You can submit a talk through this form (with at least one week advance notice please) or email Aram directly for more last minute additions/changes. If you want to see math seminars of all disciplines, you can try the following website.

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The following is a list of online conferences that are happening during the pandemic! If you have a conference you'd like to add, feel free to email me. 😃

- Dynamical Algebraic Combinatorics - Registration
**19-30 October 2020**

All times are denoted in your local computer time. Roughly the next two weeks are shown.

It is currently: **Tue 20 Oct 2020 00:44 UTC**

Last updated: Sun 18 Oct 2020 18:30 UTC

Green - Talk is currently happening.

Yellow - Talk is coming up within the hour.

Red - Talk is in under 10 minutes.

**Zoom links can be found on seminar/conference websites** (They have been removed for security reasons)

Speaker | Title | Date & Time | Duration | Abstract | Seminar |
---|---|---|---|---|---|

David Croydon (Kyoto) | Scaling limits of the two- and three-dimensional uniform spanning trees | Tue 20 Oct 2020 08:00 UTC | 60 minutes | Show | 17 |

Anita Liebenau (UNSW) | The threshold bias of the clique-factor game | Tue 20 Oct 2020 09:30 UTC | 60 minutes | Show | 17 |

Thomas Lam (University of Michigan) | Cluster configuration spaces of finite type | Tue 20 Oct 2020 15:00 UTC | 60 minutes | Show | 16 |

Federico Castillo (MPI Leipzig) | When are multidegrees positive? | Tue 20 Oct 2020 15:00 UTC | 50 minutes | Show | 13 |

Vladimir Podolskii (Steklov Mathematical Institute and HSE University, Moscow, Russia). | Max-plus polynomials and their roots | Tue 20 Oct 2020 16:30 UTC | 30 minutes | Show | 7 |

Markus Bläser (Saarland University, Saarbrücken, Germany) | Variety Membership Testing, Algebraic Natural Proofs, and Geometric Complexity Theory | Tue 20 Oct 2020 17:15 UTC | 30 minutes | Show | 7 |

Oliver Pechenik | Dynamics of plane partitions | Wed 21 Oct 2020 15:00 UTC | 45 minutes | Show | Dynamical Algebraic Combinatorics |

Dave Benson | Some exotic tensor categories in prime characteristic | Wed 21 Oct 2020 15:00 UTC | 60 minutes | Show | 19 |

Elizabeth Kelley (University of Minnesota) | Constructing scattering diagrams and the theta basis for generalized cluster algebras | Wed 21 Oct 2020 16:00 UTC | 60 minutes | Show | 15 |

Rebecca Patrias | Promotion, Webs, and Kwebs | Wed 21 Oct 2020 16:00 UTC | 30 minutes | Show | Dynamical Algebraic Combinatorics |

Emily Gunawan | Infinite friezes and bracelets | Wed 21 Oct 2020 16:30 UTC | 30 minutes | Show | Dynamical Algebraic Combinatorics |

Ed Swartz, Cornell University | Polymatroids and finite groups (pre-seminar) | Wed 21 Oct 2020 22:30 UTC | 30 minutes | Show | 31 |

Ed Swartz, Cornell University | Polymatroids and finite groups | Wed 21 Oct 2020 23:10 UTC | 50 minutes | Show | 31 |

Hao Hu (University of Waterloo) | Facial Reduction for Symmetry Reduced Semidefinite and Doubly Nonnegative Programs | Thu 22 Oct 2020 14:00 UTC | 60 minutes | Show | 8 |

Jamie Walton (University of Nottingham) | Aperiodic Order: The Mathematics of Systems of Approximate Symmetry | Thu 22 Oct 2020 14:10 UTC | 50 minutes | Show | 1 |

Ajmain Yamin (Stony Brook) | Filtering Grassmannian Cohomology via k-Schur Functions. | Thu 22 Oct 2020 15:00 UTC | 60 minutes | Show | 5 |

Nate Gallup, UC Davis | Infinite-dimensional flag varieties and other applications of well-ordered filtrations | Thu 22 Oct 2020 17:00 UTC | 50 minutes | Show | 23 |

Swee Hong Chan (UCLA) | Sorting probability for Young diagrams | Thu 22 Oct 2020 17:00 UTC | 50 minutes | Show | 24 |

Reuven Hodges | Coxeter combinatorics and spherical Schubert geometry | Thu 22 Oct 2020 17:00 UTC | 50 minutes | No abstract available | 25 |

Benny Sudakov (ETH Zurich) | The intersection spectrum of 3-chromatic intersecting hypergraphs | Thu 22 Oct 2020 19:00 UTC | 60 minutes | Show | 18 |

Matt Superdock, Carnegie Mellon University | The necklace splitting problem and robot motion planning | Thu 22 Oct 2020 19:30 UTC | 60 minutes | Show | 2 |

Christoph Koutschan, Johan Radon Institute (RICAM), Linz, Austria | On Christol's Conjecture | Thu 22 Oct 2020 21:00 UTC | 48 minutes | Show | 20 |

Eric Hanson (Brandeis) | TBA | Fri 23 Oct 2020 15:00 UTC | 60 minutes | No abstract available | 33 |

Tom Roby | Let's birational: Lifting periodicity and homomesy to higher realms | Fri 23 Oct 2020 15:00 UTC | 45 minutes | Show | Dynamical Algebraic Combinatorics |

