Algebra and Combinatorics Seminar
The current seminar's organizers are
ChunHung Liu and
Catherine Yan.

Date Time 
Location  Speaker 
Title – click for abstract 

02/02 3:00pm 
BLOC 302 
Youngho Yoo TAMU 
Minimum degree conditions for apexouterplanar minors
Motivated by Hadwiger's conjecture, we study graphs H for which every graph with minimum degree at least V(H)1 contains H as a minor. We prove that a large class of apexouterplanar graphs satisfies this property. Our result gives the first examples of such graphs whose vertex cover numbers are significantly larger than a half of its vertices, and recovers all known such graphs that have arbitrarily large maximum degree. Our proof can be adapted to directed graphs to show that every directed graph with minimum outdegree at least t contains a certain orientation of the wheel and of every apextree on t+1 vertices as a subdivision and a butterfly minor respectively. Joint work with ChunHung Liu.


02/09 4:00pm 
BLOC 302 
Tushar Pandey TAMU 
Invariants for surface diffeomorphisms and the volume conjecture
In this talk, we will discuss an invariant for the diffeomorphisms of a surface using the ChekhovFock algebra for surfaces. This invariant is a trace of an intertwiner coming from some representation theory of this algebra. We will then mention a conjecture that relates the exponential growth of the trace to the volume of the mapping torus of a surface. And at the end, we will see some recent results in this area. 

03/01 2:00pm 
BLOC 302 
Alex Lubotzky Weizmann Institute of Science 
Uniform stability of highrank Arithmetic groups
(Joint with the workshop "Groups and dynamics".)
Lattices in highrank semisimple groups enjoy several special properties like superrigidity, quasiisometric rigidity, firstorder rigidity, and more. In this talk, we will add another one: uniform ( a.k.a. Ulam) stability. Namely, it will be shown that (most) such lattices D satisfy: every finitedimensional unitary "almostrepresentation" of D ( almost w.r.t. to a submultiplicative norm on the complex matrices) is a small deformation of a true unitary representation. This extends a result of Kazhdan (1982) for amenable groups and BurgerOzawaThom (2013) for SL(n,Z), n>2.
The main technical tool is a new cohomology theory ("asymptotic cohomology") that is related to bounded cohomology in a similar way to the connection of the last one with ordinary cohomology. The vanishing of H^2 w.r.t. to a suitable module implies the above stability.
The talk is based on a joint work with L. Glebsky, N. Monod, and B. Rangarajan. 

03/22 3:00pm 
BLOC 302 
Yifan Zhang UT Austin 
Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applications
In this talk, I will prove a new upper bound on the covering number of real algebraic varieties, images of polynomial maps and semialgebraic sets. The bound remarkably improves the best known general bound by Yomdin and Comte (2004), and its proof is much more straightforward. As a consequence, our result gives new bounds on the volume of the tubular neighborhood of the image of a polynomial map and a semialgebraic set, where results for varieties by Lotz (2015) and Basu, Lerario (2022) are not directly applicable. I will first use this result to derive a nearoptimal bound on the covering number of low rank CP tensors. Then I will discuss applications on sketching (general) polynomial optimization problems as well as controlling the generalization error for deep neural networks with rational or ReLU activations. 

03/23 00:00am 
Blocker 

CombinaTexas 2024 

03/24 00:00am 
Blocker 

CombinaTexas 2024 

04/05 3:00pm 
BLOC 302 
ChunHung Liu TAMU 
Asymptotically optimal proper conflictfree coloring of bounded maximum degree graphs
Every graph of maximum degree d has a coloring with d+1 colors such that no two adjacent vertices receive the same color. Caro, Petrusevski, Skrekovski conjectured that if d >2, then one can always choose such a proper (d+1)coloring such that for every nonisolated vertex, some color appears on its neighborhood exactly once. We prove that this conjecture holds asymptotically: every graph of maximum degree d has a proper coloring with (1+o(1))d colors such that for every nonisolated vertex, some color appears on its neighborhood exactly once. Joint work with Bruce Reed. 

04/19 3:00pm 
BLOC 302 
Matthew Faust TAMU 
Irreducibility of the Bloch Variety
Given a ZZ^dperiodic graph G, a discrete periodic operator, a periodic potential together with a weighted graph laplacian, acts on functions on the vertices of G. Floquet theory allows us to study the spectrum through a finite matrix with Laurent polynomials entries. The zero set of the corresponding characteristic polynomial is called the Bloch variety. We will focus our attention on the irreducibility of this variety, which provides insight into quantum ergodicity. In particular we study how irreducibility of the Bloch variety is affected as one varies the period of the potential. 

04/26 3:00pm 
BLOC 302 
Hannah Solomon TAMU 
