Research
Graphs and Combinatorics
Graphs and Combinatorics
"The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. He to whom the emotion is a stranger, who can no longer pause to wonder and stand wrapped in awe, is as good as dead — his eyes are closed. To know what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty, which our dull faculties can comprehend only in their most primitive forms — this knowledge, this feeling is at the center of true religiousness."
Albert Einstein
I am primarily driven by the notion of translation. Our ability to translate data/information into mathematically/computationally amenable representations will enable us to acquire knowledge impervious to the mind.
The definition of data is broad: for example, consider lyrical fragments of thoughts as inputs to the conscious human system.
Current Projects:
Complexity of list coloring via maximum degree constraints in Hilbert Nullstellensatz certificates.
with Amitabh Basu
Self-chromatic number of graphs
with Calum Buchanan and Colby Muir
Remoteness of graphs with prescribed connectivity and degree constraints
with Sufiyan Mallu and Masahiro Uchida
Preprints and Papers
Enumerating Graphic List Colorings
Manuscript in preparation.
Sufficiency of Hall's Condition in Graphic List Coloring
Manuscript in preparation.
Extremal Problems on Graph-Referential Colorings of Graphs
Manuscript in preparation.
with Ariel Cook, Peter Johnson, ...
with Arman Eisenkolb-Vaithyanathan and Richard M. Low
AI-assisted
Notes
Slides
“For the absurd man, it is not a matter of explaining and solving, but of experiencing and describing. Everything begins with lucid indifference.
Describing—that is the last ambition of an absurd thought. Science likewise, having reached the end of its paradoxes, ceases to propound and stops to contemplate and sketch the ever-virgin landscape of phenomena. The heart learns thus that the emotion delighting us when we see the world’s aspects comes to us not from its depth but from their diversity. Explanation is useless, but the sensation remains and, with it, the constant attractions of a universe inexhaustible in quantity. The place of the work of art can be understood at this point.”
Albert Camus
My undergraduate major was Humanities. Reading philosophy prompted me to learn the language of mathematics.
Header image: Where Do We Come From? What Are We? Where Are We Going?, Paul Gauguin