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Graduate Seminar - 3/07, 12:00PM Duncan Hall 1064

Randy Davila

"Conjecturing with TxGraffiti"

The concept of computer assisted automated conjecturing can be traced back to the 1950's, and yet, it wasn't until the mid 1980's that the first "successful" such program appeared. This program, written by Siemion Fajtlowicz, and called Graffiti, successfully produced a myriad of research worthy conjectures in graph theory, number theory, and theoretical chemistry. Indeed, well known mathematicians such as Paul Erdos, Bella Bollobas, Fan Chung, Paul Seymour, and Noga Alon, all have written papers on the conjectures of Graffiti. Following the work of Fajtlowicz, Ermelinda DeLeVina, a former PhD student of Fajtlowicz and collaborator in the programming of Graffiti, produced a variation of Graffiti called Graffiti.pc. Originally programmed for educational purposes, Graffiti.pc was exceptionally useful in the inspiration of student research projects at the University of Houston{Downtown. However, it is also the case that Graffiti.pc led to many research publications and attracted the attention of well known mathematicians such as Michael Henning, Anders Yeo, and Doug West. Inspired by Graffiti and Graffiti.pc, the speaker designed a new conjecturing program called TxGraffiti during the summer of 2016. The original design of TxGraffiti has changed much since the first conjectures were produced, and in this talk we speak of the latest version, which includes an additional program called TxGraffiti-Light, a portable conjecturing program that will be soon be available as a phone app. We conclude this talk with a description of several open conjectures produced by these programs.

Bio: Randy Davila graduated with a bachelors of science in applied mathematics from the University of Houston-Downtown in 2012, a masters of arts in computational and applied mathematics from Rice University in 2015, and is currently in his final year of doctoral studies under the supervision of professor Michael Henning at the University of Johannesburg in South Africa, as well as a full time lecturer in the Department of Mathematics and Statistics at the University of Houston-Downtown. Mr. Davila has expertise in combinatorics, graph theory, and discrete optimization, as well as computer assisted automated conjecturing.

Department of Computational and Applied Mathematics
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