Seminars and Colloquia by Series

The Convexity Conjecture, the Kahn-Kalai Conjecture, and introduction to k-thresholds

Series
Atlanta Combinatorics Colloquium
Time
Thursday, October 30, 2025 - 04:44 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jinyoung Park – Courant Institute of Mathematical Sciences NYU –

Please Note: Light refreshments will be offered before the talk at 4pm in the atrium.

The "Convexity Conjecture" by Talagrand asks (very roughly) whether one can "create convexity" in constant steps regardless of the dimension of the ambient space. Talagrand also suggested a discrete version of the Convexity Conjecture and called it "my lifetime favorite problem," offering $1,000 prize for its solution. We introduce a reformulation of the discrete Convexity Conjecture using the new notion of "k-thresholds," which is an extension of the traditional notion of thresholds, introduced by Talagrand. Some ongoing work on understanding k-thresholds, along with a (vague) connection between the Kahn-Kalai Conjecture and the discrete Convexity Conjecture, will also be discussed. Joint work with Michel Talagrand.

Nodal Statistics for Graphs and Matrices

Series
Atlanta Combinatorics Colloquium
Time
Thursday, April 3, 2025 - 17:00 for 1 hour (actually 50 minutes)
Location
Bill Moore SSC Press Room A
Speaker
John Urschel – Massachusetts Institute of Technology –

The study of nodal statistics provides insight into the spectral properties of graphs and matrices, drawing strong parallels with classical results in analysis. In this talk, we will give an overview of the field, covering key results on nodal domains and nodal counts for graphs and their connection to known results in the continuous setting. In addition, we will discuss some recent progress towards a complete understanding of the extremal properties of the nodal statistics of a matrix.

What is a combinatorial interpretation?

Series
Atlanta Combinatorics Colloquium
Time
Tuesday, September 10, 2024 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Igor Pak – UCLA and IAS –

Please Note: There will be refreshments beforehand beginning at 3pm.

In enumerative combinatorics, one is often asked to count the number of combinatorial objects.  But the inverse problem is even more interesting: given some numbers, do they have a combinatorial interpretation?  In the main part of the talk I will give a broad survey of this problem, formalize the question in the language of computational complexity, and describe some connections to deep results and open problems in algebraic and probabilistic combinatorics.  In the last part of the talk, I will discuss our recent results on the defect and equality cases of Stanley inequalities for the numbers of bases of matroids and for the numbers of linear extensions of posets (joint work with Swee Hong Chan).  The talk is aimed at the general audience.