Enrique Treviño, Ph. D.

	Phone:	(610) 690-5764
	Office:	140 Science Center
	Office Hours:	TBD
	Email:	etrevin1 at swarthmore.edu

About Me

I am a visiting assistant professor of Mathematics at Swarthmore College. I completed my PhD in Mathematics at Dartmouth College in June 2011, working with Carl Pomerance. My main research interest is Number Theory. My dissertation is titled Numerically Explicit Estimates for Character Sums; it involves a blend of analytic number theory and some serious computing. I continue to be interested in these kinds of problems, such as estimating the least quadratic non-residue, the least inert prime in a real quadratic field, and other concrete inequalities.

I am very fond of mathematical competitions such as the Mathematical Olympiad. I have been involved either as student or as a teacher in the Olympiad since the year 2000. My love for problem solving extends to other competitions such as the Putnam.

Papers

The primes that Euclid forgot (with P. Pollack) submitted.
The Burgess inequality and the least k-th power non-residue conditionally accepted in Mathematics of Computation.
The smoothed Pólya-Vinogradov inequality (with K. Adamczewski) conditionally accepted for the Proceedings of the Integers Conference 2011.
The least k-th power non residue conditionally accepted at the Journal of Number Theory.
Sets of monotonicity for Euler's totient function (with P. Pollack and C. Pomerance), The Ramanujan Journal, DOI = 10.1007/s11139-012-9386-6.
On the maximum number of consecutive integers on which a character is constant Moscow Journal of Combinatorics and Number Theory 2012, vol.2, iss. 1, pp. 56-72.
The least inert prime in a real quadratic field, Mathematics of Computation, vol. 81, no. 279, July 2012, pp. 1777-1797.
Multi-dimensional Frobenius problem (with J. Amos, I. Pascu, V. Ponomarenko and Y. Zhang), Involve, a Journal of Mathematics 4-2 (2011), 187--197.
On the counting function for the generalized Niven numbers (with R. Daileda, J. Jou, R. Lemke-Oliver and E. Rossolimo), J. Théor. Nombres Bordeaux 21 (2009), no. 3, 503--515.

Talks

El mínimo no-rediduo cuadrático y otros problemas relacionados given at a colloquium lecture at the Universidad de Colima on May 8, 2012
On the maximum number of consecutive integers on which a character is constant given at the Joint Math Meetings on January 5, 2012.
The smoothed Pólya-Vinogradov inequality given at the Integers Conference, October 28, 2011.
The least quadratic non-residue and related problems given at a colloquium lecture at Swarthmore College on March 1st, 2011, at University of North Texas on October 2011 and at the automorphic forms seminar at Purdue University in February 2012.
The least inert prime in a real quadratic field given at the Palmetto Number Theory Series XIV, December 4, 2010.
Burgess bounds for the Burgess inequality for character sums given at the Integers conference, October 16, 2009.
On the counting function of the generalized Niven numbers given at the Québec/Maine Number Theory Conference, October 2008.
The higher-dimensional Frobenius problem given with Yan Zhang at Young Mathematician's Conference (YMC), August 2005.
Mathematical Olympiads given at a colloquim lecture at Trinity University on July 2005.

Links

Olimpiada Mexicana de Matemáticas Chihuahua

Last modified on February 26, 2013 by Enrique.

Enrique Treviño, Ph. D.

About Me

Curriculum Vitae and other job application materials

Current Classes

Classes I've Taught

Papers

Talks

Links