Future students

Title: On edge-transitive distance-regular antipodal covers of complete graphs

Title: Nash-Williams Orientation Conjecture for Infinite Graphs       

Abstract: In 1960 Nash-Williams proved that every 2k-edge-connected finite graph admits a k-arc-connected orientation. He conjectured that this is  also true for infinite graphs. We try to prove the conjecture. Joint work with Bruce Richter.

Title: New Eigenvalue Bound for the Fractional Chromatic Number

Title: From the nabla operator to the super nabla operator

Title: Coinvariants and superspace

Title: Some results on spectral Turán's type problem

Title: When all holes have the same length

Abstract: A hole is an induced cycle of length at least 4. For an integer k ≥ 4, we denote by Ck, the class of graphs where every hole has length k. We have defined a new class of graphs named blowup of ℓ-templates whose all holes have length 2ℓ + 1. Using earlier results on other related classes of graphs, we did obtain the following structural theorem :

Title: Generating k EPR-pairs from an n-party resource state

Abstract: Motivated by quantum network applications over classical channels, we initiate the study of n-party resource states from which LOCC protocols can create EPR-pairs between any k disjoint pairs of parties.

Title: Cameron-Liebler Sets in Permutation Groups

Abstract: Let $G \leq S_{n}$ be a transitive permutation group. Given $i,j \in [n]$, by $x_{i\to j}$, denote the characteristic function of the set $\{g \in G\ :\ g(i)=j\}$. A Cameron-Liebler set (CL set) in $G$ is a set which is represented by a Boolean function in the linear span of $\{x_{i\to j} \ :\ (i,j)\in [n]^2\}$. These are analogous to Boolean degree 1 functions on the hypercube and to Cameron-Liebler line classes in $PG(3,q)$. Sets of the form $\{g\ : g(i)\in X\}$ and $\{g\ : \ i \in g(X)\}$ (for $i \in [n]$ and $X \subset [n]$) are canonically occurring examples of CL sets. A result of Ellis et.al, shows that all CL sets in the $S_{n}$ are canonnical. In this talk, we will demonstrate many examples with ``exotic'' CL sets. Of special interest is an exotic CL set in $PSL(2,q)$ (with $q \equiv 3 \pmod{4}$), a 2-transitive group, just like $S_{n}$. The talk is based on ongoing joint work with Jozefien D'haeseleer and Karen Meagher.

Title: Approximation algorithm for stochastic k-TSP

Abstract: The input of the deterministic k-TSP problem consists of a metric complete graph with root p in which the nodes are assigned a fixed non-negative reward. The objective is to construct a p-rooted path of minimum length that collects total reward at least k. In this talk we will explore a stochastic variant of this problem in which the rewards assigned to the nodes are independent random variables, and the objective is to derive a policy that minimizes the expected length of a p-rooted path that collects total reward at least k. We will discuss approximation algorithms for this problem proposed in a paper by Ene, Nagarajan and Saket, and a paper by Jiang, Li, Liu and Singla.