Ambat Vijayakumar (Cochin University of Science and Technology, India) | Power domination problem - A Survey | Fri 23 Oct 2020 16:00 UTC | 60 minutes | Show | 3 |

Ivelisse Rubio (Universidad de Puerto Rico) | Arreglos periódicos multidimensionales | Fri 23 Oct 2020 16:00 UTC | 60 minutes | Show | 14 |

Richard P. Stanley (MIT and University of Miami) | TBA | Fri 23 Oct 2020 18:30 UTC | 60 minutes | No abstract available | 28 |

John Machacek (Hampden-Sydney) | Posets, Cones, and Toric Varieties | Fri 23 Oct 2020 20:35 UTC | 50 minutes | Show | 30 |

Speaker | Title | Date & Time | Duration | Abstract | Seminar |
---|---|---|---|---|---|

Ferdinand Ihringer | TBA | Mon 26 Oct 2020 15:30 UTC | Check Seminar Page | No abstract available | 32 |

Liam Solus (KTH Royal Institute of Technology) | TBA | Mon 26 Oct 2020 18:00 UTC | 60 minutes | No abstract available | 27 |

Alex McDonough (Brown U.) | TBA | Mon 26 Oct 2020 19:00 UTC | 60 minutes | No abstract available | 36 |

Rose McCarty | Colouring pseudo-visibility graphs | Mon 26 Oct 2020 19:00 UTC | Check Seminar Page | No abstract available | 9 |

Rebecca Patrias University of Saint Thomas | Webs and tableau promotion | Mon 26 Oct 2020 19:10 UTC | 50 minutes | Show | 22 |

Alex Woo (U Idaho) | TBA | Mon 26 Oct 2020 21:40 UTC | 60 minutes | No abstract available | 34 |

Igor Kortchemski (Ecole polytechnique) | TBA | Tue 27 Oct 2020 14:00 UTC | Check Seminar Page | No abstract available | 17 |

Aris Filos-Ratsikas (University of Liverpool, UK) | The Complexity of Necklace Splitting, Consensus-Halving and Discrete Ham Sandwich | Tue 27 Oct 2020 16:30 UTC | 30 minutes | Show | 7 |

Igor Shinkar (Simon Fraser University, BC, Canada) | On Percolation and NP-Hardness | Tue 27 Oct 2020 17:15 UTC | 30 minutes | Show | 7 |

Amit Hazi | TBA | Wed 28 Oct 2020 16:00 UTC | 60 minutes | No abstract available | 19 |

Chi Hoi Yip (University of British Columbia) | Improving the trivial upper bound on the clique number of Paley graphs and generalized Paley graphs | Wed 28 Oct 2020 17:00 UTC | 60 minutes | Show | 15 |

Jesús A. De Loera, University of California, Davis | The space of monotone paths of a linear program (pre-talk) | Wed 28 Oct 2020 22:30 UTC | 30 minutes | Show | 31 |

Jesús A. De Loera, University of California, Davis | The space of monotone paths of a linear program | Wed 28 Oct 2020 23:10 UTC | 50 minutes | Show | 31 |

Rosa Orellana (Dartmouth) | TBA | Thu 29 Oct 2020 15:00 UTC | Check Seminar Page | No abstract available | 5 |

Irakli Patchkoria (University of Aberdeen) | TBA | Thu 29 Oct 2020 15:10 UTC | 50 minutes | No abstract available | 1 |

Florian Aigner | TBA | Thu 29 Oct 2020 17:00 UTC | 50 minutes | No abstract available | 25 |

Laura Escobar | TBA | Thu 29 Oct 2020 17:00 UTC | 50 minutes | No abstract available | 24 |

Elizabeth Gross (University of Hawai'i at Mānoa) | TBA | Thu 29 Oct 2020 19:00 UTC | Check Seminar Page | No abstract available | 8 |

Sergey Norin (McGill) | TBA | Thu 29 Oct 2020 19:00 UTC | Check Seminar Page | No abstract available | 18 |

Nóra Frankl, Carnegie Mellon University and London School of Economics | TBA | Thu 29 Oct 2020 19:30 UTC | 60 minutes | No abstract available | 2 |

Edinah Gnang, Johns Hopkins Univesity | On Partial Differential encodings of Boolean functions | Thu 29 Oct 2020 21:00 UTC | 48 minutes | Show | 20 |

Sara Billey | TBA | Fri 30 Oct 2020 15:00 UTC | 60 minutes | No abstract available | 33 |

Miodrag Iovanov (University of Iowa) | On combinatorial Hopf algebras of multi-complexes | Fri 30 Oct 2020 16:00 UTC | 60 minutes | Show | 3 |

Alejandro Cabrera (Universidade Federal do Rio de Janeiro) | TBA | Fri 30 Oct 2020 16:00 UTC | 60 minutes | No abstract available | 14 |

Alexander Sidorenko | On graph norms for complex-valued functions | Fri 30 Oct 2020 18:30 UTC | Check Seminar Page | Show | 28 |

Melissa Sherman-Bennett (UC Berkeley) | TBA | Fri 30 Oct 2020 19:00 UTC | 50 minutes | No abstract available | 29 |

