My work is in the areas of graph theory, primarily spectral graph theory, and high performance computing, targetting the Intel Xeon Phi microarchitecture.

My main area of research is spectral graph theory, which is concerned with studying graphs through the lens of matrices associated to the graph. This approach has been extremely successful from a computational point of view: matrix statistics such as spectral radius and spectral gap capture properties of a graph that can otherwise be very expensive to quantify. I enjoy developing and using computational tools in my work, and have developed a set of tools for automating the search for graph counterexamples. If you are interested in learning more, or have a conjecture that you are interested in finding counterexamples to, drop me an email at rjtobin AT (this domain name). For specifics on my current research interests, see my most recent papers below.

I have an appointment at the San Diego Supercomputer Center, in the High Performance Geocomputing group. I develop and maintain the Intel Xeon Phi version of the AWP-ODC-OS code, used to simulate the propagation of seismic waves through three-dimensional heterogeneous media.

In the past I have worked in areas that apply mathematical techniques to problems in other disciplines. I completed my Masters degree in the Mathematical Neuroscience Lab in Trinity College Dublin, where we devised a new algorithm for computing mutual information of random variables taking values in an arbitrary vector space, with comparatively little available data. As an undergraduate I was an intern at the Hamilton Institute several times, studying algorithmic complexity attacks, in their Communication Networks group.

**Publications:**

- Accelerating Seismic Simulations using the Intel Xeon Phi Knights Landing Processor, Josh Tobin, Alexander Breuer, Alexander Heinecke, Chuck Yount, Yifeng Cui, International Supercomputing Conference 2017.
- The Spectral Graphs Arising from Substring Reversals, Fan Chung, Josh Tobin, preprint (2017).
- YASK--Yet Another Stencil Kernel: a framework for HPC stencil code-generation and tuning, Charles Yount, Josh Tobin, Alexander Breuer and Alejandro Duran, WOLFHPC 2016
- Three conjectures in extremal spectral graph theory, Michael Tait, Josh Tobin, accepted to Journal of Combinatorial Theory Series B (2017)
- Characterizing graphs of maximal principal ratio, Michael Tait, Josh Tobin, submitted (2015)
- On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs, Monfared, Horn, Kenter, Nowak, Sinkovic, Tobin, Electronic Journal of Linear Algebra (2016)
- How to Make the Perfect Fireworks Display: Two Strategies for Hanabi, Cox, De Silva, DeOrsey, Kenter, Retter, Tobin, Mathematics Magazine (2015).
- A Kernel-Based Calculation of Information on a Metric Space, R.J. Tobin and Conor J. Houghton, Entropy (2013).
- Hash Pile Ups: Using Collisions to Identify Unknown Hash Functions, R.J. Tobin and David Malone, International Conference on Risks and Security of Internet and Systems (CRiSIS 2012) (2012).
- Complexity Attack Resistant Flow Lookup Schemes for IPv6: A Measurement Based Comparison, David Malone and R.J. Tobin, European Conference on Computer Network Defence (2008).

**Posters and talks:**

*Four Conjectures in Spectral Graph Theory*, Tardes de Algebra, Combinatoria y Optimizacion seminar, CINVESTAV, Mexico City, March 2017*Porting AWP-ODC-OS to the Intel Xeon Phi*, Seismology workshop, National Supercomputing Center, Wuxi, China, January 2017*Accurate and Efficient Earthquake Simulations on Intel Xeon Phi*, IXPUG Annual Meeting, Argonne National Lab, September 2016*Accelerating AWP-ODC-OS using Intel Xeon Phi*, poster, Southern California Earthquake Center annual meeting, September 2016*A Conjecture of Erdos and Simonovits on Walks on Graphs*, PhD candidacy talk, UCSD, December 2014*Grobner Bases and Anick's Resolution, a Case Study*, bachelor's thesis talk, Trinity College Dublin, April 2011