CMSA Day (Workshop and AGM)

The Council of the Combinatorial Mathematics Society of Australasia (CMSA) will hold a one-day workshop on Tuesday 15 December 2020, as a partial replacement for the postponed conference 43ACC. The CMSA Day schedule follows (times AEDT), whereas talk abstracts can be found below.

10:30-11:30 AEDT Noga Alon,
Princeton University and Tel Aviv University
Equipartitions
11:30-12:30 Lisa Sauermann,
Institute for Advanced Study
On polynomials that vanish to high order on most of the hypercube
13:00-13:45 CMSA Annual General Meeting
14:00-15:00 Nick Cavenagh,
University of Waikato
tbc
15:00-16:00 Alice Devillers,
University of Western Australia
Some recent results on flag-transitive and block-transitive 2-designs

Registration is now open.

CMSA Day is a free event but provides a great opportunity to renew your CMSA membership or become a new member of the CMSA! When registering, you will have the option of a free ticket (without CMSA membership) or a paid ticket of approximately $26 AUD which comes with CMSA membership for 2021. If you are already a CMSA life member then you should select the free ticket option. If you have access to research funding then we encourage you to purchase a paid ticket.

The talk abstracts follow.
Noga Alon (Princeton University and Tel Aviv University)
Equipartitions
Abstract: A substantial number of problems deal with the existence of a set of prescribed type containing a fair share of an object according to several different measures, or the existence of a partition of the object in which this is the case for every part. Examples include the Ham-Sandwich Theorem in Measure Theory, the Hobby-Rice Theorem in Approximation Theory, the Necklace Theorem and the Ryser Conjecture in Discrete Mathematics, and more. The techniques in the study of the subject combine combinatorial, topological, geometric probabilistic and algebraic tools.
I will describe the topic, focusing on several recent existence results and their algorithmic aspects.

Lisa Sauermann (Institute for Advanced Study)
On polynomials that vanish to high order on most of the hypercube
Abstract: Motivated by higher vanishing multiplicity generalizations of Alon's Combinatorial Nullstellensatz and its applications, we study the following problem: for fixed k and n large with respect to k, what is the minimum possible degree of a polynomial P in R[x1,...,xn] such that P(0,…,0) is non-zero and such that P has zeroes of multiplicity at least k at all points in {0,1}n except the origin? For k=1, a classical theorem of Alon and Füredi states that the minimum possible degree of such a polynomial equals n. We solve the problem for all k>1, proving that the answer is n+2k-3. Joint work with Yuval Wigderson.