Monica Lewis (MIchigan) | TBA | Fri 30 Oct 2020 20:35 UTC | 50 minutes | No abstract available | 30 |

Speaker | Title | Date & Time | Duration | Abstract | Seminar |
---|---|---|---|---|---|

Sabrina Lato & Christino Tamon | TBA | Mon 02 Nov 2020 16:30 UTC | Check Seminar Page | No abstract available | 32 |

Sara Billey (University of Washington) | TBA | Mon 02 Nov 2020 19:00 UTC | 60 minutes | No abstract available | 27 |

Attila Joó | The Matroid Intersection Conjecture of Nash-Williams | Mon 02 Nov 2020 20:00 UTC | Check Seminar Page | No abstract available | 9 |

Sophia Elia (FU Berlin) | TBA | Mon 02 Nov 2020 20:00 UTC | 60 minutes | No abstract available | 36 |

Mariel Supina UC Berkeley | TBA | Mon 02 Nov 2020 20:10 UTC | 50 minutes | No abstract available | 22 |

Andrés Vindas Meléndez (U Kentucky) | TBA | Mon 02 Nov 2020 22:00 UTC | 60 minutes | No abstract available | 34 |

Karin Baur (University of Graz & University of Leeds) | Flips in triangulations and matchings | Tue 03 Nov 2020 15:00 UTC | Check Seminar Page | Show | 16 |

Carolina Benedetti (Universidad de los Andes) | TBA | Tue 03 Nov 2020 16:00 UTC | 50 minutes | No abstract available | 13 |

Arnaud De Mesmay (LIGM, Université Paris Est, France) | Link crossing number is NP-hard | Tue 03 Nov 2020 17:30 UTC | 30 minutes | Show | 7 |

Zuzana Patáková (Charles University, Prague) | Shellability is NP-complete | Tue 03 Nov 2020 18:15 UTC | 30 minutes | Show | 7 |

Alistair Craw | TBA | Wed 04 Nov 2020 16:00 UTC | 60 minutes | No abstract available | 19 |

Sasha Pevzner (University of Minnesota) | Wed 04 Nov 2020 18:00 UTC | 60 minutes | No abstract available | 15 | |

Amrutha P (IISER Thiruvananthapuram) | TBA | Thu 05 Nov 2020 08:30 UTC | Check Seminar Page | No abstract available | 5 |

Eric Rowell (Texas A&M University) | TBA | Thu 05 Nov 2020 15:10 UTC | 50 minutes | No abstract available | 1 |

Béatrice de Tilière | TBA | Thu 05 Nov 2020 18:00 UTC | 50 minutes | No abstract available | 24 |

Kirsten Eisenträger, Penn State U | TBA | Thu 05 Nov 2020 18:00 UTC | 50 minutes | No abstract available | 23 |

Alex Scott (Oxford) | TBA | Thu 05 Nov 2020 20:00 UTC | Check Seminar Page | No abstract available | 18 |

Vladimir Retakh, Rutgers University | Noncommutative Catalan numbers, orthogonal polynomials and beyond | Thu 05 Nov 2020 22:00 UTC | 48 minutes | Show | 20 |

Anne Dranowski | TBA | Fri 06 Nov 2020 16:00 UTC | 60 minutes | No abstract available | 33 |

Luna Lomonaco (Instituto de Matemática Pura e Aplicada) | TBA | Fri 06 Nov 2020 16:00 UTC | 60 minutes | No abstract available | 14 |

Pawel Rzazewski (Warsaw University of Technology, Poland) | TBA | Fri 06 Nov 2020 17:00 UTC | 60 minutes | No abstract available | 3 |

Ayo Adeniran (Pomona College) | Combinatorial interpretation of Goncarov polynomials over the lattice of partitions | Fri 06 Nov 2020 21:00 UTC | Check Seminar Page | Show | 28 |

Anna Weigandt (Michigan) | TBA | Fri 06 Nov 2020 21:35 UTC | 50 minutes | No abstract available | 30 |

Melissa Sherman-Bennett (Harvard) | TBA | Mon 09 Nov 2020 22:00 UTC | 60 minutes | No abstract available | 34 |

Fei Wang (KTH) | TBA | Thu 12 Nov 2020 15:00 UTC | Check Seminar Page | No abstract available | 8 |

Will Sawin, Columbia U | New results on prime polynomials | Thu 12 Nov 2020 18:00 UTC | 50 minutes | No abstract available | 23 |

Jenna Rajchgot (McMaster University) | TBA | Fri 13 Nov 2020 20:00 UTC | 50 minutes | No abstract available | 29 |

Andrés R. Vindas Meléndez (University of Kentucky) | The Equivariant Ehrhart Theory of the Permutahedron | Fri 13 Nov 2020 21:30 UTC | 60 minutes | Show | 12 |

Seminar Number | Name | Institution | Website |
---|---|---|---|

1 | Geometry, Algebra, Mathematical Physics and Topology Research Group | Cardiff Univesity | Seminar Website |

2 | Algorithms, Combinatorics and Optimization Seminar | Carnegie Mellon University | Seminar Website |

3 | New York Combinatorics Seminar | City University of New York | Seminar Website |

4 | Rocky Mountain Algebraic Combinatorics Seminar | Colorado State University | Seminar Website |

5 | Algebraic Combinatorics Seminar | Institute of Mathematical Sciences | Seminar Website |

