Combinatorics and Geometry Learning Seminar

We started a new learning seminar for anyone interested in doing a deep dive into combinatorics and geometry.  It will be in-person with a zoom option.

SPRING 2026 TALKS

Day and Time: Wednesdays at 4:15 pm  (in person)

Room: Graduate Center Room 4214.03 

https://us06web.zoom.us/j/86992051923?pwd=a3nVPVZSewvLQmwJmddFZRxNszIu2J.1

Meeting ID: 869 9205 1923
Passcode: 231443

Speaker: Mutasim Mim (Graduate Center)

Title: Introduction to Algebraic and Spectral Graph Theory

Dates:  Feb 11, Feb 18, and Feb 25, 2026

Feb 11, 2026: Introduction to Spectral Graph Theory

Abstract: In the first talk, we introduce graphs and several notions of their spectra; and work out the computation of spectra of several families. We discuss relations between the graph spectra and combinatorial properties of graphs, such regularity, connectivity, along with graph complements and diameter. We finish by discussing the Graham and Pollak theorem and how graph spectra can be used in proving (in)decomposability of complete graphs.

Feb 18, 2026: Strongly Regular Graphs

Abstract: We introduce strongly regular graphs (SRFs) and look at various families of SRGs along with their SRG parameters. We derive the computation of the spectra of an SRG from its SRG parameters and discuss the relation between integral spectra and conference graphs. We briefly discuss the problem of existence of SRGs with a given set of parameters and some techniques of proving nonexistence. We finish by discussing the spectral distinguishing problem of SRGs.

Feb 25, 2026: Further Topics in Spectral Graph Theory

Abstract: We discuss several advanced topics relating graph spectra with graph structure.

Mar 4: No talk

Speaker: Sandra Kingan (Brooklyn College and the Graduate Center, CUNY)

Title: Introduction to Higher Connectivity and Excluded Minor Results

Dates:  Mar 11, Mar 18, and Mar 25

Mar 11, 2026: Higher Connectivity in Graphs 

Abstract: We will begin with the basic definitions of vertex and edge connectivity followed by the Ear Decomposition Theorem, Mengers Theorem, Whitney's Theorem on k-connected graphs, and an excluded minor characterization of series-parallel networks. 

Mar 18, 2026: Structure of 3-Connected Graphs

Abstract: We will introduce clique sums and 2-sums and prove a structural result for 2-sums. Then we will look at edge-deletions and additions and edge-contractions and vertex splits, followed by the Wheels Theorem and the Splitter Theorem. 

Mar 25, 2026: Higher Connectivity and Excluded minors 

Abstract: We will review the previous two talks and focus on excluded minors. 

Speaker: Anna Pun (Baruch College and the Graduate Center, CUNY)

Title: Introduction to Higher Connectivity and Excluded Minor Results

Dates:  Mar 11, Mar 18, and Mar 25, 2026

Apr 22, 2026: Basic Definitions and Examples of Posets and Lattices

Abstract: In this talk I will introduce partially ordered sets and some basic terminology, including chains, antichains, ranked posets, and Hasse diagrams. I will also discuss. lattices and illustrate these ideas through examples such as the Boolean lattice and lattices of order ideals. We will briefly compare distributive and non-distributive lattices and look at examples of posets that are not lattices.

Apr 29, 2026: Möbius Functions and Other Invariants of Posets

Abstract: Many posets carry natural numerical invariants that capture aspects of their structure. In this talk I will introduce the Möbius function of a poset and explain how it appears in inclusion–exclusion formulas. I will compute the Möbius function in several examples and briefly discuss related invariants such as characteristic polynomials.

May 6, 2026: Some Structured Families of Posets

Abstract: In the final talk I will discuss several examples of posets that arise in algebraic combinatorics, including differential posets and other combinatorial lattices. I will also briefly introduce tools used to study posets, such as edge labelings, shellability, and order complexes, and illustrate these ideas through examples.