KEIVAN HASSANI MONFARED
University of Calgary

I am a postdoctoral fellow in the mathematics and statistics department at University of Calgary, working under supervision of Peter Lancaster and Alex Brudnyi. I received my PhD (2014) and MSc (2011) from University of Wyoming under supervision of Bryan Shader, and BSc (2009) from Amirkabir University of Technology (Tehran Polytechnic).

My CV: PDF
Publications Summary: PDF

Research Interests (more)

• Linear Algebra and Matrix Analysis
• Combinatorics and Graph Theory
• Dynamical Systems and Control Theory

Recent and Under Review Publications (more)

• A Structured Inverse Spectrum Problem For Infinite Graphs
• Keivan Hassani Monfared and Ehssan Khanmohammadi: PDF
• It is shown that for a given infinite graph $$G$$ on countably many vertices, and a bounded, countably infinite set of real numbers $$\Lambda$$ there is a symmetric matrix whose graph is $$G$$ and its spectrum is the closure of $$\Lambda$$.
• Existence of a Not Necessarily Symmetric Matrix with Given Distinct Eigenvalues and Graph
• Keivan Hassani Monfared, Linear Algebra and its Applications: PDF
• For given distinct numbers $$\lambda_1 \pm \mu_1 \rm{i}, \lambda_2 \pm \mu_2 \rm{i}, \ldots, \lambda_k \pm \mu_k \rm{i} \in \mathbb{C} \setminus \mathbb{R}$$ and $$\gamma_1, \gamma_2, \ldots, \gamma_l \in \mathbb{R}$$, and a given graph $$G$$ with a matching of size at least $$k$$, we will show that there is a real matrix whose eigenvalues are the given numbers and its graph is $$G$$. In particular, this implies that any real matrix with distinct eigenvalues is similar to a real, irreducible, tridiagonal matrix.
• The nowhere-zero eigenbasis problem for a graph
• Keivan Hassani Monfared and Bryan L. Shader, Linear Algebra and its Applications: PDF.
• Using previous results and methods, it is shown that for any connected graph $$G$$ on $$n$$ vertices and a set of $$n$$ distinct real numbers $$\Lambda$$, there is an $$n\times n$$ real symmetric matrix $$A$$ whose graph is $$G$$, its spectrum is $$\Lambda$$, and none of the eigenvectors of $$A$$ have a zero entry.
• On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs
• Keivan Hassani Monfared, Paul Horn, Franklin Kenter, Kathleen Nowak, John Sinkovic and Josh Tobin, Electronic Journal of Linear Algebra: PDF.
• Given an $$n\times n$$ real matrix $$A$$, the principal characteristic perrank sequence of $$A$$ is defined as $$r_0, r_1, r_2, \ldots, r_n$$, where for $$k \geq 1$$, $$r_k=1$$ iff $$A$$ has a principal submatrix of size $$k$$ with nonzero permanent, and $$r_0 = 1$$ iff $$A$$ has a zero on its main diagonal. We study the following inverse problem: given a sequence $$r_0 r_1 \cdots r_n$$ of zeros and ones, does there exist an $$n \times n$$ real matrix which achieves this sequence? As a result, we characterize all the sequences corresponding to (symmetric) entry-wise nonnegative matrices, and provide some results for the skew-symmetric case.

News

We are organizing a special session on Graphs and matrices at the Joint Mathematics Meeting 2017, in Atlanta. Check out the schedule and plan to attend some of the great talks. It is going to be a great session.

Contact Info

Department of Mathematics and Statistics, MS 472
University of Calgary
2500 University Dr. NW
T2N 1N4

Office: Math Sciences (MS) 584

email: keivan.hassanimonfar [at] ucalgary.ca

Find me on

Research Gate: Keivan Hassani Monfared