6 | LIPN Seminar | Laboratoire d'Informatique de Paris Nord | Seminar Website |

7 | Los Angeles Combinatorics and Complexity Seminar | Los Angeles | Seminar Website |

8 | Virtual seminar on algebraic matroids and rigidity theory | Massachussetts Institute of Technology | Seminar Website |

9 | Online Matroid Theory Seminar | Matroid Union | Seminar Website |

10 | Nonlinear Algebra Seminar Online | Max-Planck-Instut für Mathematik (MPI) | Seminar Website |

11 | Virtual Combinatorics Colloquium | Northeast Combinatorics Network | Seminar Website |

12 | Algebra and Representation Theory Seminar | Oklahoma University | Seminar Website |

13 | Algebra, Geometry and Combinatorics | Online | Seminar Website |

14 | Cibercoloquio Latinoamericano de Mathemáticas | Online | Seminar Website |

15 | Graduate Online Combinatorics Colloquium | Online | Seminar Website |

16 | Online Cluster Algebra Seminar | Online | Seminar Website |

17 | Oxford Discrete mathematics and probability seminar | Oxford University | Seminar Website |

18 | Princeton Discrete Mathematics Seminar | Princeton University | Seminar Website |

19 | The RepNet Virtual Seminar | RepNet | Seminar Website |

20 | Rutgers Experimental Mathematics Seminar | Rutgers University | Seminar Website |

21 | Workshop on combinatorics, discrete geometry and algorithms | St. Petersburg State University | Seminar Website |

22 | Combinatorics Seminar | UC Berkeley | Seminar Website |

23 | Algebra and Discrete Mathematics Seminar | UC Davis | Seminar Website |

24 | UCLA Combinatorics Seminar | UCLA | Seminar Website |

25 | Algebraic (and enumerative) combinatorics seminar | UWaterloo | Seminar Website |

26 | Lie Theory seminar | University of Colorado, Boulder | Seminar Website |

27 | Discrete CATS Seminar | University of Kentucky | Seminar Website |

28 | Discrete Math Seminar | University of Massachusetts Amherst | Seminar Website |

29 | Combinatorics Seminar | University of Michigan | Seminar Website |

30 | Combinatorics Seminar | University of Minnesota | Seminar Website |

31 | Combinatorics and Geometry Seminar | University of Washington | Seminar Website |

32 | Algebraic Graph Theory | University of Waterloo | Seminar Website |

33 | Séminaire de combinatoire et d'informatique mathématique du LaCIM | Université du Québec à Montréal | Seminar Website |

34 | WUSTL Combinatorics Seminar | Washington University in St. Louis | Seminar Website |

35 | WinCom Virtual Colloquium | Women in Combinatorics | Seminar Website |

36 | Applied Algebra Seminar | York University | Seminar Website |

I will introduce recent work on the two- and three-dimensional uniform spanning trees (USTs) that establish the laws of these random objects converge under rescaling in a space whose elements are measured, rooted real trees, continuously embedded into Euclidean space. (In the three-dimensional case, the scaling result is currently only known along a particular scaling sequence.) I will also discuss various properties of the intrinsic metrics and measures of the limiting spaces, including their Hausdorff dimension, as well as the scaling limits of the random walks on the two- and three-dimensional USTs. In the talk, I will attempt to emphasise where the differences lie between the two cases, and in particular the additional challenges that arise when it comes to the three-dimensional model.

The two-dimensional results are joint with Martin Barlow (UBC) and Takashi Kumagai (Kyoto). The three-dimensional results are joint with Omer Angel (UBC) and Sarai Hernandez-Torres (UBC).

Let $r>3$ be an integer and consider the following game on the complete graph $K_n$ for n a multiple of r: Two players, Maker and Breaker, alternately claim previously unclaimed edges of Kn such that in each turn Maker claims one and Breaker claims b edges. Maker wins if her graph contains a $K_r$-factor, that is a collection of n/r vertex-disjoint copies of $K_r$, and Breaker wins otherwise. In other words, we consider the b-biased $K_r$-factor Maker-Breaker game. We show that the threshold bias for this game is of order $n^{2/(r+2)}$. This makes a step towards determining the threshold bias for making bounded-degree spanning graphs and extends a result of Allen, Böttcher, Kohayakawa, Naves and Person who resolved the case r=3 or 4 up to a logarithmic factor.

Joint work with Rajko Nenadov.

I will talk about a "cluster configuration space" M_D, depending on a finite Dynkin diagram D. The space M_D is an affine algebraic variety that is defined using only the compatibility degree of the corresponding finite-type cluster algebra. In the case that D is of type A, we recover the configuration space M_{0,n} of n (distinct) points in P^1. There are many relations to finite-type cluster theory, but an especially close connection to the finite-type cluster algebra with universal coefficients.

This talk is based on joint works with Nima Arkani-Hamed, Song He, and Hugh Thomas.

The notion of multidegree for multiprojective varieties extends that of degree for projective varieties. They can be defined in geometric terms, using intersection theory, or alternatively in algebraic terms, via multigraded hilbert polynomial. We study the problem of their positivity and establish a wonderful combinatorial description that relates to polyhedral geometry. We will show applications for Schubert polynomials and mixed volumes. This is joint work with Y.Cid-Ruiz, B.Li, J.Montano, and N.Zhang.

