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Robert Schneider


Woodruff Graduate Fellow
Department of Mathematics and Computer Science
Emory University

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: Download CV here (updated Jan. 2017)

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About me

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

I am a PhD candidate in my fifth year of graduate school at Emory University, working under the supervision of Ken Ono.

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, Don Zagier, 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/engineer (Neutral Milk Hotel, Olivia Tremor Control, Minders, Beulah, Cornelius, Yoko Ono, et al.), sound sculpture artist, and co-founder of The Elephant 6 Recording Co., a musical collective.

I am currently working on an interdisciplinary project with the Kindt Research Group in the Department of Chemistry, along with my number theory colleague Olivia Beckwith; am an affiliate of Emory's Center for Mind, Brain, and Culture (CMBC); and am a participant in the Search for Extraterrestrial Intelligence (SETI), the Great Internet Mersenne Prime Search (GIMPS), and other distributed computing projects. Other active interests include physics (special relativity, string theory, gravitation, acoustics, statistical physics), history of mathematics, philosophy, poetry, astronomy, electronics, visual and conceptual art, 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, wrote 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 fellow University of Kentucky 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.


Publications and preprints

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 article). 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). Explorations in the theory of partition zeta functions (with co-authors Ken Ono and Larry Rolen). To appear in Exploring the Riemann Zeta Function, 190 years from Riemann's Birth, Springer, editors: H. Montgomery, A. Nikeghbali, and M. Rassias (2016).

12). Fibonacci numbers and the golden ratio. Parabola (December, 2016).

13). Jacobi's triple product, mock theta functions, unimodal sequences and the q-bracket. Preprint (2016).

14). The importance of being "strange". Preprint (2017).


Other writings

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

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

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


Selected undergraduate writings

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

2). Study in Egyptian fractions. Essay for History of Mathematics course at University of Kentucky (2012).

3). A metric space in predicate logic. Study for Symbolic Logic course at University of Kentucky (2012).


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


Teaching

"...The lecturer should lay [his or her] 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 have had the great pleasure of teaching Math 111 - Calculus I at Emory for six semesters, from Fall 2013 through Spring 2016 (syllabus from my Spring 2016 class here). I do not currently have a teaching assignment, as I am working on my PhD thesis. However, I encourage students to please reach out with questions, problems, or ideas.