I am a “mathemusician” holding an MPhil in mathematics from The CUNY Graduate Center (PhD en route), BA/MA in mathematics with a specialization in algebraic geometry from SUNY Potsdam, and a BA in Music Business with a concentration in double bass from The Crane School of Music Business and Entrepreneurship

My thesis regards progress toward the problem of resolution of singularities.

One perspective is that of a frog (in the words of Freeman Dyson ~ this is not meant with any offense: I happen to adore frogs): given a hyperelliptic curve over a (insert pleasant adjectives here) field whose ring of integers is of mixed characteristic (0, 2), explicitly produce a regular model. This project is advised by Andrew Obus.

Another, more akin to a bird: establish topological obstructions to the existence of a resolution of the singularities of a variety (over a field of any characteristic, e.g. positive characteristic). In fact, the existence of alterations suggests there are no “étale obstructions“. This project is advised by Dennis Sullivan.

I aim to graduate from the Graduate Center (GC) at the City University of New York (CUNY) before 2024’s end.

Two other projects are also currently on my mind (and in progress):

An effort (joint with Raymond van Bommel & Michael Montoro) to establish a new algorithm (expected to be faster than existent algorithms, e.g. normalization and iterative blowups) to resolve the singularities of a curve defined over a field of positive characteristic via adaptation of a recent algorithm of Dan Abramovich, Michael Temkin, and Jaroslaw Wlodarcyzk (and indepedently, Gianluca Marzo & Michael McQuillan).

I also believe the existence of a regular alteration of any variety (defined over a field of positive characteristic) implies the decidability of (the theory of) F_p[[t]], inspired by this paper of Jan Denef & Hans Schoutens, and am working to prove this…

I have several years of teaching experience, having taught precalculus, differential and integral calculus and the calculus of several variables, finite mathematics, discrete mathematics and proof theory for computer scientists and also for mathematicians, linear algebra, differential equations, and historically the first undergraduate course in quantum computing within CUNY wherein students literally wrote programs for a quantum computer in the Cirq programming language, at Fordham University, The City College of New York, and Queens College. I have mentored a few undergraduate students while pursuing my PhD. One project regarded an exploration of the rudiments of (the consequences of) Falting’s Theorem. Another (two) regard exploration of quantum computation. Prior to entering my PhD program, I worked as a professional assistant at Suffolk County Community College in their mathematics lab, as a teacher with the Turkish-American Education and Cultural Foundation of Moriches, Inc. to develop curriculum and teach young Turkish immigrants, as a private tutor with WyzAnt, Inc. with a 4.8/5 rating (over 200 ratings) and over 880 hours tutored, and as a tutor in the mathematics lab in SUNY Potsdam.

I am also an avid musician, performing and recording with several musical artists in the NYC area, including playing bass and singing with Quiet Car, Blaise Ambrose, and Motyka, and playing with several orchestras and jazz groups. I spearhead this band alongside Russell Boeger and Eli Shifrin.

I have separate, but related interest in quantum computing and artificial intelligence.