CloseIn this talk we will discuss polynomials over max-plus semiring and their roots. Max-plus polynomial is basically a piece-wise linear convex function and the roots are points of non-smoothness of the function. We will discuss analogs of Combinatorial Nullstellensatz, Schwartz-Zippel Lemma and Universal Testing Set for max-plus polynomials.

The talk is aimed at the general audience.

We study the variety membership testing problem in the case when the variety is given as an orbit closure and the ambient space is the space of all 3-tensors. The first variety that we consider is the slice rank variety, which consists of all 3-tensors of slice rank at most $r$. We show that the membership testing problem for the slice rank variety is NP-hard. While the slice rank variety is a union of orbit closures, we define another variety, the minrank variety, expressible as a single orbit closure. We also prove the NP-hardness of membership testing in the minrank variety, establishing the NP-hardness of the orbit closure containment problem for 3-tensors.

Algebraic natural proofs were recently introduced by Forbes, Shpilka and Volk and independently by Grochow, Kumar, Saks and Saraf. We prove that there are no polynomial algebraic natural proofs for testing membership in the slice rank and minrank variety unless coNP is a subset of exists-BPP.

The talk is aimed at the general audience.

I shall talk about some recent joint work with Etingof and Ostrik, producing some new incompressible symmetric tensor categories in prime characteristic and explain some of their properties and potential role in the theory. The input for the construction is the theory of tilting modules for SL(2).

CloseCluster algebras, as defined by Fomin and Zelevinsky, are characterized by binomial exchange relations. A natural generalization of these algebras, introduced by Chekhov and Shapiro, relaxes this restriction and allows the exchange polynomials to have arbitrarily many terms. Scattering diagrams have been used as a powerful tool for proving structural properties of cluster algebras. Following the work of Gross, Hacking, Keel, and Kontsevich, we discuss the construction of scattering diagrams for generalized cluster algebras, focusing on the subclass of generalized cluster algebras with reciprocal exchange coefficients. We then define the theta basis for these algebras. This talk will not require any previous familiarity with cluster algebras or scattering diagrams; each idea will be developed via concrete examples.

CloseThe speaker will try to convince you that the analogy “Polymatroids are to finite groups as matroids are to finite fields” is nowhere near as crazy as it sounds.

CloseThe speaker will try to convince you that the analogy “Polymatroids are to finite groups as matroids are to finite fields” is nowhere near as crazy as it sounds.

CloseWe consider both facial reduction, FR, and symmetry reduction, SR, techniques for semidefinite programming, SDP. We show that the two together fit surprisingly well in an alternating direction method of multipliers, ADMM, approach. In fact, this approach allows for simply adding on nonnegativity constraints, and solving the doubly nonnegative, DNN, relaxation of many classes ofhard combinatorial problems. We also show that the singularity degree does not increase after SR, and that the DNN relaxations considered here have singularity degree one, that is reduced to zero after FR. The combination of FR and SR leads to a significant improvement in both numerical stability and running time for both the ADMM and interior point approaches. We test our method on various DNN relaxations of hard combinatorial problems including quadratic assignment problems with sizes of more than n=500. This translates to a semidefinite constraint of order 250,000 and 625x10^8 nonnegative constrained variables.

CloseSymmetry is frequently exploited in Mathematics, but there are many situations in which systems exhibit long-range recurrence without precise periodic repetition. A simple example is given by a coding of an irrational circle rotation. With Shechtman's discovery of quasicrystals - physical materials with long-range order but also rotational symmetry precluding the standard periodicity of usual crystals - it seems that "aperiodically ordered" patterns can appear in nature too. In this talk I will introduce the field of Aperiodic Order, which investigates intriguing infinite idealisations of such patterns. A prototypical family of examples is given by Penrose's famous rhomb, or kite and dart tilings. I will then explain what sorts of mathematical structures can be introduced to systemise their study. I will focus on the construction of the tiling space of an aperiodic pattern, through which one may construct fundamental invariants using standard tools from Algebraic Topology.

CloseThis talk concerns the cohomology rings of complex Grassmannians. In 2003, Reiner and Tudose conjectured the form of the Hilbert series for certain subalgebras of these cohomology rings. We build on their work in two ways. First, we conjecture two natural bases for these subalgebras that would imply their conjecture using notions from the theory of k-Schur functions. Second, we formulate an analogous conjecture for Lagrangian Grassmannians.

CloseSubspace filtrations of infinite-dimensional vector spaces behave differently from their finite-dimensional counterparts in a very important way: not every infinite filtration has an adapted basis. This fact causes many interesting difficulties (in the representation theory of infinite quivers for example), but can be fixed by adding a well-ordered hypothesis which allows the use of transfinite induction. We'll use this idea to define an infinite-dimensional full flag variety, and to prove a Bruhat-like decomposition for it. In an effort to take the closure of an infinite Schubert cell, we'll use the "functor of points" approach to extend our definition of the infinite-dimensional flag variety, and discuss various properties (representability, descent, etc.) of the resulting presheaf on the category of schemes.

CloseCan you always find two elements $x$, $y$ of a partially ordered set, such that, the probability that x is ordered before y when the poset is ordered randomly, is between $1/3$ and $2/3$?

