Eigenvalues of subcubic graphs
Abstract: This talk concerns spectral properties of subcubic graphs and presents results from two recent papers, one joint with Hricha Acharya and Benjamin Jeter, and the other with Shenwei Huang. Both works address problems in spectral graph theory through a common approach: constructing linear-algebraic bridges that translate eigenvalue constraints into structural graph-theoretic conditions.
In the first part of the talk, we study the median eigenvalues of connected subcubic graphs. We resolve questions raised by Fowler and Pisanski and by Mohar by showing that, with the sole exception of the Heawood graph, the median eigenvalues of any connected subcubic graph lie in the open interval (−1,1).
In the second part, we turn to the classification of connected subcubic graphs with no eigenvalues in (−1,1), completing an investigation initiated by Guo and Royle. We determine all such graphs, showing that only two infinite families and finitely many sporadic examples occur.
We conclude the talk by discussing se…
Event Type: Seminar. Research Area: Discrete Math and Combinatorics. Location: MSC E406. Speaker Name: Zilin Jiang. Speaker Institution: Arizona State University.
Thursday, February 26, 2026, 4:00 PM – 5:00 PM.
Existence of Nonuniform Cocycles
Abstract: Peter Walters asked in 1986 whether any uniquely ergodic homeomorphism with a non-atomic invariant probability measure admits a non-uniform GL(2,R) cocycle. We discuss the history and context of this question and then present joint work with Artur Avila that gives an affirmative answer to it.
Event Type: Colloquium. Research Area: Analysis and Differential Geometry. Location: MSC W303. Speaker Name: David Damanik. Speaker Institution: Rice University.
Friday, February 27, 2026, 11:00 AM – 12:00 PM.
Classifying Possible Density Degree Sets for Hyperelliptic Curves
Abstract: Let C be a smooth, projective, geometrically integral hyperelliptic curve of genus g → 2 over a number field k. To study the distribution of degree d points on C, we introduce the notion of P1- and AV-parameterized points, which arise from natural geometric constructions. These provide a framework for classifying density degree sets, an important invariant of a curve that records the degrees d for which the set of degree d points on C is Zariski dense. Zariski density has two geometric sources: If C is a degree d cover of P1 or an elliptic curve E of positive rank, then pulling back rational points on P1 or E give an infinite family of degree d points on C. Building on this perspective, we give a classification of the possible density degree sets of hyperelliptic curves.
Event Type: Dissertation. Research Area: Mathematics. Speaker Name: Jasmine Camero. Speaker Institution: Emory University. Speaker Website: https://scholarblogs.emory.edu/math/files/2025/12/Camero-Dissertation-Announcement.pdf.
Thursday, March 5, 2026, 4:00 PM – 5:00 PM.
White Hall 103.
For more info visit scholarblogs.emory.edu.