood--Richardson rules for many products of Schubert classes. This is joint work (separately) with Wei Gu and Linda Chen.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm,

Algebraic Graph Theory-Blas Fernandez

Cody Miller-Sweeney — Thu, 05 Jun 2025 12:58:39 +0000

Algebraic Graph Theory-Blas Fernandez Cody Miller-Sweeney Thu, 06/05/2025 - 08:58

Title: 2-Y-homogeneous distance-biregular graphs

Speaker:	Blas Fernandez
Affiliation:	IMFM, Ljubljana; UP FAMNIT, Koper, Slovenia
Location:	Please contact Sabrina Lato for Zoom link.

Abstract: Distance-biregular graphs (DBRGs) generalize distance-regular graphs by admitting a bipartition of the vertex set, where each part satisfies local distance-regularity under distinct intersection arrays. In recent years, a particular subclass of these graphs, those satisfying the so-called 2-Y-homogeneous condition, has garnered increasing attention due to its rich connections with combinatorial design theory and the representation theory of Terwilliger algebras. In this talk, we will examine the key structural conditions that characterize 2-Y-homogeneous DBRGs. We will survey recent progress in their classification under various combinatorial constraints, highlighting both known results and open problems.