This is the celebrated $1/3 - 2/3$ Conjecture, which has been called "one of the most intriguing problems in the combinatorial theory of posets".

We will explore this conjecture for posets that arise from (skew-shaped) Young diagrams, where total orderings of these posets correspond to standard Young tableaux. We will show that that these probabilities are arbitrarily close to $1/2$, by using random walk estimates and the state-of-the-art hook-length formulas of Naruse.

This is a joint work with Igor Pak and Greta Panova. This talk is aimed at a general audience.

For a hypergraph H, define its intersection spectrum I(H) as the set of all intersection sizes |E \cap F| of distinct edges E,F in H. In their seminal paper from 1973 which introduced the local lemma, Erdos and Lovasz asked: how large must the intersection spectrum of a k-uniform 3-chromatic intersecting hypergraph be? They showed that such a hypergraph must have at least three intersection sizes, and conjectured that the size of the intersection spectrum tends to infinity with k. Despite the problem being reiterated several times over the years by Erdos and other researchers, the lower bound of three intersection sizes has remarkably withstood any improvement until now. In this talk, we discuss the proof of the Erdos-Lovasz conjecture in a strong form which shows that there are at least k^{1/2-o(1)} intersection sizes.

Joint work with M. Bucic and S. Glock.

In the necklace splitting problem, two thieves steal a necklace with k types of jewels and want to partition the necklace so that each thief gets half the jewels of each type, using the minimum number of cuts. At most k cuts are required; this result has a nice topological proof via the Borsuk–Ulam theorem, which involves representing the configuration space of possible cuts as a sphere. I will present several combinatorial results using similar techniques.

Recently, Lazarev and Lieb proved a smooth variant of the necklace splitting result. I will explain how the same technique, of representing the configuration space as a sphere and applying the Borsuk–Ulam theorem, can be used to generalize their result and improve the best-known quantitative bounds. Our approach also yields a result on motion planning algorithms; a motion planning algorithm is a continuous choice of paths for a robot to travel from any starting point to any ending point in a space.

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.

CloseAbstract on Conference Website

CloseThe notion of power domination problem in graphs is motivated by the problem of placing Phasor Measurement Units (PMU) in an electric power system. This problem is viewed as a graph theoretic problem by Haynes et al. in 2002. The power domination problem in graphs consists of finding a minimum set of vertices S that monitors the entire graph following the two "monitoring rules" - domination and propagation rules. The domination rule allows a vertex v in S to monitor itself and all its neighbours. After applying the domination rule on every vertex of S, if a monitored vertex u has all its neighbours monitored except one neighbour w, then the propagation rule permits the vertex u to moniotor w. If every vertex is monitored after the repeated application of the propagation rule, we call S a power dominating set (PDS) of G. The minimum cardinality of a PDS of G is called the power domination number of the graph. Power domination can be viewed as a variation of domination in which there is an additional propagational behaviour of monitored vertices. Later in 2012, as a generalization of domination and power domination, Chang et al. introduced the notion of k-power domination by adding the possibility of propagating up to k vertices. In this talk, we shall give a short survey on the power domination problem in graphs, including the recent works of Seema Varghese and Seethu Varghese.

CloseEn esta charla describiremos construcciones algebraicas y métodos para analizar arreglos periódicos multidimensionales que pueden ser utilizados en aplicaciones a radares y de criptografía. Las construcciones algebraicas de los arreglos permiten que se implementen fácilmente, usen poca memoria y que propiedades de los arreglos puedan ser determinadas de antemano. Utilizando la teoría de bases de Groebner, presentaremos una generalización para arreglos multidimensionales de la definición de complejidad lineal y una teoría para estudiarla.

CloseTo any poset on [n] we can associate a cone in a natural way. This is done by a correspondence between $i < j$ and the half-space $x_i \leq x_j$. To any cone (or fan of cones) we have a toric variety.

We consider translations back and forth between properties of posets and toric varieties. From this point of view we can establish Oda's strong factorization conjecture in the special case of fans arising from posets.

We will also preview in progress work joint with Josh Hallam on crepant resolutions and the Gorenstein property for toric varieties associated to posets.

We will start with an introduction to webs, standard Young tableau promotion, and the relationship between web rotation and tableau promotion. We will then discuss increasing tableaux---a K-theoretic analogue of SYT---and K-promotion. A big open question in this area deals with the order of K-promotion on increasing tableaux. We will talk about results in the 3-row case (in joint work with O. Pechenik) as well as current efforts to relate this problem to web promotion (joint with O. Pechenik, J. Striker, and J. Tymoczko).

CloseThe Necklace Splitting problem and its continuous counterpart, the Consensus-Halving problem, as well as the Discrete Ham Sandwich problem, are classical problems in combinatorics, with applications to fair division and social choice theory. A distinctive characteristic of these problems is that they always have a solution, but it was not known until recently whether such a solution can be found efficiently. We study the computational complexity of these problems and show that they are complete for the computational class PPA. A direct implication of this result is that the problems are unlikely to be solvable in polynomial time.

CloseWe study the computational complexity of problems whose inputs are obtained by applying random noise to worst-case instances. For an appropriate notion of noise we show that a number of classical **NP**-complete problems on graphs remain essentially as hard on the noisy instances as they are in the worst-case.

