Robert Schneider, PhD

E-mail: robert.schneider@emory.edu

Office: MSC W431

Office hours: By appointment, open to all students with questions or interest in mathematics

Curriculum vitae/research statement: CV here / research statement here (updated May, 2018)

PhD dissertation (successfully defended on April 3, 2018): dissertation here

About me

"I am seeking, I am striving, I am in it with all my heart." - Vincent Van Gogh

I am a recent PhD graduate from Emory University (and former Woodruff Fellow and Dean's Teaching Fellow) having worked under the supervision of Ken Ono. (My graduation date was May 14, 2018, so maybe I'm a Lecturer at University of Georgia by the time you read this.)

My research interests lie primarily in number theory and combinatorics, in particular the theory of integer partitions, special functions in the orbit of modular forms (q-series, basic hypergeometric series, mock theta functions, quantum modular forms), and analytic number theory (prime distribution, Riemann zeta function and other L-functions). My mathematical heroes are Euler and Ramanujan, and in the modern day George Andrews and my awesome advisor, Ken Ono.

I completed my BS in Mathematics (2012) at the University of Kentucky, and my MS in Mathematics (2016) at Emory. I am also a pop musician (lead singer of The Apples in stereo), composer, indie record producer (Neutral Milk Hotel, Olivia Tremor Control, Minders, Beulah, Cornelius, Yoko Ono, et al.), recording/mixing/mastering engineer, and co-founder of The Elephant 6 Recording Co., a collective of musicians and artists.

I am currently working on an interdisciplinary project in the Emory Working Group on Molecular Simulation and Number Theory under Prof. James Kindt in the Chemistry Department (along with my number theory colleague Olivia Beckwith, see Phys.org article here); and am a participant in the Search for Extraterrestrial Intelligence (SETI), PrimeGrid, and other distributed computing and citizen science projects. Other active interests include physics (special relativity, string theory, gravitation, acoustics, statistical physics), history of mathematics, ethnomathematics, philosophy, poetry, astronomy, electronics, visual and conceptual art, sound sculpture and experimental music.

Among a number of nerdy side projects, I have invented a "non-Pythagorean" musical scale based on logarithms, invented and composed for a mind-controlled synthesizer (the Teletron) using a circuit-bent Mattel MindFlex toy (download instructions here), composed a score based on prime numbers "Reverie in Prime Time Signatures" for a play by number theorist Andrew Granville (download score here), scored the Sieve of Eratosthenes (an ancient Greek method for finding prime numbers) for church bells, written a score related to primes and abstract algebra (math explained here) that lasts anywhere from months to millions of years, designed a board game based on abstract algebra Al-Jabar with Georgia Tech PhD student Cyrus Hettle (download game rules here), and recorded a geometry-themed version of a hit song from 1916 (lyrics by "Blanche Descartes") for Gathering for Gardner in honor of Richard Guy's 100th birthday. I am also engaged in a long-term study of musical properties of flowing water, with the goal of composing a piece to be played by an artificial river.

As of Summer 2018, I have an Erdős-Bacon-Sabbath (EBS) number of 7 (E3+B2+S2).

Publications and submitted papers

1). A non-Pythagorean musical scale based on logarithms. Proceedings of Bridges: Mathematics, Music, Art, Architecture, Culture Conference (June, 2012).

2). Uncovering Ramanujan's "lost" notebook: an oral history. Ramanujan Journal (December, 2012).

3). A "strange" vector-valued quantum modular form (co-author Larry Rolen). Archiv der Mathematik (July, 2013).

4). A golden product identity for e. Mathematics Magazine (April, 2014).

5). A golden connection (short expository note). Mathematics Magazine (April, 2014).

6). Combinatorial applications of Moebius inversion (co-author Marie Jameson). Proceedings of the AMS (September, 2014).

7). Encounter with the infinite (co-author Benjamin Phelan). The Believer (January/February, 2015), reprinted in Namarupa: Categories of Indian Thought (Spring, 2016).

8). Partition zeta functions. Research in Number Theory (December, 2016).

9). Arithmetic of partitions and the q-bracket operator. Proceedings of the AMS (November, 2016).

10). Why Ramanujan Matters (with co-author Ken Ono). Sloan Science & Film (May 10, 2016), reprinted in Ramanujan Mathematical Society Newsletter (March-June, 2016), reprinted in Asia Pacific Mathematics News (November, 2016).