Focusing on the *Graph Coloring problem*, we establish the following result: Given a graph $G$, consider a random subgraph of $G$ obtained by deleting the edges of $G$ independently with probability $0.5$. We show that if the chromatic number of $G$ is large, then with high probability the chromatic number of the random subgraph remains large. That is the chromatic number of any graph is ``robust'' to random edge deletions.

Joint work with Huck Bennett and Daniel Reichman.

Finding reasonably good upper and lower bounds for the clique number of Paley graphs and generalized Paley graphs is an old and open problem in additive combinatorics. For a (generalized) Paley graph over the finite field F_q, the trivial upper bound on its clique number is \sqrt{q}. In this talk, I will discuss how to improve the trivial upper bound. I will also talk about its connection to the number of directions determined by a Cartesian product in an affine Galois plane.

CloseGiven a polytope $P$ and linear function $f$ (this pair makes a linear program). We investigate the possible monotone paths inside the oriented graph of $P$ (oriented by the objective function $f$). We consider both the shortest and the longest monotone paths possible and estimate the (monotone) diameter and the height of some famous combinatorial polyhedra (such as TSP, fractional matching polytopes, and others). As we look at the set of all monotone paths put together we see a rich topological CW-space structure which was first studied by Billera and Sturmfels in their theory of fiber polytopes and can be used to count how many monotone path are there or to generate them randomly. Our main enumerative results include bounds on the number of monotone paths, and on the flip diameter of the CW-complex of monotone paths (how far are two monotone paths from each other?). The picture is fairly complete in dimension three, but plenty of open problems remain for high dimensional polytopes. These new theorems presented in my talk com from two papers, the first joint work with Moise Blanchard (MIT) and Quentin Louveaux (U. Liege) and the second joint work with Christos Athanasiadis (U. Athens) and Zhenyang Zhang (UC Davis)

CloseGiven a polytope $P$ and linear function $f$ (this pair makes a linear program). We investigate the possible monotone paths inside the oriented graph of $P$ (oriented by the objective function $f$). We consider both the shortest and the longest monotone paths possible and estimate the (monotone) diameter and the height of some famous combinatorial polyhedra (such as TSP, fractional matching polytopes, and others). As we look at the set of all monotone paths put together we see a rich topological CW-space structure which was first studied by Billera and Sturmfels in their theory of fiber polytopes and can be used to count how many monotone path are there or to generate them randomly. Our main enumerative results include bounds on the number of monotone paths, and on the flip diameter of the CW-complex of monotone paths (how far are two monotone paths from each other?). The picture is fairly complete in dimension three, but plenty of open problems remain for high dimensional polytopes. These new theorems presented in my talk com from two papers, the first joint work with Moise Blanchard (MIT) and Quentin Louveaux (U. Liege) and the second joint work with Christos Athanasiadis (U. Athens) and Zhenyang Zhang (UC Davis)

CloseWe 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.

CloseA fruitful idea in combinatorics is to consider the totality of objects of a certain type, and encode natural operations on these objects in operations of some algebra with coefficients in a field of characteristic 0. We introduce a general class of combinatorial objects, which we call multi-complexes, which simultaneously generalizes graphs, multigraphs, hypergraphs and simplicial and delta complexes. We introduce a natural algebra of multi-complexes which is defined as the algebra which has a formal basis C of all isomorphism types of multi-complexes, and multiplication is to take the disjoint union. This is a Hopf algebra with an operation encoding the dissasembly information for such objects, and extends and generalizes the Hopf algebra of graphs. Such Hopf algebras are connected, graded commutative and cocommutative, and by general results of Cartier-Kostant-Milnor-Moore, are just a polynomial algebra. However, it comes with additional structure which encodes combinatorial information, and the main goal is to describe its structure in a way relating to combinatorics. Such structures have been of high interest in literature, both intrinsically and due to applications to combinatorial problems.

We give a solution to the problem in this generality and find an explicit basis B of the space of primitives, and which is of combinatorial relevance: it is such that each multi-complex is a polynomial with non-negative integer coefficients of the elements of B, and each element of B is a polynomial with integer coefficients in C. The coefficients appearing in all these polynomials are, up to signs, numbers counting multiplicities of sub-multi-complexes in a multi-complex. Using this, we also solve the antipode formula problem, and find the cancellation and grouping free formula for the antipode. Such formulas are usually very difficult to obtain, and constitute a main question for such algebras.

The main method is to use certain Mobius type formulas for posets of sub-objects of multi-complexes. As examples, we will explicitly illustrate how our results specialize to the formulas for graphs and simplicial complexes, or how they specialize to results in all of the above mentioned particular cases. Time permitting, I will show relations to applications of these results to the graph reconstruction conjectures, and rederiving some results in the literature on these questions.

Joint work with Joonkyung Lee (University College, London).

One of the key concepts in the theory of quasirandomness is the *Gowers octahedral norms*, introduced by Gowers for his proof of hypergraph regularity lemma. The simplest example is the $C_4$-norm, written as

$$

\|f\|_{C_4} := \left(\int f(x_1,y_1)\,\overline{f(x_1,y_2)}\,\overline{f(x_2,y_1)}\,f(x_2,y_2)\,

dx_1 dy_1 dx_2 dy_2 \right)^{1/4}.

$$

This is in fact a graph-theoretic interpretation of *Gowers uniformity norms* in additive combinatorics, a crucial tool in Gowers' proof of celebrated Szemerédi's theorem. In the context of additive combinatorics, complex-valued functions are naturally considered because of the connections to the Fourier transform.