11). Fibonacci numbers and the golden ratio (expository article for high school students). Parabola (December, 2016).

12). Explorations in the theory of partition zeta functions (with co-authors Ken Ono and Larry Rolen). Exploring the Riemann Zeta Function, 190 years from Riemann's Birth, editors: H. Montgomery, A. Nikeghbali, and M. Rassias, Springer (2017).

13). Extracting aggregation free energies of mixed clusters from simulations of small systems: application to ionic surfactant micelles (co-authors Xiaokun Zhang, Lara Patel, Olivia Beckwith, Christopher Weeden, James Kindt). Journal of Chemical Theory and Computation (September, 2017).

14). Partition-theoretic formulas for arithmetic densities (co-authors Ken Ono and Ian Wagner). Proceedings of Number Theory in Honor of Krishna Alladi's 60th Birthday, Springer (2018). 15). Alternating "strange" functions. Ramanujan Journal (May, 2018). 16). Jacobi's triple product, mock theta functions, unimodal sequences and the q-bracket. International Journal of Number Theory (To appear). 17). Digit sums and generating functions (co-author Maxwell Schneider). Submitted for publication (July, 2018). Other writings

1). Infinite series for π/3 and other identities. LaTeX transcription of my first mathematics paper (2006).

2). Building Lambert's W-function with Bell polynomials. Notes from personal study (2015).

3). Results from a computational study of cyclotomic phenomena in the mock theta function f(q) (co-author Amanda Clemm). Notes from 2013 project (Posted 2016).

4). Faà di Bruno's formula with product representation. Expository note about the classical formula (2016).

5). Universal scale forms for guitar from Indian classical music. Method for constructing interesting musical scales on guitar (2017).

6). Partitions,π and the golden ratio. Curious formulas for the golden ratio in terms of π and the Riemann zeta function (2018).

7). Sequentially congruent partitions. Notes from personal study of an interesting class of partitions (2018).

8). Eulerian series, zeta functions and the arithmetic of partitions. My PhD dissertation (2018).

Recent talks

March 2014 - Patterns Etched in Sound, TEDx at Emory University, Atlanta, Georgia

September 2015 - Partition Zeta Functions, Palmetto Number Theory Series (PANTS) XXIV, Emory University, Atlanta, Georgia

October 2015 - Partition Zeta Functions, Combinatorics seminar, Pennsylvania State University, State College, Pennsylvania

December 2015 - Partition Zeta Functions, SASTRA University, Kumbakonam, India

March 2016 - Arithmetic of Partitions, AMS Southeast Sectional Meeting, University of Georgia, Athens, Georgia

March 2016 - Arithmetic of Partitions, International Conference on Number Theory in Honor of Krishna Alladi for His 60th Birthday, University of Florida, Gainesville, Florida

November 2016 - Partitions, Statistical Physics and the Universe, Probability and Statistics class guest lecture, Emory University, Atlanta, Georgia

January 2017 - Jacobi's triple product, mock theta functions and the q-bracket, AMS Contributed Papers Session on Number Theory, Joint Mathematics Meetings, Atlanta, Georgia

May 2017 - Partition Zeta Functions, Algebra seminar, University of Tennessee, Knoxville, Tennessee

November 2017 - Number theory in statistical physics: using integer partitions to compute expected values, Computational Sciences seminar, Georgia Southern University, Statesboro, Georgia

November 2017 - Partition Zeta Functions, Number Theory seminar, Georgia Southern University, Statesboro, Georgia

January 2018 - Toward an algebra of partitions, AMS Contributed Papers Session on Partitions, Paths and Permutations, Joint Mathematics Meetings, San Diego, California

February 2018 - Music of the Primes (Literally), Invited lecture, University of Georgia, Athens, Georgia

April 2018 - Jacobi's triple product, mock theta functions, unimodal sequences and the q-bracket, Invited lecture, AMS Western Sectional Meeting, Portland State University, Portland, Oregon

June 2018 - Toward an algebra of partitions, Contributed paper, Combinatory Analysis 2018: A Conference in Honor of George Andrews' 80th Birthday, Pennsylvania State University, State College, Pennsylvania

Teaching

"...The lecturer should lay [her or his] hands on the plough, the loom, the forge, the workshop, the mine, the sea, the stars, all things on earth or under heaven which may help to arouse the attention or interest the imagination." - J. J. Sylvester

I encourage all students to please reach out with questions, problems, or ideas.

Attempted humor