However, generalizations of the $C_4$-norm have been mostly studied in a real-valued setting. Namely, Lovész asked to characterize *real-norming* graphs $H$, such that

$$

\|f\|_H := \left\vert\int \prod_{uv \in E(H)} f(x_u,y_v) d\mu^{{\rm v}(H)} \right\vert^{1/{\rm e}(H)}

$$

defines a norm on the vector space of bounded measurable functions $f:[0,1]^2\rightarrow \mathbb{R}$. A real-norming graph is necessarily bipartite.

To define a norming property for complex-valued functions, one should pair a graph with its $2$-edge-coloring $\alpha : \: E(H) \to \{0,1\}$ to assign conjugates, as was done above. Let $\mathcal{F}_{\mathbb{C}}$ be the class of all bounded measurable functions $f:\: [0,1]^2 \to \mathbb{C}$. For $f\in\mathcal{F}_{\mathbb{C}}$, define

$$

t_{H,\alpha}(f) : = \:

\int \prod_{e=uv \in E(H)}

f(x_u,y_v)^{\alpha(e)} \:

\overline{f(x_u,y_v)}^{1-\alpha(e)} \; d\mu^{{\rm v}(H)} .

$$

We say that the pair $(H,\alpha)$ is *norming* if $|t_{H,\alpha}(f)|^{1/{\rm e}(H)}$ is a norm on $\mathcal{F}_{\mathbb{C}}$. A graph $H$ is called *complex-norming* if there exists a $2$-edge-coloring $\alpha$ of $H$ that makes $(H,\alpha)$ norming.

We prove that if $H$ is real-norming then it is also complex-norming, and the corresponding coloring $\alpha$ is unique up to isomorphism. Our proof is surprisingly indirect: we do not construct any 2-edge-coloring~$\alpha$ but prove its existence and uniqueness.

As a consequence, we are able to show that hypercubes are not norming, which resolves the last outstanding problem posed in Hatami's pioneering work on graph norms.

Plane perfect matchings of 2n points in convex position are known to be in bijection with triangulations of convex polygons of size n + 2; they are both counted by the Catalan numbers. We explain how to give a direct bijection and how it can be extended to a bijection between monochromatic matchings on k colours and tilings by (k+2)-gons. Edge flips are a classic operation to perform local changes in both sets. We use the above bijection to determine the two types of edge flips are related. We use this to give an algebraic interpretation of the flip graph of triangulations in terms of elements of the corresponding Temperley-Lieb algebra. This is joint work with O. Aichholzer, L. Donner (Andritsch), B. Vogtenhuber.

CloseMost invariants in knot theory are very hard to compute in practice, yet only few computational hardness proofs are known. In this talk, we survey the computational complexity of many problems coming from knot theory, emphasizing the numerous open problems, and we present a proof of NP-hardness for the crossing number of a link.

Joint work with Marcus Schaefer and Eric Sedgwick.

Shellability is an important notion that lead to such mathematical discoveries as the Dehn-Sommerville relations, the Upper Bound Theorem, and characterization of topology of the Bruhat order. Roughly speaking, a simplicial complex is shellable if it can be build inductively while controlling its topological properties. In this talk we show that starting from dimension two, deciding shellability is NP-complete.

Joint work with Xavier Goaoc, Pavel Paták, Martin Tancer, and Uli Wagner.

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

CloseClassical Goncarov polynomials arose in numerical analysis as a basis for the solutions of the Goncarov interpolation problem. These polynomials provide a natural algebraic tool in the enumerative theory of parking functions. Parking functions are combinatorial objects which were introduced in 1966 by Konheim and Weiss. They have been well-studied in the literature due to their numerous connections and have several generalizations and extensions. In this talk, we present a complete combinatorial interpretation for any sequence of generalized Goncarov polynomials. Indeed, we show that they can be realized as weight enumerators in the lattice of partitions. This is joint work with Catherine Yan.

CloseIn 2010, motivated by representation theory, Stapledon described a generalization of Ehrhart theory with group actions. In 2018, Ardila, Schindler, and I made progress towards answering one of Stapledon’s open problems that asked to determine the equivariant Ehrhart theory of the permutahedron. We proved some general results about the fixed polytopes of the permutahedron, which are the polytopes that are fixed by acting on the permutahedron by a permutation. In particular, we computed their dimension, showed that they are combinatorially equivalent to permutahedra, provided hyperplane and vertex descriptions, and proved that they are zonotopes. Lastly, we obtained a formula for the volume of these fixed polytopes, which is a generalization of Richard Stanley’s result of the volume for the standard permutahedron. Building off of the work of the aforementioned, Ardila, Supina, and I determine the equivariant Ehrhart theory of the permutahedron, thereby resolving the open problem. This project presents formulas for the Ehrhart quasipolynomials and Ehrhart Series of the fixed polytopes of the permutahedron, along with other results regarding interpretations of the equivariant analogue of the Ehrhart series. This is joint work with Federico Ardila (San Francisco State University, Anna Schindler (North Seattle College) and Mariel Supina (UC Berkeley).

Close